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# In[ ]:
get_ipython().run_cell_magic('javascript', '', '\nIPython.OutputArea.prototype._should_scroll = function(lines) {\n return false;}\n')
# # Introducing the Sticky-Price Model: TEXTBOOK DRAFT
#
# # Part IV Sticky Price Macroeconomics
#
# Chapters 4 through 7 do not give a complete picture of the macroeconomy. In Chapters 4 through 7, growth is smooth from year to year. But in the real world growth is not. In Chapters 4 through 7, supply and demand in the labor market are always in balance.
#
# But in the real world the labor market is not always in equilibrium.
#
# To understand these business-cycle fluctuations in economic growth and unemployment, we need a model that does not require that employment be full and real GDP be equal to potential output. The full-employment model of Part 3 is not of help because its flexible-price assumption guarantees full employment. Here in Part 4, therefore, we need to break this flexible-price assumption to build a useful model of the business cycle.
#
# From this point forward, prices, wages, and debts will be "sticky": They will not move freely and instantaneously in response to changes in demand and supply. We will use this sticky-price model to account for business-cycle fluctuations.
#
# Building this sticky-price model of the macroeconomy is the task of Part 4. Chapter 9 focuses on how, when, prices are sticky, the inventory adjustment process is the key to understanding how GDP can fall below or rise above potential output. Chapter 10 analyzes how changes in the interest rate affect investment, exports, and GDP. Chapter 11 focuses on equilibrium in the money market and the balance of aggregate demand and aggregate supply. Chapter 12 focuses on monetary policy, expectations, and inflation. It links the sticky-price model of Part 4 back to the flexible-price model of Part 3 by analyzing which model is most useful in which sets of circumstances.
#
#
# # 9 The Sticky-Price Income-Expenditure Framework: Consumption and the Multiplier
#
# **QUESTIONS**
#
# 1. What are "sticky" prices?
# 2. What factors might make prices sticky in the short run?
# 3. In the short run when prices are sticky, what determines the level of real GDP?
# 4. When prices are sticky, what happens to real GDP if some component of planned total expenditure rises or falls?
# 5. What is the spending multiplier? What factors determine its size?
#
#
#
# **flexible prices**: When wages and prices in an economy are not sticky but move smoothly and rapidly to keep supply equal to demand in the labor market and in the goods market.
#
# **sticky prices**: When wages and prices do not move smoothly and immediately to keep supply equal to demand in the labor and goods markets.
#
# **menu costs**: The costs to a firm of changing the price(s) of a good(s) or service(s).
#
# **imperfect information**: The information workers or managers have for decision making when they lack full information about the state of the economy.
#
# **autonomous spending**: Those components of planned expenditure that are independent of the level of national income.
#
# **marginal propensity to expend (MPE)**: The increase in total spending—on consumption goods through the marginal propensity to consume and on net exports—from a one- dollar increase in national income.
#
# **income-expenditure diagram**: The tool for figuring out what the equilibrium level of planned expenditure and gross domestic product is. Also known as the Keynesian cross diagram.
#
# **aggregate demand line**: Found on the income-expenditure (or Keynesian cross) diagram that shows aggregate demand on the vertical axis and national income on the horizontal axis. The planned-expenditure line shows planned total expenditure, AD = C + I + G + NX, as a function of the level of national income.
#
# **aggregate demand function**: The relationship AD = C + I+ G+ NXusedto build planned expenditure for domestically produced products from the determinants of each of its components: consumption spending C, investment spending /, government purchases G, and net exports NX.
#
# **spending multiplier**: The change in national income and total expenditure that follows from a one-dollar change in any component of autonomous spending. Also known as the _Keynesian multiplier_.
#
#
#
# Over the past two-and-a-half decades, real GDP in the American economy has nearly doubled in size: the inflation-adjusted measured production of useful marketable goods and services has grown at an average rate of 2.51 percent per year. Growth has not been smooth and even. From 1993 to 2000, on President Clinton's watch, the economy-as-measured grew at 3.85% per year. From 2000 to 2007, on President Bush's watch but before the catastrophe of 2008, the economy-as-measured grew at a rate of 2.40 percent per year. In 2008 and 2009 the economy collapsed: it shrank by 3.7 percent. And from 2009 to the third quarter of 2018 the economy-as-measured has grown at 2.29 percent per year.
#
# 
#
# Over this same 25-year period, the unemployment rate has varied widely and wildly as well. In September 1993 it was 6.7 percent: civilians who said that they were looking for a job but could not (yet) find one amounted to 6.7 percent of the total of all those who reported that they had jobs or were looking for jobs. By April 2000 this civilian unemployment rate was 3.8 percent. June 2003 saw it up to 6.3 percent. May 2007 saw it down to 4.4 percent. In October 2009 it was at a catastrophic 10.0 percent—although that was much lower than the truly horrific 23 percent unemployment rate of the Great Depression back in 1993. And as of September 2018 the unemployment rate is back down to 3.7 percent.
#
# 
#
# An alternative measure to the unemployment rate is the non-employment rate: those who do not have jobs, whether or not they are currently looking, as a fraction of all adults. Before 1993 interpreting the non-employment rate as an indicator of whether production is near to or well below potential output is made difficult by the sociological changes that are the rise of feminism. Since 1993 the share of men and women together who wish to hold paid jobs has, adjusted for the business cycle, been constant.
#
# 
#
# All three of these graphs show the same pattern: times when it appears easy to get and hold jobs and time when it appears to be difficult, which are the same as times when it appears that the nation's production and national income are more-or-less on their long-run trend and times when production is low relative to trend. And it is not the case that production and employment have been artificially and unsustainably elevated above sustainable levels on average due to some outbreak of inflationary and devaluationary policies: the inflation rate excluding volatile food and energy prices—the so-called "core" inflation rate—for the Consumer Price Index or CPI was 3.3 percent in 1993; it is 2.2 percent today.
#
# 
#
# If Chapters 4 through 7 gave a complete picture of the macroeconomy, this would simply not have happened. Economic growth would have been smooth as the economy converged to and then grew along its Solow Growth Model balanced-growth path. At most, there might have been speed-ups or slow-downs as changes in the savings-investment rate, in investment requirements, or in the rate of efficiency-of-labor growth caused the long-run balanced-growth path to shift. But there would have been no jumps and no rapid accelerations or decelerations: convergence to the balanced-growth path is a generations-long process. And there certainly would have been no declines in production, and no elevations of the unemployment rate to double-digit levels.
#
# But growth is not at all smooth. On a year-to-year time scale, it is not even guaranteed.
#
# The economy undergoes substantial fluctuations around, along, and at times signficiantly below its long-run sustainable growth trend—business cycles. In a business-cycle expansion or boom. production, employment, and perhaps prices all grow rapidly. In a business-cycle recession or depression, inflation falls or prices slump, unemployment rises, and production falls. During booms, output grows faster than trend and investment spending amounts to a higher-than-average share of GDP as unemployment falls. During recessions, output falls, investment spending is a low share of real GDP, unemployment rises, and inflation usually decelerates.
#
# Compared to the overall upward trend of long-run growth, these short-run fluctuations (with the exception of the Great Depression) appear relatively small. But they have a large impact on the lives of those of us unlucky enough to lose our jobs or to fail to find jobs when a recession hits.
#
#
# In[ ]:
# growth rate calculations and figures
import numpy as np
RGDP_2018Q3 = 18.672 # in trillions of chained 2012 dollars
RGDP_1993Q3 = 9.956 # in trillions of chained 2012 dollars
RGDP_2000Q2 = 13.161 # in trillions of chained 2012 dollars
RGDP_2007Q4 = 15.762 # in trillions of chained 2012 dollars
RGDP_2009Q3 = 15.189 # in trillions of chained 2012 dollars
nplusg_1993to2018 = np.log(RGDP_2018Q3/RGDP_1993Q3)/25
nplusg_1993to2000 = np.log(RGDP_2000Q2/RGDP_1993Q3)/7.25
nplusg_2000to2007 = np.log(RGDP_2007Q4/RGDP_2000Q2)/7.5
nplusg_2007to2009 = np.log(RGDP_2009Q3/RGDP_2007Q4)/1.75
nplusg_2007to2009total = np.log(RGDP_2009Q3/RGDP_2007Q4)
nplusg_2009to2018 = np.log(RGDP_2018Q3/RGDP_2009Q3)/9
# graph: last quarter century of real gdp growth:
# https://fred.stlouisfed.org/graph/?graph_id=515794&rn=813
# graph: last quarter century of the civilian unemployment rate:
# https://fred.stlouisfed.org/graph/?graph_id=515799&rn=43#0
# graph: last quarter century of the prime-age non-employment rate:
# https://fred.stlouisfed.org/graph/?graph_id=515810&rn=431
# graph: last quarter century of core inflation:
# https://fred.stlouisfed.org/graph/?graph_id=515825&rn=398#0
# ## 9.1 Sticky Prices
#
# ### 9.1.1 Understanding Sticky-Price Business Cycles
#
# To understand business cycles, we need a model that does not guarantee full employment and in which real GDP does not always equal potential output. Business cycles are not fluctuations in potential output. They are fluctuations of actual production around potential output — above potential output when the economy is “overheated,” and below potential output when the economy possesses substantial “slack.”
#
# Thus the full-employment model of Chapters 6 and 7 is of no help here.
#
# Its assumption that prices are flexible guarantees full employment leads us down the wrong road. The flexible-price assumption allowed us to start our analysis in a simple and straightforward way, by noting that _if_ the labor market would clear, _then_ as a result firms would fully employ workers who wanted to work, and _thus_ that real GDP and household income would be equal to potential output and both would be equal to aggregate demand because:
#
# 1. the real wage W/P adjusts to balance demand and supply for labor at full employment
# 2. the price level P adusts to keep aggregate demand—total spending—equal to the amount needed to purchase the full-employment value of production
# 3. the long-term real risky interest rate r adjusts to balance supply and demand in the flow-of-funds through financial markets, and so match the components of aggregate demand—household consumption spending C, business investment spending I, government purchases G, and net exports NX—so that their sum adds up to aggregate demand.
#
# This flexprice analysis is an analysis filled with "ifs" that are not so: they are useful for clarifying thought and for setting a baseline to which we can compare the behavior of actual economies, not for understanding why actual economies undergo the business cycle fluctuations that they do.
#
# (Moreover, the flexible-price assumption may not be a terrible one to make for purposes of empirical analysis if employment is and remains nearly full. Perhaps it does so because there have been no large disturbances to demand in a while, so that wages and prices in labor and product markets have had time to adjust. Perhaps it does so because the Federal Reserve has done a good job of neutralizing disturbances to aggregate demand.)
#
# But we cannot afford to keep the flexible-price assumption if we wish to make any further progress. We need to break it if we are to build a more useful model of the business cycle. Thus from this point on wages and prices will be “sticky”: They will not move freely and instantaneously in response to changes in demand and supply. Instead, prices will remain fixed at predetermined levels as businesses expand or contract production in response to changes in demand and costs.
#
# As you will see, such sticky prices make a big difference in economic analysis; they will drive a wedge between real GDP and poten tial output and between the supply of workers and the demand for labor. We will then be able to use this sticky-price model to account for business-cycle fluctuations.
#
# Building this sticky-price model of the macroeconomy will take up all of Part 4. In this chapter, we will focus on how, when prices are sticky, firms hire or fire workers and expand or cut back production on the basis of whether their inventories are falling or rising. Inventory adjustment is the key to understanding how the level of real GDP can fluctuate around potential output. Chapter 10 focuses on how changes in the interest rate affect the levels of investment, exports, and real GDP in the sticky-price model.
#
# Chapter 11 takes a deeper look at equilibrium in the money market: How are interest rates in the short run really determined? It is an optional chapter. You can simply say that the Federal Reserve—the Fed—sets interest rates, not inquire into how, and skip Chapter 11. But if you want to understand what happens when there is no interest rate-pegging central bank around, or how the Federal Reserve pegs interest rates, or what happens if the Federal Reserve pegs not interest rates but the money stock, then you need to study Chapter 11.
#
# The last chapter of Part 4, Chapter 12, takes up the topics of expectations and inflation in an environment in which the Fed sets interest rates. By the end of Chapter 12 we will have linked up the sticky-price model of Part 4 with the flexible-price model of Part 3. We will understand the sorts of situations for which the sticky-price model is appropriate. And we will understand under what sets of circumstances wages and prices are flexible enough and have enough time to adjust for the flexible- price model to be the most useful way of analyzing the macroeconomy.
#
# At each stage in the building of our sticky-price macroeconomic model, the preceding topic serves as a necessary foundation. The analysis of inflation and expectations in Chapter 12 rests on the analysis of how changes in interest rates affect investment, exports, and real GDP in Chapter 10. And the analysis of Chapter 10 in turn rests on the analysis of income, expenditure, and equilibrium in a sticky- price economy carried out here in Chapter 9. Chapter 11 also rests on Chapters 9 and 10, and it provides a fuller foundation for Chapter 12.
#
# Up to this point, this book has not been cumulative. You could understand the long-run growth analysis in Chapters 4 and 5 without a firm grasp of the introductory material in Chapters 1 through 3. You could understand the flexible-price analysis in Chapters 6 and 7 without a firm grasp of either the introductory or the long-run-growth chapters.
#
# But from this point on, the chapters of this book become interdependent and very cumulative indeed.
#
#
#
# ### 9.1.2 Consequences of Flexible and Sticky Prices: Flexprice Logic
#
# To preview the difference between the flexible-price and the sticky-price models, let us analyze a decline in consumers’ propensity to spend under both sets of assumptions. Suppose there is a sudden fall in the consumer confidence parameter $ c_o $, the parameter that determines the baseline level of consumption in the consumption function and thus shifts the function up or down on the income-spending graph:
#
# > $ C= c_o + c_y(1-t)Y $
#
# where Y is GDP or national income, t is the tax rate, C is consumption spending, and $ c_y $ is the marginal propensity to consume parameter of the consumption function that determines captures how much consumption increases for a 1 dollar increase in national income.
#
# To make this concrete, consider what happens when baseline consumption spending falls. Suppose that the function for annual consumption spending (in billions of dollars at an annual rate) is shifted down on the income-spending graph by an amount $ {\Delta}c_o = 250 $: declines from:
#
# > $ C = 750 + (0.75)(1-t)Y $
#
# to:
#
# > $ C = 500 + (0.75)(1-t)Y $
#
# In the full-employment model of Chapters 6 and 7, such a 250 billion dollar fall in annual baseline consumption spending would have no impact on the level of real GDP. No matter what the flow of total expenditure, the labor market would still reach its full-employment equilibrium because flexible wages and prices would make it so. And because the economy remains at full employment, real GDP would still equal potential output.
#
#
#
# 
#
# >>_**Flexible-Price Logic: Labor-Market Equilibrium**: No matter what the flow of planned expenditure, flexible wages and prices mean that employment remains at full employment and the level of real GDP
# produced remains at potential output._
#
#
#
# The fall in consumption spending would have an effect on the economy—just not on the level of real GDP. In the flexprice model a fall in household consumption spending with national and thus household income unchanged is also an increase in private saving $ S^p $. As consumption falls, the total saving curve shifts rightward on the flow-of-funds saving-interest rate diagram. The fall in consumption spending reduces the equilibrium real interest rate. The fall in the interest rate then leads to increases in the equilibrium level of investment and net exports.
#
#
#
# 
#
# >>_**Flexible-Price Logic: The Effect on Saving of a Fall in Consumption Spending**: With flexible prices, a fall in consumption spending means a rise in household saving and an increase in the flow of saving through financial markets. Thus the real interest rate falls, and more investment projects are undertaken. The fall in the real interest rate also raises the value of the ex change rate and boosts net exports._
#
#
#
# By how much does investment plus net exports increase? By 250 billion dollars at an annual rate, the amount necessary to offset the fall in consumption spending and keep real GDP equal to potential output.
#
# Thus these are the flexible-price-model consequences of a fall in households’ desired baseline consumption spending:
#
# * consumption falling.
# * household private saving rising.
# * the real interest rate falling.
# * real investment rising.
# * the value of foreign currency rising.
# * exports rising.
#
# These adjustments keep the flow of planned expenditure from changing: flexible wages and prices mean that employment remains at full employment, and the level of real GDP produced remains at potential output.
#
#
#
# ### 9.1.3 Consequences of Flexible and Sticky Prices: Sticky-Price Logic
#
# Sticky-price logic is different.
#
# If wages and prices are sticky, we have to carry out a different analysis. The first consequence of consumers’ cutting back their spending will be a fall in expenditure for goods—in aggregate demand. Consumer spending is falling, yet nothing has happened or is happening to change the flow of spending on investment goods, the flow of net exports, or the flow of government purchases.
#
# As businesses see spending on their products begin to fall, they will not cut their nominal prices (remember, prices are sticky). Instead, they will respond to the fall in the quantity of their products demanded by reducing their production. They see their invenstories rising, and they do not want that—they want to avoid accumulating unsold and unsellable inventory.
#
# As they reduce production, they will fire some of their workers. The incomes of the fired workers will drop, and so national income will start dropping.
#
# By how much will total national income drop? Initially, it will fall by the amount of the fall in baseline consumption spending: by 200 billion dollars at an annual rate. And that will have consequences—as we see a bit later on—that will amplify its magnitude.
#
# Thus the consequences of a fall in consumption spending under the sticky-price assumption are
#
# * consumption falling.
# * production and employment declining.
# * national income declining.
#
# In the flexprice model, when consumption falls, investment and net exports rise. Why doesn’t the same thing happen in the sticky-price model? Why doesn’t a rise in investment spending keep GDP equal to potential output and keep employment full? What goes wrong with the flexprice logic, according to which a fall in consumption spending generates an increase in saving that then boosts both investment spending and net exports?
#
#
#
# 
#
# >>_**Sticky-Price Logic: The Effect on Saving of a Fall in Consumption Spending**: With sticky prices, a fall in baseline consumption spending carries with it a fall in income. Because both total consumption spending and ultimately income decline by the same amount, there is no change in total saving through financial markets. Thus the real interest rate remains unchanged. There is no change in investment spending or gross exports._
#
#
#
# The answer is that in the sticky-price model, firms respond to falling demand not by cutting prices but by cutting back production and employment, and so total income falls. The fall in total income reduces saving just as a fall in consumption raises saving. Under the sticky-price assumption, the effect on total saving of the fall in consumption and the fall in income cancel each other out; there is no change in the flow of saving. Thus there is no rightward shift in the position of the total saving curve on the flow-of-funds saving-interest rate diagram. There is thus no fall in interest rates to trigger higher investment (and a higher value of the exchange rate and expanded net exports). There is nothing to offset the fall in consumption spending and keep GDP from falling below potential output.
#
# Why doesn’t this sticky-price unemployment-generating logic work when prices are flexible? When flexprice firms see a fall in total spending, they respond not by cutting production and employment but by cutting the prices they charge and the wages they pay. The real incomes households earn thus remain constant, and falling real consumption spending does induce rising real saving. That rising real saving is what induces a falling real interest rate, rising investment spending, increasing value of foreign currency, and rising net exports.
#
#
#
# ### 9.1.4 Expectations and Price Stickiness
#
# If managers, workers, consumers, and investors had time to foresee a fall in consumption and gradually adjust their wages and prices to it in advance, even considerable stickiness in prices would not be a problem. With sufficient advance notice unions and businesses would strike wage bargains, and businesses could adjust their selling prices to make sure demand matched productive capacity. Both the stickiness of prices and the failure to accurately foresee changes far enough ahead to adjust to them in advance are needed if the sticky-price framework is to create business cycles in employment and output like the ones we see.
#
# One way to think about this is that the analysis in Part 4 is a short-run analysis, and the analysis in Part 3 is a longer-run analysis—although it is a longer-run business cycle analysis, and thus it is still much shorter in terms of its run than the truly long-run growth economics analysis conducted in Part 2.
#
# In the Part 4 short-run, prices are sticky; shifts in policy or in the economic environment that affect the components of planned total expenditure will affect real GDP and employment.
#
# In the Part 3 business-cycle longer-run, prices are flexible and workers, bosses, and consumers have time to react and adjust to changes in policy or the economic environment. Thus in the long run, such shifts do not affect real GDP or employment.
#
# Why do we need a sticky-price short-run model as well as the longer-run business-cycle flexprice model? Why don’t economists simply say that once wages and prices have fully adjusted (however long that takes), employment will be full and real GDP will be equal to potential output and stop their analyses there? Economists focus on equilibrium, right? And the equilibrium is the one taht the flexprice model reaches, right?
#
# The most famous and effective criticism of such let’s-look-only-at-the-longer-run when we are analyzing the business cycle was made by John Maynard Keynes in a 1924 book, his _Tract on Monetary Reform_. Criticizing one such long-run-only analysis, Keynes wrote:
#
# >In the long run [this] is probably true.... But this long run is a misleading guide to current affairs. _In the long run we are all dead_. Economists set themselves too easy, too useless a task if in tempestuous seasons they can only tell us that when the storm is long past the ocean will be flat once more...
#
# Where is the line that divides the sticky-price short-run from the flexprice business-cycle longer-run? Do we switch from living in the short run of Part 4 to the long run of Part 3 on June 19, 2023?
#
# No, we do not.
#
# The “business-cycle longer-run” is an analytical construct. It covers circumstances in which enough people have enough time to have seen it coming far enough in advance and have had time to adjust to it—to renegotiate their contracts and change their standard operating procedures accordingly. The length of the business-cycle longer-run, and thus how many of us will be dead before it comes, depends in turn on the degree of price stickiness and the process by which people form their expectations—both hot topics for academic research in modern macroeconomics.
#
# Would an economy in which prices and wages were more flexible than they are in our economy have smaller business cycles? It is doubtful. Not just prices and wages but debts are set in money terms in our economy. In a flexprice world a fall in aggregate demand is kept from having a large depressing effect on production because the price level falls in synch. But in an economy in which firms have debts, falling prices make it impossible for the firms to repay those debts and lead to massive chains of firm bankruptcies. Bankrupt firms do not produce, even if there is ample demand for their low-priced products.
#
#
#
# ### 9.1.5 Why Are Prices Sticky?
#
# Why don’t prices adjust quickly and smoothly to maintain full employment? Why do businesses respond to fluctuations in demand first by hiring or firing workers and accelerating or shutting down their production lines? Why don’t they respond first by raising or lowering their prices?
#
# Economists have identified any number of reasons that prices could be sticky, but they are uncertain which are most important. Some likely explanations are:
#
# 1. Managers and workers find that changing prices or renegotiating wages is
# costly and hence best delayed as long as possible.
# 2. The level of prices is as much a sociological as an economic variable—determined as much by what levels people think are “fair” as by the balance of supply and demand.
# 3. Closely related: sorkers take a cut in their wages as an indication that their employer does not value them; hence managers avoid wage cuts because they fear the consequences for worker morale. Managers would rather fire 10 percent of their workers than attempt to impose a 10 percent wage cut on their current workforce because the second would have a catastrophic effect on worker morale, while the first is more likely to make workers work harder out of fear of behing the next ones laid off.
# 4. Managers and workers suffer from simple “money illusion”; they overlook the effect of price-level changes when assessing the impact of changes in wages or prices on their real income or sales.
# 5. Managers and workers lack information and so confuse changes in total economy-wide spending with changes in demand for their specific products.
#
# Let’s look more closely at each of these likely explanations.
#
# Economists call the costs associated with changing prices _menu costs_, a shorthand reference to the fact that when a restaurant changes its prices, it must print up a new menu. In general, changing prices or wages may be costly for any of a large number of reasons. Perhaps people want to stabilize their commercial relationships by signing long-term contracts. Perhaps reprinting a catalog is expensive. Perhaps customers find frequent price changes annoying. Perhaps other firms are not changing their prices and what matters most to a firm is its price relative to the prices of competitors. Hence managers and workers prefer to keep their prices and wages stable as long as the shocks that affect the economy are relatively small—or, rather, as long as the change they might want to make in their prices and wages is small.
#
# Yet a third reason why prices and wages are sticky is that workers and managers are really not the flinty-eyed rational maximizers of economic theories.
#
# Closely related and fourth, in real life, work effort and work intensity depend on whether workers believe they are being treated fairly. A cut in nominal wages is almost universally perceived as unfair; wages depend on social norms that evolve slowly. Thus wages are by nature sticky. And if wages are sticky, firms will find that their best response to shifts in demand is to hire and fire workers rather than to change prices.
#
# Next, workers, consumers, and managers suffer from money illusion: They confuse changes in nominal prices with changes in real (that is, inflation-adjusted) prices. Firms react to higher nominal prices by thinking falsely that it is more profitable to produce more — even though it isn’t because their costs have risen in proportion. Workers react to higher nominal wages by searching more intensively for jobs and working more overtime hours, even though rises in prices have erased any increase in the real purchasing power of the wage paid for an hour’s work. Such money illu sion is a powerful generator of price stickiness and business-cycle fluctuations.
#
# A final possible source of price stickiness is imperfect information: a misperception of real and nominal price changes. If managers and workers lack full information about the state of the economy, they may be unsure whether a change in the flow of spending on their products reflects a change in overall aggregate demand or a change in demand for their particular products. If it is the latter, they should respond by changing how much they produce, not necessarily by changing the price. If it is the former, they should respond by changing their price in accord with overall inflation, not by changing how much they produce. If managers are uncertain which it is, they will split the difference. Hence firms will lower their prices less in response to a downward shift in total nominal demand than the flexible-price macroeconomic model would predict. If they keep their prices too high, they will have to fire workers and cut back production. Imperfect information is a possible source of sticky prices.
#
# This last explanation seems to us to be highly implausible: people and firms do not know what the things they buy cost? People and firms go to the market and pay their bills every day: they know what things currently cost just as well as they know what they currently earn. Yet many economists of note and reputation seem to believe this as a principal explanation.
#
# All these factors are potential sources of price stickiness. Your professor may have strong views about which is most important. We find ourselves more confused and agnostic. Our reading is that economists’ knowledge is more limited. We are not sure the evidence is strong enough to provide clear and convincing support for any particular single explanation as the most important one. A safer position is to remain agnostic about the causes of sticky wages and prices, and so we focus on analyzing not their causes but their effects.
#
#
#
# #### 9.1.6 RECAP: Sticky Prices
#
# The full-employment model of Chapters 6 and 7 does not help explain business cycles. Its assumption that prices and wages are flexible guarantees that real GDP is always equal to potential output.
#
# To build a more useful model of the business cycle, we need to assume that prices are sticky. If prices are sticky, the first consequence of ashock like consumers cutting back their spending will be a reduction in production, not a cut in prices.
#
# Prices might be sticky for a number of reasons: menu costs, Imperfect information, concerns of fairness, or simply money illusion. All seem plausible. No one explanation indisputably dominates all the others.
#
#
# In[ ]:
# calibrating the simple macro model to the U.S. in 2018
Y = 20000
C = 13500
I = 3250
G = 3750
GX = 2500
IM = 3000
NX = GX-IM
I_0 = 3650
I_r = 20000
e_r = 10
x_e = 500
t = 0.15
c_0 = 750
c_y = 0.75
im_y = 0.15
x_f = 0.10
Y_f = 25000
e = 0
r = 0.02
C_calc = c_0 + c_y*(1-t)*Y
I_calc = I_0 - I_r*r
GX_calc = x_f*Y_f + x_e*e_r*e
GX_calc
# ## 9.2 Income and Expenditure: National Product, National Income, and Aggregate Demand
#
# If prices are sticky, higher planned expenditure boosts production, and this boosts income. Higher income gives a further boost to consumption, and this in turn boosts planned expenditure some more. Thus any shift in a component of aggregate demand upward or downward leads to an amplified shift in total production because of the induced shift in consumption. The early-twentieth-century British economist John Maynard Keynes was one of the first to stress the importance of this multiplier process.
#
# Whereas in booms the multiplier process induces an upward spiral in production, in bad times it is a source of misery. The downward shock is amplified as those who have been thrown out of work cut back on their consumption spending in turn.
#
# Because consumption spending is more than two-thirds of planned expenditure, this multiplier effect can be significant because the positive-feedback loop is so large—if the tax system has not been designed to provide the economy with so-called “automatic stabilizers,” and if the government does not take active steps to cushion the effects of shocks to aggregate demand.
#
#
#
# ### 9.2.1 Building Up Planned Total Expenditure—Aggregate Demand
#
# The rest of this chapter shows how the level of planned total expenditure—aggregate demand AD—is determined in the sticky-price macroeconomic model. We will use a bottom-up approach, building aggregate demand AD on domestically produced products up from the determinants of each of its components, consumption spending C, investment spending I, government purchases G, and net exports NX. The circular flow principle tells us that PE is the sum of C, I, G, and NX:
#
# >AD = C + I + G + NX
#
# As long as prices are sticky, the level of real GDP is determined by the level of aggregate demand:
#
# >Y = AD
#
# and not by the level of potential output Y*.
#
# Why? Recall our sticky-price assumption: Firms respond to falling spending by cutting back production and bring workers (and respond to rising spending by increasing production and hiring workers).
#
#
#
# 
#
# >>_**The Multiplier Process**: In the multiplier process, an increase in spending causes an increase in production and income, which leads to a further increase in spending. This positive-feedback loop
# amplifies the effect of any initial shift._
#
#
#
# ### 9.2.2 The Consumption Function
#
# The two-thirds of GDP that is consumption spending is made up of spending by households on things they bnd useful: services such as haircuts, nondurable goods such as food, and durable goods such as washing machines. When national income Y rises consumption spending C rises with it, increasing aggregate demand and setting what we call the multiplier process in motion. As we saw, consumption spending rises with but does not rise dollar for dollar with total income. Economists call the share of an extra dollar of disposable income that is added to consumption spending the marginal propensity to consume (MPC), the parameter $ c_y $ in our consumption function equation:
#
# > $ C = c_o + c_y(1 - t)Y $
#
# The share of an extra dollar of national income that shows up as additional consumption spending is equal to the marginal propensity to consume times the share of income that escapes taxes: $ c_y(l — t) $.
#
#
#
# 
#
# >>_**The Consumption Function and the Marginal Propensity to Consume**: When drawn on a graph with economywide income on the horizontal axis and consumption spending on the vertical axis, the slope of the consumption function is the marginal propensity to consume times (1 - t)._
#
#
#
# If changes in income are considered permanent, the MPC will be high: A 1 dollar increase in income will lead to an increase in consumption of as much as 80 cents. But if changes in income are considered transitory, the MPC will be low: A 1 dollar increase in income will lead to an increase in consumption of only 20 cents or less. Transitory increases in income have only a small effect on consumption because as we discussed in Appendix 6a people seek to smooth out their consumption spending over time.
#
# For reasonably long-lasting shifts in the level of income, the MPC is roughly 0.6. That is, 60 cents of every extra dollar of disposable income shows up as higher consumption.
#
#
#
# 
#
# >>_**Consumption as a Function of After-Tax Disposable Income**: Three different factors drive the wedge between GDP and consumption spending. The first is depreciation: goods produced that merely replace obsolete and worn-out capital and so are a component of total cost rather than total income. The second is the tax system—both direct and indirect taxes. The third is household saving._
#
#
#
# #### 9.2.2.1 Calculating Consumption: An Example
#
# Begin with the consumption function:
#
# > $ C = c_o + c_y(1-t)Y $
#
# Suppose statistical evidence tells us that the marginal propensity to consume out of disposable income $ c_y = 0.75 $. Suppose further that taxes amount to 40 percent of national income: $ t = 0.4 $. Suppose further that when real GDP—total national income—equals 20 trillion, consumption equals 13 trillion.
#
# The fact that 4 c_y = 0.75 $ and that $ t = 0.4 $ fillS in some of the parameters in the consumption function:
#
# > $ C = c_o + (0.75)(1-0.4)Y $
#
# By substituting in for C and Y:
#
# > $ 13 = c_o + (0.75)(1-0.4)20 $
#
# we can then solve for $ c_o $:
#
# > $ 13 = c_o + (0.45)(20) $
#
# > $ 13 = c_o + 9 $
#
# > $ 4 = c_o $
#
# So the arithmetic form of the consumption function for this particular economy is:
#
# > $ C = 4 + (0.45)Y $
#
#
# In[ ]:
# consumption function calculations
Y = 20
C = 13
c_y = 0.75
t = 0.4
c_o = C - c_y*(1-t)*Y
# ### 9.2.3 Other Components of Total Expenditure
#
# The determinants of the other components of aggregate demand—investment spending I, government purchases G, and net exports NX=GX-IM—are familiar. The level of investment spending is determined by the real interest rate and by "animal spirits" influencing assessments of profitability made by business investment committees. In our model we represent these determinants by making investment spending I a function of the real interest rate r, and of the parameters $ I_o $ and $ I_r $, the baseline "animal spirits" level of investment spending and the interest sensitivity of investment, respectively.
#
# > $ I= I_o - I_rr $
#
# The level of government purchases G is set by politics.
#
# Net exports NX are equal to gross exports GX (a function of the real exchange rate $ \epsilon $ and the level of foreign national income $ Y^f $) minus imports IM, which are modeled as a constant share of domestic national income:
#
# > $ NX = GX - IM= \left(x_fY^f + x_{\epsilon}{\epsilon}\right)- im_yY $
#
#
#
# 
#
# >>_**Components of Total Expenditure**: By far the largest component of GDP is made up of consumption spending. Government purchases come second, and gross investment comes third. For the past two decades the United States has imported more than it has exported; hence net exports have been negative, not a contribution to but a subtraction from GDP.
#
#
#
# ### 9.2.4 Autonomous Spending and the MPE
#
# Let’s take the equation for aggregate demand—total expenditure;
#
# >AD = C + I + G + NX
#
# then separate net exports into its gross exports and imports components:
#
# >AD = C + I + G + (GX - IM)
#
# and replace the two components of total expenditure that depend directly on national income Y—consumption spending C and imports IM—with their determinants:
#
# > $ AD = c_o + c_y(1-t)Y + I + G + GX - im_yY $
#
# We can classify the components of planned total expenditure into two groups. The first group is so-called autonomous spending, which we will call A. Autonomous spending is made up of the components of planned total expenditure that do not depend directly on national income Y. Baseline consumption C0, investment spending I, government spending G, and gross exports GX are the components of autonomous spending A:
#
# > $ A = c_o + I + G + GX $
#
# The second group includes the other two components of total expenditure—the rest of consumption spending, and a negative contribution from imports. Let's call this second group the Marginal Propensity to Expend Income on Domestically-Produced Goods, or MPE for short:
#
# > $ MPE = (c_y(1-t) - im_y)Y $
#
# Then we can write aggregate demand in the simple form:
#
# > AD = A + (MPE)Y
#
# We then plot aggregate demand on an income-expenditure diagram.
#
#
#
# 
#
# >>_**The Income-Expenditure Diagram**: On the income-expenditure diagram, the line showing the relationship between total economywide income and planned expenditure—aggregate demand—is determined by two things: autonomous spending A, the level at which the planned- expenditure line intercepts the vertical axis; and the marginal propensity to expend income on domestically produced goods, MPE, the slope of the aggregate demand line._
#
#
#
# The vertical intercept of the aggregate demand line is the level of autonomous spending A. The aggregate demand line’s slope is the MPE. A change in the value of any determinant of any component of autonomous spending A—the baseline levels of consumption $ c_o $, "animal spirits" investment $ I_o $, or government purchases G; the real interest rate r; and foreign-determined variables that affect exports directly or indirectly (like foreign interest rates $ r^f $, foreign national income $ Y^f $, or speculators’ view of exchange rate fundamentals $ {\epsilon}_o $)—will shift the aggregate demand line up or down. The higher autonomous spending, the further from the horizontal axis the aggregate demand line will be.
#
# Changes in the marginal propensity to consume $ c_y $, the tax rate t, or the propensity to spend on imports $ im_y $ will change the MPE, and thus change the slope of the aggregate demand line. The higher the MPE, the steeper is the slope.
#
#
#
# 
#
# >>_**An Increase in Autonomous Spending**: An increase in autonomous spending shifts the aggregate demand line upward._
#
#
#
# 
#
# >>**An Increase in the Marginal Propensity to Expend**: A change in the marginal propensity to expend changes the slope of the aggregate demand line._
#
#
#
# #### 9.2.4.1 Autonomous Spending and the MPE
#
# In the aggregate demand function:
#
# >PE = A + (MPE)(Y)
#
# the marginal propensity to expend (MPE) will be less than the slope of the consumption function $ c_y(l — t) $ because of the effect on the economy of imports. Thus if the marginal propensity to consume $ c_y = 0.75 $ and the tax rate $ t = 0.4$, the 0.45 slope of the consumption function is an upper bound to the MPE. If imports are 15 percent of real GDP, then:
#
# > $ MPE = c_y(1-t) - im_y $
#
# > $ MPE = (0.75)(1 - 0.4) - 0.15 $
#
# > $ MPE = 0.3 $
#
# Such relatively small values of the MPE are typical for modern industrialized economies that are relatively small, which have high relatively values of for $ im_y $ because they are very open to the world economy, large social-democratic social-insurance states (that is, relatively high values for t), and deep and well-developed financial systems that provide ample room for household borrowing and lending to smooth out consumption (that is, relatively small values for $ C-y $ as well). However, in the past, in relatively closed economies, or in economies with undeveloped financial systems, the MPE can be significantly higher.
#
#
#
# ### 9.2.5 Sticky-Price Equilibrium
#
# The economy will be in equilibrium when planned total expenditure equals real GDP—which is, according to the circular-flow principle, the same as national income. Under these conditions there will be no short-run forces pushing for an immediate expansion or contraction of national income, real GDP, aggregate demand, total expenditure.
#
# On the income-expenditure diagram, the points at which total expenditure equals national income are a line running up and to the right at a 45-degree angle with respect to the horizontal axis. This 45-degree line shows all the possible points of equilibrium: all the points where aggregate demand equals national income and product. The actual equilibrium the economy will find in the sticky-price short run will be that point at which aggregate demand is equal to actual national income; the point where this aggregate line intersects the 45-degree equilibrium-condition line is the economy’s equilibrium.
#
#
#
# 
#
# >>_**Equilibrium on the Income-Expenditure Diagram: On the income-expenditure diagram, the equilibrium point of the economy is that point where aggregate demand (as a function of national income) is equal to national income and product.
#
#
#
# In algebra, the equilibrium values of aggregate demand and national income and product Y must satisfy both the aggregate demand function:
#
# > AD = A + (MPE)Y
#
# and the equilibrium condition:
#
# > AD = Y
#
# Substituting Y for AD in the first of these equations and regrouping, the solution is:
#
# > $ Y = \frac{A}{1-MPE} $
#
# If the numerical values of the parameters of the aggregate demamd function are A = 12,000 billion and MPE = 1/3, then aggregate demand as a function of national incpome is
#
# > AD = 12000 + (1/3)(Y)
#
# The equilibrium level of national income and product and total expenditure is then
#
# > Y = 18,000 billion
#
# What forces drive the economy to its short-run sticky-price goods market equilibrium? If the economy is not on the 45-degree line, then aggregate demand AD does not equal real GDP Y. If Y is greater than AD, there is excess supply of goods. If AD is greater than Y, there is excess demand for goods. In neither case is the economy in equilibrium.
#
#
#
# 
#
# >>_**Inventory Adjustment and Equilibrium: The Income-Expenditure Diagram**: If the economy is not at its equilibrium point, then either actual production exceeds planned expenditure (in which case inventories are rising) or planned expenditure exceeds actual production (in which case inventories are falling)._
#
#
#
# 
#
# >>_**The Inventory-Adjustment Process**: If planned expenditure is greater than total production, inventories are falling. Businesses will hire more workers and increase production. But increasing production just by the fall in inventory won't bring the economy to equilibrium because planned expenditure rises with production and income.
#
#
#
# In the first case, in which production exceeds aggregate demand, inventories are rising rapidly. Firms are unwilling to accumulate unsold and unsellable inventories. Thus firms are about to cut production and fire workers.
#
# In the second case, in which aggregate demeand exceeds production, inventories are falling rapidly. Businesses are selling more than they are making. Some businesses will respond to the fall in inventories by boosting prices, trying to earn more profit per good sold. But the bulk of businesses will respond to the fall in inventories by expanding production to match planned expenditure. They are about to hire more workers. Real GDP and national income are about to expand.
#
# Now suppose that businesses see their inventories falling and respond by boosting their production to equal last month’s aggregate demand. Will such an increase bring the economy into goods market equilibrium, with aggregate equal to national income and real GDP? The answer is that it will not. To boost production, firms must hire workers, paying more in wages and causing household income to rise. But when income rises, total spending rises as well. Thus the increase in production and income generates a further expansion in planned expenditure.
#
# Even after production has increased to close the initial gap between planned expenditure and national income, the economy will still not be in equilibrium. Inventories will be falling even though hiring more workers has increased production. Because hiring more workers has also boosted total income and further increased planned expenditure, production will have to expand by a multiple of the initial gap in order to stabilize inventories. The process will come to an end, with planned expenditure equal to national income, only when both have risen to the level at which the planned-expenditure line crosses the 45-degree income-equals-expenditure line. Box 9.5 provides a worked example. And the process works in reverse to lower production and expenditure if planned expenditure is initially below national income.
#
#
#
# #### 9.2.5.1 How Fast Does the Economy Move to This Equilibrium?: Some Details
#
# At any one particular moment the economy does not have to be in short-run equilibrium. Aggregate demand can exceed real GDP and national income, and inventories can fall, for periods as long as a year. Strong forces are pushing the economy toward short-run equilibrium. Businesses do not like to lose money by producing things that they cannot sell or by not having things on hand that they could sell. But it takes at least months, usually quarters, and possibly more time for businesses to expand or cut back production.
#
# For example, between the summer of 1990 and the summer of 1991 inventories fell for five straight quarters. Real GDP was less than planned expenditure as businesses decided that their high levels of inventories were too large given the economic uncertainties created by the Iraqi invasion of Kuwait and the subsequent recession. Between the winter of 1994 and the summer of 1995, for six quarters, inventories rose. For a year and a half GDP was greater than aggregate demand.
#
#
#
# 
#
# >>_**Inventories as the Balancing Item: Inventory Investment in the Early and Mid-1990s**_
#
#
#
# #### 9.2.5.2 The September 11, 2001 Terrorist Attack on the World Trade Center: An Example
#
# The U.S. economy was already in recession in the summer of 2001 when the ter- 1rorist attack on the World Trade Center sent it into a further downward spiral. The attack on September 11, 2001, reduced autonomous spending through two different channels:
#
# First, the attack shook consumer confidence: The Conference Board’s index fell from 114 in August 2001 to 85 in November. Baseline consumption spending, the parameter $ c_o $ in the consumption function, is closely linked to consumer confidence.
#
# Second, the attack increased uncertainty Would there be further attacks? What would the U.S. military response be? How would U.S. government
# spending shift in response to the attack? The first rule of planning for the future is that whenever uncertainty is unusually high, you are better off delaying whatever decisions you can until some of this uncertainty is resolved. Thus businesses undertaking investment projects adopted a wait-and-see approach. Their "animal spirits" became more pessimistic, and $ I_o $ declined. The result was that autonomous spending A fell.
#
# Had the terrorist attack been the only major shock to the U.S. economy, the recession would have been longer and deeper than turned out to be the case. However, three countervailing forces boosted aggregate demand:
#
# First, the Federal Reserve greatly reduced interest rates, and so stimulated investment.
#
# Second, the Bush tax cut of 2001 boosted consumers’ incomes in 2002 by some 80 billion and so boosted consumption spending. Most of this money went to high-income consumers with relatively low marginal propensities to consume, so it was not the most effective stimulus, but it was still welcome at the time.
#
# Third, the mobilization for the War against Terror boosted government purchases G.
#
# Thus the economy began to rebound in 2002. But because the downward shock had been large and because the tax cut was not well designed to be the most effec tive employment-generating stimulus, the recovery from September 11, 2011 was slower than average as far as employment growth was concerned.
#
#
#
# 
#
# >>_**Month-to-Month Changes in U.S. Industrial Production, 2000-2002**: Industrial production in the United States had been declining since late 2000 but was showing signs of recovery when the attack on the World Trade Center on September 11, 2001, shook consumer and business confidence. As consumers cut back on spending and as businesses adopted a wait-and-see attitude, U.S. industrial production dropped an additional 2.2 percent in the four months before recovery began._
#
#
#
# #### 9.2.5.3 Calculating the Difference Between Aggregate Demand and National Income and Product: An Example
#
# Suppose that our aggregage-demand function has numerical values for its coefficients such that in trillions
#
# >AD = A + (MPE)(Y) = 12 + (1/3)Y
#
# Suppose first that the current level of national income Y were 15 trillion. Then aggregate demand is:
#
# >AD = A + (MPE)(Y) = 12 + (1/3)15 = 17
#
# and business inventories are being drawn down at a rate of>
#
# >AD - Y = 17 - 15 = 2
#
# of 2 trillion per year. Businesses, seeing their inventories fly off the shelves, are about to hire workers and open production lines.
#
# Suppose, alternatively, that the current level of national income Y is 21 trillion. Then:
#
# >AD = A + (MPE)(Y) = 12 + (1/3)21 = 19
#
# and business inventories are being added to at a rate:
#
# >Y - AD = 21 - 19 = 2
#
# of 2 trillion per year. Businesses, seeing unsold and unsellable inventories accumulate, are about to fire workers and close production
#
# However, if the current level of national income Y were 18 trillion, then:
#
# >AD = A + (MPE)(Y) = 12 + (1/3)Y = 12 + (1/3)(18) = 18
#
# Then national income and aggregate demand are in balance: inventories are stable. Businesses are neither hiring nor firing workers _en masse_. And the economy is in equilibrium.
#
#
#
# ### RECAP: Income and Expenditure
#
# The force that pushes national income and product Y to equal aggregate demand AD is the inventory-adjustment process. If real GDP excreeds planned expenditure, inventories are rising rapidly. Firms are unwilling to accumulate unsold and unsellable inventories, so they are about to cut production and Are workers to reduce real GDP. If real GDP is less than planned expenditure, inventories are falling rapidly, as businesses are selling, more than they are making. Businesses are about to expand production, hire more workers, and thus raise real GDP.
#
#
# ## 9.3 The Multiplier
#
# ### 9.3.1 Determining the Size of the Multiplier
#
# Suppose something happens to change the level of aggregate demand at every possible level of national income. Anything that affects the level of autonomous spending will do. What would then happen to the equilibrium level of national income and product?
#
# An upward shift in the aggregate demand line would increase the equilibrium level of national income. At the prevailing level of national income, aggregate demand would be larger than national income and product. Businesses would find themselves selling more than they were making, and their inventories would fall. In response, businesses would boost production to try to keep inventories from being exhausted, and production would expand.
#
# How much production would expand depends on the magnitude of the change in autonomous spending and the value of the _spending multiplier_.
#
# The value of this spending multiplier depends on the slope of the aggregate demand line, the marginal propensity to expend (MPE). The higher the MPE, the steeper is the line and the greater is the multiplier. A large multiplier can amplify small shocks to spending patterns into large changes in total production and income.
#
# To calculate the multiplier, recall the equation for the short-run sticky-price equilibrium level of real GDP:
#
# > $ Y = \frac{A}{1 - MPE} $
#
# Suppose autonomous spending changes by an amount $ {\Delta}A $. Then the change $ {\Delta}Y $ in the equilibrium level of real GDP is:
#
# > $ Y = \left(\frac{1}{1 - MPE}\right){\Delta}A $
#
# The factor 1/(1 —MPE) is the multiplier: It multiplies the upward shift in the planned-expenditure line as a result of the increase in autonomous spending into a change in the equilibrium level of real GDP, total income, and total expenditure.
#
# We are going to use for the multiplier the symbol $ \mu $, the Greek letter mu, which is the Greek equivalent of the Roman letter m. M for multiplier. Why not use M? Because M in macroeconomics is reserved for the economy's _money stock_.
#
# $ \mu = \frac{1}{1 - MPE} $
#
# $ Y = {\mu}A $
#
# $ {\Delta}Y = {\mu}{\Delta}A $
#
#
#
# 
#
# >>_**The Multiplier Effect**: An increase in au tonomous spending will generate an amplified increase in the equilibrium level of national income. Why? Because planned expenditure will rise not just by the increase in autonomous spending but by the increase in autonomous spending plus the marginal propensity to expend times the increase in the equilibrium level of national income._
#
#
#
# Why the factor 1/(1 — MPE)? Think of it this way: The MPE—the marginal propensity to expend—is the slope of the aggregate line. A 1 increase in national income raises the equilibrium level of total expenditure by 1, because expenditure has to go 1 higher to balance income and production.
#
# It also raises the level of aggregate demand by $MPE. Thus a 1 increase in the level of total income closes (1 — MPE) of the gap between aggreate demand and national income. To fully close an initial gap of $ {\Delta}A $, the equilibrium level of national income must increase by $ {\Delta}A/(1 —MPE) $.
#
# Because autonomous spending is influenced by a great many factors:
#
# > $ A = c_o + (I_o - I_rr + G + x_fY^f + (x_{epsilon}{epsilon}_o + x_{epsilon}{epsilon}_rr^f - x_{epsilon}{epsilon}_rr) $
#
# almost every change in economic policy or the economic environment will set this multiplier process in motion.
#
#
#
# ### 9.3.2 Changing the Size of the Multiplier
#
# One factor that tends to minimize the multiplier is the tax system: whether the tax system has been designed to provide the government with fiscal auto matic stabilizers. The government doesn’t levy a total lump-sum tax independ ent of the state of the economy. Instead the government imposes roughly pro portional (actually slightly progressive) taxes on the economy, so government tax collections are equal to a tax rate t times the level of GDP Y: the total tax take equals tY.
#
# This means that when GDP is relatively high the government collects more in tax revenue than it would with a lump-sum tax. The collection of extra revenue dampens swings in after-tax income and thus reduces consumption. Similarly, the government collects less in tax revenue when GDP is relatively low; thus after-tax income is higher than that under lump-sum taxes, and this higher income boosts consumption. Because the fall in consumption is smaller with a proportional rather than a lump-sum tax, the multiplier is smaller. Disturbances to spending are not amplified as much as they would be with a lump-sum tax, and so shocks to the economy tend to cause smaller business cycles. The automatic working of the government’s tax system (and, to a lesser extent, its social welfare programs) functions as an _automatic stabilizer_, reducing the magnitude of fluctuations in real GDP and unemployment.
#
# Substituting our detailed expression for calculating the MPE:
#
# > $ MPE = c_y(1-t) - im_y $
#
# into our definition of the multiplier:
#
# > $ \mu = \frac{1}{1 - MPE} $
#
# tells us that under a proportional tax system the multiplier is:
#
# > $ \frac{{\Delta}Y}{{\Delta}A} = \mu = \frac{1}{1-\left[c_y(1-t)-im_y\right]} $
#
# If the government levied lump-sum taxes, the multiplier would be:
#
# > $ \frac{{\Delta}Y}{{\Delta}A} = \mu = \frac{1}{1-\left[c_y-im_y\right]} $
#
# The difference is the (1 — t) term that is missing from the denominator of the last expression in the equation above.
#
# How important is this (1 — t) term? How large are fiscal automatic stabilizers in the United States today? When national product and national income drop by a dollar, income tax and social security tax collections fall automatically by at least one-third of a dollar. Thus the fall in consumers’ disposable income is only two-thirds as great as the fall in national income, and the fall in consumption is only two-thirds as large as it would be without fiscal automatic stabilizers.
#
# A more globalized economy will also have a smaller multiplier. An economy that is more open to world trade will have a smaller multiplier than will a less open economy. The more open the economy, the greater is the marginal propensity to expend on imports. The more of every extra dollar of income spent on imports, the less is left to be devoted to planned expenditure on domestic product —and therefore the smaller is the multiplier. If the share of imports in GDP is large, the potential change in the multiplier from an _open economy_:
#
# > $ \frac{{\Delta}Y}{{\Delta}A} = \mu = \frac{1}{1-\left[c_y(1-t)-im_y\right]} $
#
# to that for a _closed economy_:
#
# > $ \frac{{\Delta}Y}{{\Delta}A} = \mu = \frac{1}{1-\left[c_y(1-t)\right]} $
#
# can be considerable. The difference is the missing IMy term in the denominator of the equation above. In modern industrialized economies where the share of imports in real GDP is certainly more than 10 percent, any calculation of the multiplier will be significantly off unless it takes account of the effects of world trade.
#
#
#
# #### 9.3.2.1 The Value of the Multiplier: An Example
#
# Suppose that the planned-expenditure function has values for its parameters of A = 12 trillion and MPE = 1/3, so that:
#
# >AD = A + (MPE)(Y) = 12 + (1/3)Y
#
# Then the equilibrium value of national income (and of real GDP) Y is 18trillion, for only at Y = 18 trillion is aggregate demand equal to national income.
#
# Now suppose that autonomous spending A were to increase by an amount of 0.1 trillion: $ {\Delta}A = 0.1 $. Then the aggregate demand function is
#
# >AD = A + (MPE)(Y) = 12.1 + (1/3)Y
#
# and the equilibrium value of national income (and real GDP) Y is 18.15 trillion.
#
# The change in Y divided by the change in autonomous spending is:
#
# > $ \frac{{\Delta}Y}{{\Delta}A} = 1.5
#
# This is equal to:
#
# > $ 1.5 = \frac{1}{1-(1/3)} = \frac{1}{1 - MPE} = \mu $
#
# which we saw above is the definition of the multiplier.
#
#
#
# ### 9.3.3 RECAP: The Multiplier
#
# If prices are sticky, higher planned expenditure boosts production, and this boosts income. Higher income gives a further boost to consumption, and this in turn boosts aggregate demand some more. Thus any shift in a component of planned expenditure upward or downward leads to a multiplied shift in total production.
#
# The early-twentieth-century British economist John Maynard Keynes was one of the first to stress the importance of this multiplier process. The multiplier arises because planned expenditure PE is equal to autonomous spending A plus the marginal propensity to expend MPE times national income Y: PE = A + (MPE)(Y).
#
# In equilibrium, planned expenditure PE equals national income Y, which is true if and only if Y = A[l/(1 - MPE)]. The term 1/(1 - MPE) is the value of the multiplier, which we label with the Greek letter mu: $ \mu $:
#
# > $ \mu = \frac{1}{1 - MPE} = \frac{1}{1 - \left[c_y(1-t) - im_y\right]} $
#
#
# 
#
# ## Catch Our Breath
#
# * Ask me two questions…
# * Make two comments…
# * Further reading…
#
#
#
# ----
#
# Lecture Support:
# Introducing the Sticky-Price Model:
#
#
#
# ----
# # Introducing the Sticky-Price Model: PRESENTATION SLIDES
# # Part IV Sticky Price Macroeconomics
#
# In this part we shift our point of view. Now we are looking at it over such a short period that its productive resources are fixed and that wages and prices are not fully flexible.
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# In this analysis, the/key questions are:
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# * What are the economic forces that determine the short-runs sticky-price equilibrium value of real GDP?
# * In an economy with sticky wages and prices, what determines the values of:
# * consumption spending,
# * investment spending,
# * government purchases, and
# * net exports?
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# Part 4 contains...
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# # Sticky-Prices: Introduction
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# * Okun’s Law
# * Potential output and actual national income and product
# * The unemployment rate and the NAIRU
# * The output gap and cyclical unemployment
# * Okun's Law coeffient of 2
# * Determinants of the NAIRU:
# * Frictional unemployment
# * Structural unemployment
# * The economy as a societal calculating machine…
# * The economy as a societal calculating machine gone mad…
# * Market failure:
# * What kind of market failure?
# * Sticky prices, wages, and debts
# * An excess demand for money is a general glut of goods and services
# * A volatile demand for "money"
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# ## Pause to Note: AD = Y IS NOT Y*!
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# * Falls below potential output, not fluctuations around potential output
# * Asymmetry in changes
# * Crashes, but no upward jumps
# * We use potential output as a benchmark
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# # Sticky-Prices: Our Model
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# * Build it up in stages
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# * It is a _model_: it is not reality
# * We are going to feel free to step outside the model whenever we think it is good to do so
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# * This model is the minimum deviation needed to gain traction from the flexprice medium-run model of chapters 6-7
# * That model assumed that wages, prices, and real interest rates were fully flexible
# * The real wage W/P would move to set $ Y = Y^* $, output to potential
# * The price level P would move to set $ AD = Y $, aggregate demand equal to output
# * Thus eliminating any excess supply or demand for money
# * The real interest rate r would move to make the components of aggregate demand add up: $ AD = C + I + G + NX $
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# ----
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# ## Pieces of the Sticky-Price Model: Many Are the Same
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# * The consumption function: $ C = c_o + {c_y}(1-t)Y $
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# * Investment spending: $ I = I_o - {I_r}r $
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# * Government purchases: $ G $
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# * The international sector: $ NX = GX - IM = x_fY^f + {x_{\epsilon}}{\epsilon} - im_yY $
# * Exchange rate determination: $ \epsilon = {\epsilon}_o + {\epsilon}_r\left(r^f - r\right) $
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#
# ----
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# ## Pieces of the Sticky-Price Model: One Is Different
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# * The national income identity: $ Y = AD = C + I + G + NX $
# * Production demand determined: inventory adjustment mechanism
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# ----
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# ## Pieces of the Sticky-Price Model: One Is New
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# * The real interest rate: $ r = i + \rho - \pi $
# * i :: determined by the Federal Reserve (with zero lower bound)
# * $ \rho $ :: determined in financial markets
# * $ \pi $ :: expected inflation
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# ----
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#
# ## The Business Cycle Compared to the Growth Trend
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# **Small numbers or big numbers?**:
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# * Lose five years of the economic growth trend, max, in a recession or depression
# * Lose ten years of the labor productivity growth trend, max, in a recession or depression
# * And—most of the time—recession or depression losses are transitory
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# ## Spending on Domestically-Produced Goods
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# **Aggregate demand**
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# * Total spending, planned expenditure, aggregate demand
# * AD = C + I + G + NX
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# **Four components**
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# * C: consumption spending by households
# * I: investment spending by businesses
# * G: government purchases of goods and services
# * NX = GX - IM: net exports
# * Alternatively: AD = Cd + Id + Gd + GX
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#
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# **Demand-determined equilibrium**
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# * C + I + G + NX = AD = Y
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# ----
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# ## The Consumption Function
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# **Household decisions**:
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# * Net taxes: $ T = tY $
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# * Disposable income: $ Y^d = Y - T = (1-t)Y $
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# * Consumption, savings, disposable income, taxes: $ C = Y^d - S^p = Y - T - S^p $
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# **The consumption function**:
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# * $ C = c_o + {c_y}Y^d = c_o + {c_y}(1-t)Y $
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# * Baseline consumption: $ c_o $
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# * The marginal propensity to consume: $ MPC = \frac{dC}{dY^d} = c_y $
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# * Other terms:
# * Wealth terms in consumption?
# * Income terms in consumption?
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# ## Investment Spending
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# **The investment function**
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# * $ I = I_o - {I_r}r $
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# * The real interest rate: $ r = i + \rho - \pi $
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# * The nominal _risky_ interest rate: $ i + \rho $
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# * The nominal _safe_ interest rate: $ i $
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# * The inflation rate: $ \pi = \frac{dP}{dt}$
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# * The investment accelerator version: $ I = I_o - {I_r}r + {I_y}Y $
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# **The stock market and investment**
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# * The value of the stock market: $ V = \frac{D}{r - (n + g)} $
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# * The Tobin's Q version of the investment function: $ I = I_o + I_{q}\left(\frac{V}{B}\right) $
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# **The peculiar role of inventories**
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# * Part of investment—a business needs inventories, goods-in-process and goods-on-disply, as much as it needs machines, software, and buildings
# * But also a big jump in inventories is a sign of _mistakes_: something has gone wrong
# * Hence sometimes a distinction between _planned_ investment and _realized_ investment...
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# ## Government Purchases
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# * Government purchases of goods and services (including wages of government workers): $ G $
# * The government surplus (or deficit): $ DEF = -S^p = G - T = G - tY $
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# ----
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# ## International Trade
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# **The international sector**
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# * Net exports: $ NX = GX - IM $
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# * Gross exports: $ GX = x_fY^f + {x_{\epsilon}}{\epsilon} $
# * Foreign economic product: $ Y^f $
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# * The real exchange rate: $ \epsilon = \frac{eP^f}{P} $
# * The nominal exchange rate—the dollar value of foreign currency: $ e $
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# * The foreign price level $ P^f $
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# * Imports: $ IM = im_yY $
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# ----
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# ## Real Exchange Rate (Value of Foreign Goods/Currency) Determination
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# * $ \epsilon = {\epsilon}_o + {\epsilon}_r\left(r^f - r\right) $
# * Foreign real interest rate: $ r^f $
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# * Baseline real exchange rate: $ {\epsilon}_o $
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# Elasticity of the exchange rate to interest rate differentials: $ {\epsilon}_r $
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# The longer that interest rate differentials are expected to continue, and the more slowly that real exchange rates are expected to revert to trend, the higher $ {\epsilon}_r $ will be and the larger will be the effect of a given interest rate differential on the exchange rate.
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# Remember: The exchange rate is the value of foreign goods/currency. If foreign goods/currency becomes more valuable, the exchange rate rises; if domestic goods/currency becomes more valuable, the exchange rate falls. Often you will hear people talk of an _appreciation_ or _revaluation_ of the dollar or of a depreciation or devaluation of the dollar. An appreciation or revaluation of the dollar is a _fall_ in the value of the exchange rate—the value of foreign currency and goods. A depreciation or devaluation of the dollar is a _rise_ in the value of the exchange rate—the value of foreign currency and goods.
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# I will try to say "the exchange rate—the value of foreign currency/goods" whenever I can...
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# ## Recap: Pieces of the Sticky-Price Model
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# * The consumption function: $ C = c_o + {c_y}(1-t)Y $
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#
# * Investment spending: $ I = I_o - {I_r}r $
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# * Government purchases: $ G $
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# * The international sector: $ NX = GX - IM = x_fY^f + {x_{\epsilon}}{\epsilon} - im_yY $
# * Exchange rate determination: $ \epsilon = {\epsilon}_o + {\epsilon}_r\left(r^f - r\right) $
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# * Demand determined national income and product: $ Y = AD = C + I + G + NX $
# * Interest rate determination: $ r = i + \rho - \pi $
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# # The Multiplier
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# > $ Y = C + I + G + NX $
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# > $ Y = c_o + c_y(1-t)Y + I + G + GX - im_yY $
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# > $ (1 - c_y(1-t)+ im_y)Y = c_o + I + G + GX $
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# >> $ A = c_o + I + G + GX $
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# > $ Y = \frac{c_o + I + G + GX}{1 - c_y(1-t)+ im_y} = \frac{A}{1 - c_y(1-t)+ im_y} $
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# > $ Y = {\mu}A $
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# >> $ {\mu} = \frac{1}{1 - c_y(1-t)+ im_y} $
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# * A: autonomous spending—"autonomous" because it does not depend on the level of national income
# * $ \mu $: the multiplier
# * What is the multiplier? $ c_y = 0.67 $, $ im_y = 0.17 $ $ t = 0.25 $
# * What is the multiplier? > 1.5 (investment accelerator?)
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# ## Catch Our Breath
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# * Ask me two questions…
# * Make two comments…
# * Further reading…
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# Lecture Support:
# Keynote File:
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