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# III Flexible-Price Macroeconomics¶

In this part we shift our point of view and take a snapshot" of the economy, looking at it over such a short period that its productive resources are effectively fixed, but also over such a long period that prices, wages, and debts can be taken as fully flexible: none of the prices in the macroeconomy are "stuck" at levels that keep the macroeconomy from reaching a full-employment equilibrium.

In this analysis, the/key questions are:

1. What are the economic forces that keep real GDP at its equilibrium value?
2. In an economy with flexible wages and prices (and debts), what determines the division of real GDP among consumption spending, investment spending, government purchases, and net exports?

Part III contains three chapters. Chapter 6 assembles the building blocks. It analyzes the determinants of the components of spending that make up GDP. The answers to the questions above are the same whether prices are flexible (Part III) or sticky (as they will be in Part IV). So our building blocks form the basis for both our long-run and our short-run stories.

In Chapter 7 these building blocks are put together. Chapter 7 demonstrates how to use the flexible-price model to analyze the composition of real GDP and how a flexible-price macroeconomy reacts to disturbances and shocks.

Chapter 8 turns the focus of attention from production to the price level. It performs the straightforward task of analyzing the determinants of the price level and inflation in the flexible-price model.

# 6 Building Blocks of the Flexible-Price Model¶

#### QUESTIONS¶

1. What Is a full-employment analysis?
2. What keeps the economy at full employment when wages and prices are flexible?
3. What determines the level of consumption spending?
4. What determines the level of investment spending?
5. What determines the level of net exports?
6. What determines the level of the real exchange rate?

potential output: The level at which national product would be if all resources were fully employed.

production function: The relationship between the total amount of output produced in an economy and the quantities of labor and capital and the levels of technology and organization used to produce it.

classical assumption: The assumption that wages and prices and debts are flexible, and respond quickly to always balance supply and demand.

labor market: The market in which workers are hired by firms.

marginal product of labor (MPL): The increase in potential output from a 1-unit increase in the quantity of labor employed by the firm.

labor supply The number of workers who want to work.

real wage: The wage paid to the average worker divided by the price level.

labor market equilibrium: When, save for those in the process of changing jobs, the economy is at full employment.

disposable income: What is left of income after taxes have been paid and transfer payments received.

marginal propensity to consume (MPC) The increase in consumption spending resulting from a one-dollar increase in disposable income.

consumption function: The relationship between baseline consumption $c_o$, the marginal propensity to consume $c_y$, disposable income $Y^D$, and consumption spending $C$.

real interest rate: The nominal interest rate minus the inflation rate.

present value: The value in today's dollars of a sum of money to be received in the future.

investment function: The relationship between the real interest rate r and investment spending.

government purchases: Things the government buys in the way of goods and services. Note that this includes the wages of government employees. Opposed to transfer payments by which the government transfers money to people for reasons unconnected with their providing it with goods or services.

transfer payments: Spending by the government that is not a purchase of goods or services but instead simply a transfer of income from taxpayers to program recipients.

net taxes: The difference between taxes collected by the government and transfer payments received by households and businesses.

net exports: The difference between exports and imports.

gross exports: Total goods and services produced at home and sold to purchasers in foreign countries.

imports: Goods and services produced in other countries and purchased by residents of our country.

In the previous two chapters we looked at long-run growth—at how the economy develops and evolves over periods as long as generations. In this chapter we look at the economy over such a short period that its productive resources are fixed but such a long period that wages and prices are fully flexible.

This chapter, Chapter 6, first answers the question: What are the economic forces that keep real GDP at its equilibrium value? In Section 6.1 we show that if wages and prices are flexible enough (as we assume they are here in Part 3), then markets clear: Quantities demanded are equal to quantities supplied. In particular, the labor market clears: Employment is equal to the labor force (save for some “frictional” unemployment), and production is equal to potential output. Should production not be equal to potential output, rising or falling real wages will quickly lower or raise firms’ demands for labor and bring the economy back to equilibrium at full employment.

Then this chapter assembles the building blocks we need for nearly every remaining chapter in the book. How do consumers decide on consumption spending—how much to spend on themselves and their households? How do businesses decide on the level of investment spending? How are net exports determined? The answers to these questions are the same whether prices are flexible (Part 3) or sticky (as they will be in Part 4 of this book). So our building blocks form the basis for both our long-run and short-run stories.

A word is needed about the flexible-price "classical" assumption made in this part. Part 3 answers the first question above in the case where wages and prices are flexible, in which the market system works well, in which markets clear—every buyer finds a willing seller and every seller finds a willing buyer. This means, most important, that labor supply equals demand: No firms wanting to hire workers are left unsatisfied, and no workers willing to work are left permanently unemployed. In Part 4 we will drop this flexible-price full-employment assumption. From Part 4 on, we will instead make the “Keynesian” assumption that wages and prices and debts are sticky. This leads to a number of important differences in the analysis: the market system does not work perfectly, or even well; real GDP is not always equal to potential output; and unemployment can rise high enough to become a critical economic problem.

Part III vs. Part IV: "Classical" flexible-price versus "Keynesian" sticky-price analyses.

## 6.1 Potential Output and Real Wages¶

The assumption that wages and prices are flexible was commonly made by the classical economists, who wrote before World War II. Thus this assumption is also called the classical assumption. The classical assumption guarantees that markets work—that prices adjust rapidly to eliminate gaps between the quantities demanded and the quantities supplied. No businesses find their inventories of unsold goods piling up, and there is full employment: Everyone who wants a job (at the market-clearing level of wages) can get a job. Every business that wants to hire a worker (at the market-clearing level of wages) can hire a worker. Thus actual output is equal to potential output: There is no gap between the economy’s pro­ ductive potential and the level of output the economy produces.

This classical assumption that we make in this part of the book is not always, indeed not often, a good one. Experience has shown that a market economy does not always have flexible prices. Prices and wages turn out to be sticky, or sluggish, or stuck. Thus the economy does not always work well, and does not always provide full employment.

If the classical flexible-price assumption is not always a good one to make, why make it at all? First, it can be a very good assumption if conditions are right. It is a good assumption if wages and prices are relatively flexible, and if we are look­ ing at processes that take enough time for prices in all of the economy’s markets to adjust in order to balance supply and demand. Second, starting with the classical assumption makes this course easier. It simplifies the analysis of several issues and facilitates an understanding of how the macroeconomy works in the long run. One habit of economists is to start with the simpler cases, and only after they are well understood, to look at more complicated ones.

Moreover, the way an economy functions under the flexible-price assumption provides a useful baseline against which to assess economic performance. If we want to assess the costs to society of sticky prices and periods of high unemployment, we need a benchmark against which to make comparisons, and the behavior of the economy in the flexible-price model provides such a benchmark.

Nevertheless, we must remember that Part 3 presents only one model of the economy. The Keynesian sticky-price model behaves very differently in a number of ways. So Part 3 does not tell the full story.

### 6.1.1 The Production Function¶

In the flexible-price model of the macroeconomy, two sets of factors determine the levels of potential output and of real wages: the production function and the balance of supply and demand in the labor market. Once we have determined potential output—the economy’s full-employment productive potential—we then know what its actual level of output is, for in the flexible-price model potential output and actual output are the same. Why are they the same? We will see shortly that it is the flexibility of prices and wages that guarantees that potential output and the actual level of output are equal.

Chapter 4 introduced the production function, the rule that tells us how much the economy can produce given its available productive resources. In the Cobb-Douglas form of the production function, as we learned, potential output Y* is determined by the size of the labor force L, the economy’s capital stock K, the efficiency of labor E, and a parameter $\alpha$ between 0 and 1 that tells us the extent to which growth is oriented toward investment, or how fast returns to investment diminish as the capital-output ration increases. A high value of $\alpha$ tells us that diminishing returns to investment set in only slowly; hence growth is oriented more toward investment and less toward improvements in the efficiency of labor.

The production function tells us that potential output Y* is:

$Y^* = K^{\alpha}(LE)^{1-\alpha}$

The graph below shows us just one slice of this production function for one particular value of the efficiency of labor E and one particular value of the labor force L—the relationship between the capital stock K and potential output Y*. It holds the supply of labor L and the efficiency of labor E fixed.

The Production Function: Holding the labor force and the efficiency of labor constant, real GDP increases as the capital stock increases. Because each successive addition to the capital stock produces a smaller increase in output, the production function is curved. The smaller the level of $\alpha$, the greater the curvature and the more rapidly the returns to investment diminish.

In our economic growth chapters, we were looking at changes over time. In this chapter we are looking at the economy at one instant, and we will be comparing alternative and counterfactual scenarios—not over time, as it grows.

### 6.1.2 The Labor Market¶

When markets work well, what keeps the economy at full employment and actual production equal to potential output? One way to look at this issue is that the answer lies in the adjustment of prices and supply and demand in the labor market. When the supply of and demand for labor balance, real GDP will equal potential output.

#### 6.1.2.1 Labor Demand¶

Economists try to suppress every detail and difference that does not matter for the overall result in order to simplify the analysis and focus it on the important factors—the ones that really count. Because differences between businesses will not matter, let uss think about an economy with K typical—identical—representative firms, each of which owns 1 unit of the economy’s capital stock.

Each of these firms hires a number of workers—let’s call the number of workers each firm hires $L_{firm}$. Each of these firm in the economy pays each worker the same nominal wage W. Each firm sells $Y_{firm}$ units of its product at a per-unit price P. The typical firm does not control either the wages it must pay or the prices it receives; those are determined by the market, and each firm takes the wages and prices it is offered. And each firm tries to make as much profit as it can.

Thus we have a very simple and standard supply-and-demand model of a typical firm. The firm’s profits are simply its revenues minus its costs, and its only costs are the wages it pays to workers:

$Profits = Revenues - Costs = PY_{firm} - WL_{firm}$

To figure out how many workers to hire in order to maximize its profits, the firm must:

1. Hire workers in order to boost output.
2. Stop hiring workers when the extra revenue from selling the output produced by the last worker hired just equals the value of the last worker’s wage.

The value of the output produced by the last worker hired is the product’s price times what economists call the marginal product of labor (MPL). What is the marginal product of labor? The marginal product of labor is the difference for some time period between what the firm can produce with its current labor force $L_{firm}$ and what it would produce if it hired one more worker, as the shows for the benefit of those of you who prefer graphs to sentences with subclauses.

Firm Output as a Function of Firm Employment: Holding the capital stock of the typical firm constant, each extra worker the firm employs produces smaller and smaller increases in total output. As the level of employment increases, this marginal product of labor (MPL) decreases.

Since a typical firm owns 1 unit of capital, its output is what can be produced using that single unit of capital and the firm’s workers, according to the production function:

$Y_{firm} = F\left(1, L_{firm}, E\right)$

And so the marginal product of labor (MPL) is:

$MPL = \frac{dY_{firm}}{dL_{firm}}$

The MPL for the representative firm with a Cobb-Douglas production function, where K = 1, is just the derivative with regard to labor L of the production function:

$MPL = \frac{(1-\alpha)E^{1-\alpha}}{{L_{firm}}^{\alpha}}$

There is nothing deep in this math. Indeed, the Cobb-Douglas function was tweaked so that it would yield such simple forms for quantities like the MPL. That is why economists use it so often.

Now that we know the MPL, determining how many workers this representative firm will hire is straightforward. It will keep hiring workers as long as doing so remains profitable. As the figure below shows, the firm hires workers up to the point where the product of the price it sells its goods for and the marginal product of labor has fallen so that it equals the wage:

$P(MPL) - W = 0$

For the Cobb-Douglas production function, this profit-maximizing level of labor demand for the firm is

${L_{firm}}^{*} = \left[{(1-\alpha)E^{1-\alpha}}\left(\frac{P}{W}\right)\right]^\left(\frac{1}{\alpha}\right)$

The Typical Firm's Hiring Policy: The typical firm chooses to hire the number of workers that make marginal revenue product—the MPL times the product price P—equal to the wage W. At that point the revenue and cost curves are parallel, and profit is maximized.

Since there are K firms in the economy—one for each unit of capital—this gives us an economywide demand for labor by firms equal to:

$L^d = K{L_{firm}}^* = K\left[{(1-\alpha)E^{1-\alpha}}\left(\frac{P}{W}\right)\right]^\left(\frac{1}{\alpha}\right)$

##### 6.1.2.1.1 Calculating Firm Labor Demand: An Example¶

For example, suppose that we have a specific Cobb-Douglas production function—suppose that for the typical firm with one unti of capital the value of labor efficiency E equals 1, the parameter $\alpha$ equals 1/2, and so the production function is:

$Y_{firm} = \left(K_{firm}\right)^{(1/2)}\left(L_{firm} x 1\right)^{(1/2)} = \left(1\right)^{(1/2)}\left(L_{firm} x 1\right)^{(1/2)} = \sqrt{L_{firm}}$

The annual output of the firm is equal to the square root of the firm’s labor force.

Suppose further that the wage the firm pays each of its workers is 25,000 dollars a year, that output is measured in millions of gallons, and that each gallon of output sells for 1 dollar.

Let’s think about how many workers the firm should hire. Raising employment from 0 to 1 increases production from 0 to 1 million gallons per year, and raises the firm’s total sales by 1,000,000 dollars. Since the first worker has to be paid only 25,000 dollars, this looks like a very good deal.

Raising employment from 100 to 101 would increase output from 10 million gallons to 10.049876 million gallons (that’s the square root of 101). That amounts to an extra 49,876 dollars in annual revenue at an extra wage cost of 25,000 dollars. This still looks like a very good deal.

How about raising employment from 400 to 401?

That raises output from 20 million-gallon-units to 20.024984 million-gallon-units. That’s an extra 24,984 dollars in extra revenue, but at an extra wage cost of 25,000 dollars.

The 401st worker lowers profits.

So at 400 workers it is time to stop.

Should the firm have stopped hiring workers earlier?

Suppose that you cut employment from 400 to 399. You save 25,000 dollars a year in reduced wage costs. But you also cut your output from 20 million gallons to 19.974984 units: 20 minus 19.974984 = 0.025016. So you lose 25,016 dollars in revenue. The 400th worker earns his or her keep.The firm should not cut employment below 400.

### 6.1.2.2 Labor Market Equilibrium¶

Economywide labor demand is only half of the labor market. To understand what is going on in the labor market we also need to know what is going on with the labor supply. The answer is simple: The labor supply is the number of workers who want to work. The labor market will be in equilibrium when firms’ total demand for workers is equal to the economy’s labor force L.

Can the labor market be out of equilibrium if wages and prices are flexible? No. Think about what happens when wages and prices are flexible if labor supply is not equal to demand. Suppose there are more workers who want to work than the number of workers that firms want to hire at current wages and prices. Some of the workers will find themselves unemployed. Then some of the unemployed will underbid the employed workers, offering to take their jobs and work for less. The workers who are employed will respond by offering to accept lower wages to keep their jobs.

The wage W will thus decline relative to the price level P, and so the real wage W/P will fall. Unless the firm changes its labor demand, the marginal product of the last worker hired will now exceed the real wage. To maximize profit, the firm should change its labor demand until the MPL falls to the point where it equals the new lower real wage. The firm knows that the marginal product of the last worker hired will fall as it hires more workers—something we economists call diminishing returns. So as this real wage falls, firms wishing to profit maximize will hire more workers.

Suppose, on the other hand, that firms want to hire more workers than there are people in the labor force. Some firms will try to bid workers away from other firms by offering higher wages. The real wage W/P will rise. As the real wage rises, other employers will reduce the quantity of labor they demand. Thus in labor market equilibrium, total economy-wide labor demand $L^d$ will equal the labor force L:

$L = L^d = K{L_{firm}}^* = K\left[{(1-\alpha)E^{1-\alpha}}\left(\frac{P}{W}\right)\right]^\left(\frac{1}{\alpha}\right)$

We can rearrange this equation and solve for the equilibrium real wage W/P. Because we already know from Chapter 4 that $\left(E^{(1-\alpha)}\right)(K/L)^{\alpha}$ is equal to output per worker Y/L,we see that labor demand is equal to the labor force when the real wage W/P is:

$\frac{W}{P} = \left[(1-\alpha)E^{(1-\alpha)}\right]\left(\frac{K}{L}\right)^\alpha = (1-\alpha)\left(\frac{Y}{L}\right)$

As long as wages and prices are flexible enough for this adjustment process to work and for the real wage to converge to this, its equilibrium level, the economy will be at and will remain at full employment. (Note that this full-employment economy is not necessarily the best or even a good economy. The real incomes of people who don’t own chunks of the capital stock are their real wages: $W/P = (1 — \alpha)(Y/L)$. If $\alpha$ is large, their real incomes will be small, and social welfare may be low.)

Equilibrium in the Labor Market: The equilibrium level of employment is equal to the labor force. At the equilibrium level of the real wage, there is neither excess demand for nor excess supply of labor.

The conclusion is clear: If markets work well—if wages and prices are flexible and adjust to balance supply and demand, and if markets are competitive so that firms take wages and prices as given rather than controlling them—then we can expect the labor market to be at full employment, and the actual level of production in the economy Y to be equal to the economy’s potential output Y*.

In a Full-Employment Economy, Real GDP Equals Potential Output: When the economy is at full employment, the level of employment is equal to the labor force and real GDP is equal to potential output.

As long as we are looking at a short enough interval of time that the labor force, the capital stock, and the efficiency of labor do not change, in the flexible-price model the answer to a great many questions is simple and straightforward. If somebody asks you what is the effect on real GDP of a change in government spending or an increase in interest rates overseas or of a stock mar­ ket boom or pretty much anything else, the answer will always be the same: Real GDP doesn’t change, because the economy’s output is equal to its productive potential. In the flexible-price model the questions that have more complicated answers are those that relate to the division of real GDP among its various main components: consumption, investment, government spending, and net exports.

### 6.1.3 RECAP: Potential Output and Real Wages¶

A flexible-price, economy is a full-employment economy: Wages are flexible enough to keep supply and demand in balance in the labor market. Because there areenough jobs io%all the workers who want to work at the prevailing market-clekring wage, real GDP in a flexible-price economy is always equal to potential Output and unemployment is not a problem.

This classical model of the macroeconomy is the polar opposite of the sticky-price Keynesian model, where prices and wages are sticky, markets do not always clear with supply and demand in balance, high unemployment is possible, and there are gaps between real GDP and potential output.

## 6.2 Spending on Domestic Production¶

In Chapters 2 and 3 we saw, through the national income identity, that total spending on—aggregate demand for—domestically-produced goods and services can be divided into four components:

• Consumption spending C
• Investment spending I
• Government purchases G
• Net exports NX—which are equal to gross exports GX, foreigners' purchases of domestically-produced goods and services, minus imports IM as a balancing item to take account of those elements of consumption, investment, and government purchases that are spent on goods produced abroad.

Every dollar spent on final goods and services, whether spent by households on their own consumption (C), spent by businesses in maintaining or expanding their capital stock (I), purchased by the government (G), or purchased by foreigners (GX), flows to firms as revenue—except for that part of the spending flows C, I, and G that is spent buying imported goods IM. So total net receipts by business firms—canceling out payments that one firm makes to another—are equal to the four components of total spending or aggregate demand C + I + G + NX.

Moreover, every dollar that firms receive is counted as somebody’s income, whether paid out to workers or retained to become the property of the firm’s owners or shareholders. So national income is also equal to total spending or aggregate demand C + I + G + NX. And, in addition, the circular flow principle tells us that total spending and national income are essentially the same thing as real GDP: the value of income is the same as the value of what is produced, and the same as the value of what is sold and purchased. National income, national product, and aggregate demand are, save for small accounting details, essentially the same.

In this section of Chapter 6 we look at the determinants of the three domestic components of spending: C, I, and G. International trade and net exports will be deferred until the next section.

Note that the rest of this chapter offers no big payoff, no single lesson to be learned at the end. The big lesson comes at the end of Chapter 7. The rest of this chapter simply sets out the factors that determine the components of spending; it does not show how all the pieces fit together.

### 6.2.1 Consumption Spending¶

The spending and saving decisions that determine the magnitude of the flow of consumption spending are made by households, so this subsection lays out how households make their big decisions. The decisions we focus on are those that determine how households divide their income up among taxes, saving, and consumption spending.

#### 6.2.1.1 Household Decisions¶

The circular flow principle tells us that the wages of workers plus the profits of property owners (rent, interest, dividends, and retained earnings) add up to national income, which is—because at this level of analysis we are uninterested in picky accounting distinctions—essentially the same as real GDP. So for simplicity let’s use the symbol Y for both national income and total output.

Households pay some of their income to the government in net taxes—taxes less transfer payments from the government—which we write as T. To keep the analysis simple, throughout this book we will assume that net taxes are equal to the constant average tax rate t multiplied by national income Y:

$T = tY$

In the real world, taxes are not proportional to income. Our tax system is somewhat progressive, which means that richer taxpayers on average pay more of their income in taxes than do the relatively poor. Once again, however, the complications introduced by the fact that our tax system is not proportional to income are not central to the analysis, so we follow economists’ standard practice of simplifying wherever possible.

The amount left after households pay their net taxes is their disposable income, written $Y^D$:

$Y^D = Y - T = (1 - t)Y$

Households also save some of their income to boost their wealth and future spending. We represent private household saving by $S^p$ S for “saving” and p for “private.” (Note that household saving includes the retained earnings of corporations: The NIPA treats undistributed corporate earnings that are retained by the corporation as if they were distributed to the shareholding households and then immediately reinvested back into the corporation.) Households spend the rest of their income—everything that is not saved or paid to the government—on consumption goods:

$C = Y^D - S^p = Y - T - S^p$

From National Income to Consumption Spending To get disposable income, subtract taxes from and add transfers to national income. To get consumption spending, subtract household saving (including the retained earnings of businesses) from disposable income.

In the United States today, consumption spending—purchases by households for their own use, from pine nuts and flour to washing machines and automobiles, from Big Macs and haircuts to rent and financial consulting—accounts for roughly two-thirds of GDP.

We will break consumption spending down into a baseline level of consumption, labeled the parameter $c_o$—think of this as "consumer confidence"—and into a fraction, labeled the parameter $c_y$—think of this as the margintal propensity to consume—of disposable income $Y^D$; or a fraction $c_y(l —t)$ of total income Y:

$C = c_o + c_yY^D = c_o + c_y(1- t)Y$

The parameter $c_y$ tells us the change in consumption spending when disposable income changes by one dollar:

$c_y = \frac{ dC}{dY^D}$

Thus we assume that consumption spending C is a simple linear function of real GDP Y: If we plot consumption on the vertical axis and real GDP on the horizontal axis of a graph, the consumption function will be a straight line.

The Consumption Function: Consumption spending depends on the level of disposable income and two parameters: Cy (the marginal propensity to consume, or MPC) and Co (the baseline level of consumption). If we know both these parameters and the value of disposable income Y°, we can plot the level of consumption spending at each possible level of disposable income.

Notice that in writing this particular consumption function, we again follow the economists’ principle (or vice) of ruthless simplification. In our more complicated world, consumption spending does not depend on disposable income alone. Many other factors affect consumption, including changes in the real interest rate, household total stock market and real estate wealth, the demographic structure of the population, income distribution, consumers’ relative optimism, expected future income growth, tolerance for risk, and whether consumers see changes in disposable income as transitory or permanent. (If consumers expect an income increase to be transitory, they will save most of it and spend only a little; if they expect an income increase to be permanent, they will spend most of it.)

_Other Determinants of Consumption Spending: Other factors besides taxes and saving affect consumption spending. Each of these factors can change baseline consumption $c_o$._

But here and throughout the book we will sweep these complications under the rug. We will think only about baseline consumption $c_o$, the marginal propensity to consume $C_Y$, and disposable income YD as the determinants of consumption spending and allow all these other factors in by saying that they change baseline consumption$c_o$.

#### 6.2.1.2 The Marginal Propensity to Consume¶

The marginal propensity to consume (MPC), the parameter $c_y$ in the consumption function, is the amount by which consumption spending rises in response to a one dollar increase in disposable income. We are sure that $c_y$ is greater than zero: If disposable incomes rise, households will use some of their extra income to boost their consumption spending. We are also sure that $c_y$ is less than one: As disposable incomes rise, households will increase their saving as well; they will not spend all their extra disposable income on consumption goods.

The value of the marginal propensity to consume also depends on how long people expect the change in disposable income $Y^D$ to last. If people expect the change in disposable income to be permanent, then the MPC is likely to be relatively large and the change will have a large effect on the value of $C$. If they expect the change in disposable income to be transitory—and think their disposable income next year will revert back to its normal pattern—the MPC is likely to be relatively small.

The value of the marginal propensity to consume also depends on to whom the change in disposable income accrues. A shift in the economy-wide total disposable income $Y^D$ will have a large effect on consumption spending $C$ if the extra income reaches the pockets of relatively poor people living paycheck-to-paycheck. It will have little effect on consumption spending for those with ample cushions of wealth.

#### 6.2.1.3 Baseline Consumption¶

Although sometimes we say the baseline level of consumption, the consumer confidence parameter $c_o$, is the amount households would spend on consumption goods if they had no income at all, that’s somewhat misleading. Such a definition invites you to (incorrectly!) think of the consumption function as some sort of individual consumption function for an individual household. But it’s not. The consumption function tells us, for the economy as a whole, how consumption varies with changes in real GDP and total national income.

Since we draw the consumption function as a linear function—a straight line on an income-spending graph—the parameter $c_o$ does tell us where the aggregate consumption function hits the vertical axis. But would this economy truly consume Cq if the entire economy produced not one single good or service and its real GDP was zero? No one knows. And because knowing requires observing a completely devastated economy, we hope no one ever will!

#### 6.2.1.4 Calculating Consumption Spending C: An Example¶

With these two parameters, $c_o$ and $c_y$, we can calculate what the total level of consumption spending would be for each possible level of disposable income $Y^D$.

Suppose the tax rate t is 25 percent, total national income Y is 20 trillion dollars, the baseline level of consumption $c_o$ is 2 trillion dollars, and the marginal propensity to consume $c_y$ is 0.6.

We first calculate disposable income: how much households have left after paying their taxes. Disposable income is equal to (1 —t)Y, which for these parameter values and this level of national income is, in trillions of dollars:

$Y^D = (1-t)Y = (1 - 0.25)(10) = 7.5$

We can then calculate consumption spending:

$C = c_o + c_yY^D = 2 + (0.6)(7.5) = 6.5$

What would happen if disposable income were to rise from 7.5 trillion to 8 trillion dollars? Consumption spending would then rise from 6.5 trillion to 6.8 trillion dollars—the change ${\Delta}C$ in consumption spending of 0.3 trillion would equal to the marginal propensity to consume $c_y$, 0.6, times the change ${\Delta}Y$ in disposable income, 0.5 trillion.

### 6.2.2 Investment Spending¶

In the United States. today investment spending averages only about 15 percent of GDP. But investment spending is the most volatile and variable component of GDP. When economists use the term “investment,” they mean something different from what most people mean by the word. Most people use it to mean activity such as buying a stock or bond, a certificate of deposit, or commodity futures. But such purchases do not directly increase the economy’s capital stock or have any place in the national income and product accounts.

When economists use the term “investment” or “investment spending,” they are talking about transactions that replace depreciated machinery and equipment, or add to the capital stock and increase potential output. Such transactions include the purchase and installation of new business machinery and equipment, the construction and purchase of new buildings or residential structures (or the repair of old ones), and a change in business inventories. Box 6.3 highlights two different ways economists break down total investment spending.

#### 6.2.2.1 Kinds of Investment Spending: Some Details¶

Economists categorize investment in two different ways. The first distinction they draw is between gross investment and net investment. Gross investment is the total sum of spending on machines, construction (houses, factories, office buildings, privately owned roads, dams, and bridges), and additions to inventories.

Some of gross investment adds to the capital stock of machines, goods in process, buildings, and other structures. The rest of gross investment replaces worn-out and obsolete pieces of capital. The amount of gross investment spending that increases the capital stock is called net investment. The amount of investment spending that replaces obsolete and worn-out capital is called depreciation or capital consumption.

Economists also categorize investment according to use, as follows:

1. Residential construction
2. Nonresidential construction
3. Equipment investment
4. Inventory investment

To some degree, these four subcategories of investment have different determinants and different consequences. But in order to simplify and construct a useful model, we ignore those differences.

#### 6.2.2.2 Why Firms Invest¶

Fluctuations in economywide investment spending have two sources.

First is the interest rate: The higher the real interest rate, the lower is investment spending. A higher real interest rate makes investment projects more expensive for firms to undertake, so they undertake fewer of them.

Second is business managers’ and investors’ confidence—what John Maynard Keynes called their "animal spirits". The higher their confidence, the higher is investment spending. Optimistic managers and investors are more willing than pessimistic ones to bet their careers and fortunes on the belief that an expansion of productive capacity or some other investment will pay off.

Interest Rates: A business invests because its managers believe that the investment project will be profitable. One way managers decide if a project is profitable is by comparing the appropriately discounted return on the investment with the investment’s cost. Their rule: Undertake the investment project only if the return is at least as great as the investment’s cost. The higher the interest rate, the lower is the appropriately discounted return on the investment project. And so the higher the interest rate, the smaller is the number of potential investment projects that will be profitable. Thus a higher interest rate leads to lower investment spending.

Why does the discounted return fall when interest rates rise? The answer uses the economists’ concept of present value—the amount of wealth that you would have to set aside today and put into financial assets earning the real interest rate to generate some particular amount of purchasing power in the future. If the real interest rate is 5 percent per year, to have 130 million of inflation-adjusted purchasing power in five years you would have to take 101.85 million dollars today, put it aside, and let it compound in the bond market: $101.85 x (1.05)^5 = 130$. Thus the present value of $130 million in five years at an interest rate of 5 percent is 101.85 million. To calculate the present value PV of a sum of inflation-adjusted purchasing power SUM to be received n years in the future at an interest rate of r percent per year, you discount the future sum back to the present at the rate r using the formula:$ PV = \frac{SUM}{(1+r)^n} $because PV invested in the bond market at an interest rate of r for n years will compound to SUM. (If whether or not the SUM will actually be paid in the future is subject to more than the usual amount of risk found in the bond market, the present value will be lower: You can either risk-adjust the SUM to a lower value or risk-adjust the discount rate r by adding a risk premium$ \rho $and discounting at$ R + \rho $) At a real interest rate of 6 percent, the present value of 130 million received in five years is$ 130/(1.06^5) = 97.14 $million. When we used an interest rate of 6 percent rather than 5 percent, the present value of 130 million received in five years fell from 101.85 million to 97.14 million. What’s true in our example is true in general: The higher the real interest rate, the lower the discounted value—the present value—of an investment project that will generate revenue in the future. With present value, the decisions of business managers become easier. One investment project will be a better use of resources than another only if the first has a higher present value than the second. Most investment projects don’t yield returns in the shape of a single, lump-sum payment n years into the future. Most yield a stream of profits each year for a prolonged period. Thus more useful than the formula for the present value of a SUM n years in the future is the STREAM formula for the present value of a stream of payments each year from now into the indefinite future:$ PV = \frac{STREAM}{r} $Think of how much a flow of real purchasing power of 1 million per year each year into the indefinite future is worth. If you wanted to receive such an annual flow, how much would you have to put into the bond market today? l/r million invested in the bond market yields an annual flow of real purchasing power of 1 million per year. Thus an investment project that you expect to yield a cash flow of STREAM in real purchasing power per year each year has a present value of STREAM/r. You can see from these financial formulas how important the real interest rate is for determining whether investments are worthwhile or not. If an investment project promises a long-running stream of returns—as in the example above—a small change in the real interest rate can have an enormous impact on present value. How many investment projects will a higher interest rate discourage? How much lower will investment be if the interest rate is higher? The answer is captured by a parameter we call “investment’s response to a change in the interest rate”:$ I_r $. The greater is$ I_r $, the greater is the change in investment spending in response to a change in the real interest rate. The interest rate most relevant to determining investment is the long-term, real, risky interest rate. The relevant interest rate is long-term because investment projects affect the business’s profits and costs for a long time to come. The relevant interest rate is real—that is, inflation-adjusted—because an investment project gives the business that undertakes it a real, physical asset, not a financial claim denominated in dollars. The relevant interest rate is risky because investment proj­ects are risky. In calculating whether investment projects are worthwhile, be sure to compare apples to apples. Discount the long-term, real, risky profits anticipated from undertaking an investment project by the long-term, real, risky interest rate. Animal Spirits: A number of factors other than changes in interest rates can affect investment spending; we capture all these other factors in what Keynes called “animal spirits.” When businesspeople’s optimism soars, their expected return from an investment project soars too. More projects become profitable at every interest rate. Investment spending rises. When businesspeople’s perception of risk increases — when their certainty about the future return on an investment project becomes, well, less certain — then they tend to become more cautious in committing large quantities of money to a long-term investment project. At every interest rate, investment spending falls. #### 6.2.2.3 The Investment Function¶ To model the inverse relationship between the level of investment spending and the long-term, real, risky interest rate, set investment spending I equal to the baseline level of investment parameter—the "animal spirits" parameter—$ I_O $minus the real interest rate r times the slope of the investment function, the parameter$ I_r $:$ I = I_o - I_rr $_The Investment Function: Investment spending increases as the real interest rate decreases. The parameter$ I_r $is how much investment spending changes in reponse to a one-unit shift in the real interest rate. Changes in baseline investment spending—in "animal spirits'—shift the investment function up or down on the interest rate-investment spending diagram._ ##### 6.2.2.3.1 How Investment Responds to a Change in Interest Rates: An Example¶ From the parameters$ I_o $(the baseline "animal spirits" level of investment) and$ I_r $(the responsiveness of investment to a change in real interest rates) we can calculate the level of investment spending for each possible value of the real interest rate r. For example, suppose that$ I_o $is 2 trillion and that$ I_r $is 20. Then we can use the equation:$ I = I_o - I_rr $to calculate that if the real interest rate were to be 5 percent (r = 0.05), then the level of investment spending would be 1 trillion:$ I = I_o - I_rr = 2 - (20)(.05) = 1

And if the real interest rate were to be 0 percent, the level of investment spending would be 2 trillion:

$I = I_o - I_rr = 2 - (20)(0) = 2 ##### 6.2.2.3.2 Investment and the Stock Market: Some Details¶ An alternative way of thinking about the investment function focuses on the stock market, not on interest rates. Think about what determines stock market values. Most investors in the stock market face a choice between holding stocks—shares of ownership of a corporation that also give you ownership of that corpo­ ration’s profits or earnings—or holding bonds: pieces of paper that represent loans that pay interest. If you hold your wealth in bonds, you earn the real interest rate r. If you buy shares of stock, your return is equal to your share of the profits of the companies whose stock you own. When expected future profits are high, investors find stocks more attractive than bonds and thus bid up stock prices. When the real interest rate falls, investors also find stocks more attractive than bonds and bid up stock prices. In either case, the stock market will rise. However, when expected future profits are high, businesses invest more. When the real interest rate falls, businesses find investment projects cheaper and also invest more. The same things that determine the value of the stock market also determine the level of investment spending. The stock market and investment move together: What raises or lowers one raises or lowers the other. The only significant difference is that causes of fluctuations in investment affect the stock market first and investment spending second. The stock market is thus a very useful leading indicator of investment spending. Keep a close watch on the stock market if you want to forecast the level of investment spending. Notice the regular pattern used for parameters so far:$ c_o, c_y, I_o, I_r $. This regular pattern is an attempt to make the names of parameters used in our algebraic equations clearer and easier to remember. In general, the first letter in the name of each parameter tells you what variable is on the left-hand side of the equation in which the parameter appears. A "c" means that the parameter is part of an equation determining the level of consumption spending C; an "I" means it is part of an equation determining the level of investment spending I (why not a lower case "i"? because we reserve lower-case "i" to stand for the short-term safe nominal interest that the Federal Reserve conttrols); and so forth. The subscripted letter tells what variable by which the parameter is multiplied in that equation. For example,$ I_r $is the effect on investment spending I (that goes on the left-hand side of the equation) of the real interest rate r. Thus the parameter$ I_r $multiplies the variable r—the real interest rate—in the equation with the variable I—investment spending—on its left-hand side. Like the consumption function, the investment function is an enormous simplification of real-world investment patterns. In the real world, firms’ investment decisions depend not only on the real interest rate but also on how much money the firms have available. Total profits are also an important determinant of investment. In the real world, some components of investment—construction, for example—are very sensitive to changes in the real interest rate. Other components of investment—for example, inventory investment by small firms with little access to outside sources of funding—are not. #### 6.2.2.3.3 Boosting Investment: Policy Issues¶ As we saw in Chapters 4 and 5, a high level of saving and investment is one of the keys to a prosperous economy. The higher the share of GDP devoted to investment spending, the higher is the equilibrium capital-output ratio and the richer is the economy. Governments seeking to boost investment have two major tools at their disposal. First, they can induce the central bank to lower real interest rates. If real interest rates are lowered, more investment projects will be undertaken and investment spending will rise. Second, governments can try to raise the baseline level of investment by encouraging private decision makers. They can exhort and reassure them—although the tactic sometimes backfires, as in President Herbert Hoover’s repeated declaration during the Great Depression that “prosperity is just around the comer.” More important, policy makers can try to reduce or eliminate sources of risk. Instilling confidence that the economy will be stable and risks will be managed is perhaps the best way to boost investment by encouraging optimism. ### 6.2.3 Government Purchases¶ The federal government buys the labor of government employees— judges, air traffic controllers, customs inspectors, FBI agents, National Oceanic and Atmospheric Administration researchers, and others—as well as military hardware, sections of the interstate highway system, and other goods and services. All these expenditures plus those of state and local governments make up the government purchases component of GDP. Such government purchases of goods and services add up to about 20 percent of GDP. Note that government spending is larger than government purchases. In addition to buying goods and services (including the work time of its employees), the government also spends by transferring money to citizens through Social Security and other programs, disability benefits, food stamps, and other transfer payments. Because transfer payments do not themselves represent demand for final goods and services, they do not show up directly as a portion of GDP in government pur­ chases G. Rather, transfer payments show up in the NIPA as negative taxes. The variable T represents net taxes, taxes less transfer payments. It is the net amount by which the government’s tax and transfer system reduces disposable income. As noted previously, in this book we assume net taxes T, taxes less transfers, are equal to the average tax rate t times income Y:$ T = tY $We do not inquire into what determines either government purchases G or the average tax rate t. We leave that for the political scientists. We will look at what happens when government spending G or the tax rate t changes. ### 6.2 RECAP: Domestic Spending¶ Consumption spending C depends on four factors: the baseline level of consumption$ c_o $, the marginal propensity to consume (MPC)$ c_y $, the tax rate t, and the level of real GDP (or national income) Y:$ C= c_o + c_y(l- t)Y $Investment spending t depends on three things: the baseline "animal spirits" level of investment$ I_o $, the interest sensitivity of investment$ I_r $, and the long-term risky real interest rate r:$ I = I_o - I_rr $We leave the determinants of government purchases G to the political scientists. ## 6.3 International Trade and Finance¶ The final thing we add to get aggregate demand—which is equal to national product, GDP, and to national income—is net exports NX. Net exports are the difference between gross exports GS and imports IM. Gross exports are made up of goods and services that are produced in the home country and then sold abroad. GDP is a measure of production, and since gross exports are part of production, they need to be counted in GDP. But first imports need to be subtracted from GDP, since it is a measure of domestic production. Not all the goods and services that make up consumption, investment, and government purchases are produced domestically. Consumption, for instance, includes spending on Chinese toys, Irish computers, Brazilian coffee, and Scottish tweeds as well as on domestically made goods. Investment includes spending on British airplanes and Italian machinery. Federal, state, and local government purchases include German buses and Japan­ ese subway cars. So adding up C, I, and G overestimates domestic demand for U.S.-made products. By adding net rather than gross exports to C + I + G, economists (1) take account of goods made domestically that are sold to foreigners and don’t show up in C + I + G and (2) correct C + I + G for the amount of foreign-made goods it counts. ### 6.3.1 Gross Exports¶ The volume of gross exports from the United States depends on two variables. The first is the real GDP of our trading partners—call it$ Y^f $, "Y" because it is a measure of total production, but the superscript "f" to remind us that it is foreign production. The second is the real exchange rate—how much foreign goods cost relative to domestic goods, which is the same thing as the value of foreign currency adjusted for inflation: call it$ \epsilon $. The higher the value of the real exchange rate—the more valuable and expensive the foreign currency is—the cheaper do U.S.-made goods appear to be to foreigners, and so the more of our gross exports GX they buy. <img style="display:block; margin-left:auto; margin-right:auto;" src="https://delong.typepad.com/.a/6a00e551f080038834022ad39d8a4f200d-pi" alt="DeLong Olney 2nd ed chs 6 8 pdf page 23 of 94" title="DeLong-Olney-2nd-ed-chs-6-8_pdf__page_23_of94.png" border="0" width="600 /> Gross Exports and the Real Exchange Rate: Gross exports of goods and services to the rest of the world increase as the real exchange rate increases. How much gross exports GX change in response to a one-unit change in the real exchange rate is measured by the parameter$ x\epsilon $._ Thus our function for gross exports GX will be:$ GX = xfY^f + x{\epsilon}{\epsilon}

Here, just as in the investment and consumption equations, $x_{\epsilon}$ and $x_f$ are parameters that define the properties of the gross exports function for the particular economy we are studying—parametrise how foreign national income and the value of the real exchange rate determine gross exports. $x_f$ is the increase in exports generated by a one-unit increase in foreign incomes. $x_\epsilon$ measures the increase in exports produced by a one-unit increase in the real exchange rate $\epsilon$.

#### 6.3.1.1 The J-Curve: Some Details¶

In the real world, the relationship between the real exchange rate and exports is not as simple. Many determinants of gross exports are suppressed in order to keep the model simple. Moreover, the process entails substantial lags. A change in the real exchange rate has little or no effect on gross exports this year but will have effects on gross exports one, two, and three years into the future. But as we move forward we again follow the economist’s pattern of simplifying whenever doing so doesn’t alter our essential story, and simply assume gross exports GX respond to changes in foreign income and the real exchange rate $\epsilon$.

Nevertheless, trade links across countries take time to create, time to modify, and time to destroy. So while an increase of the U.S. real exchange rate causes an increase in foreign purchases of U.S. goods, a year or more will pass before we see the change in the volume of trade. In the short run, a rise in the real exchange rate—an increase in the purchasing power of foreign currency—may generate a fall, not a rise, in exports.

Economists call this the J curve, because the plot of exports over time after a rise in the exchange rate looks a little like a “J.” The real exchange rate began to rise very steeply in 1986, butreal exports in 1986 were flat. It was not until 1987 and 1988 that the increased competitiveness of U.S. exporters led to an export boom.

The J Curve in the 1980s: During the 1980s the U.S. real exchange rate, the purchas­ ing power of foreign currency, fell from 20 percent above its 1973 level to 25 percent below its 1973 level and then reversed itself. As the real exchange rate fell, U.S.-made goods became more expensive to foreigners, and exports fell. As the real exchange rate rose in the late 1980s, U.S.-made goods became cheaper to foreign purchasers, and exports ultimately rose but changes in export volumes lagged behind changes in the real exchange rate by more than a year.

### 6.3.2 Imports and Net Exports¶

The value of demand for imports—for products produced abroad — depends on domestic national income: The higher national income, the more money consumers and businesses and government agencies spend on imported goods and services. The higher, that is, the value of imports IM will be.

The quantity of imports demanded depends as well on the real exchange rate $\epsilon$. The higher the real exchange rate—the higher the purchasing power of foreign currency—the more expensive are foreign-made goods and the fewer of them do domestic consumers and investors buy. However, we are interested not in the quantity but in the U.S. made good-equivalent value of imports. When the quantity of imports falls as the real exchange rate rises, the real dollar and the real U.S. good-equivalent value of each import rises. Thus total imports remain about the same: The value of imports IM is largely independent of the real exchange rate.

Therefore, we simplify. we model gross imports IM as a constant share—a share measured by the propensity to import $im_y$— of national income Y:

$IM = im_yY$

Net exports NX are the difference between gross exports and imports. Thus they depend on the real exchange rate e; on real GDP abroad Y^; and on real GDP here at home Y:

$NX = GX - IM = x_fY^f + x_{\epsilon}{epsilon} - im_yY$

### 6.3.3 The Exchange Rate¶

We have seen that the real exchange rate is an important determinant of net exports. And in Chapter 2 we had the definition of the real exchange rate $\epsilon$ in terms of the nominal exchange rate e—the rate at which currencies exchange for one another at the bank or at the airport money machine—and the price levels at home and abroad P and $P^f$:

$\epsilon = e\frac{P^f}{P}$

The real exchange rate is the product of the nominal exchange rate and the price ratio between the foreign and domestic economies. But what determines the nominal and real exchange rates? What is the behavioral story?

Greed and Fear in Foreign Exchange Markets

Consider foreign exchange speculators whose job is to trade currencies and make money. They spend their days glued to computer terminals, watching the prices of bonds denominated in different currencies flash across the screen. They buy and sell bonds and stocks of different countries and governments denominated in different currencies—dollars, euros, pounds, yen, pesos, ringgit, and more than 100 others. Their lives are ruled by greed and fear:

• Greed: Suppose a trader sees higher interest rates paid on the dollar-denominated bonds of U.S. companies than on the euro-denominated bonds of German companies. In this case, there is money to be made by selling (“going short on”) German companies’ bonds, buying (“going long on”) U.S. companies’ bonds, and pocketing the extra interest.

• Fear: Suppose that the trader is long on dollar-denominated bonds (owns many of them) and short on euro-denominated bonds (owns few of them) and the U.S. exchange rate then rises. At a higher real exchange rate, each dollar will be worth fewer euros; whatever profits were expected from the interest rate spread are wiped out by the loss caused by the exchange rate movement. So if today’s value of the exchange rate is below long-run historical trends, the fear that exchange rates will soon rise to their normal relationships and impose large foreign exchange losses will be immense. Traders will shy away from dollar- denominated bonds if they fear an imminent depreciation of the dollar.

The greater the difference in interest rates in favor of dollar-denominated securities, the higher is the greed factor. Foreign exchange traders demand more dollar-denominated assets and demand fewer assets denominated in other currencies. They thus need less foreign currency and so they decrease their demand for foreign currency. By the laws of supply and demand, this lowers the price of for­ eign currency which is the nominal exchange rate e, which makes the real exchange rate s drop also. So when the gap between domestic and foreign real interest rates increases, the greed factor leads to a lower real exchange rate.

But at this lower real exchange rate, fear is heightened. Foreign exchange traders worry that a future exchange rate movement might wipe out their gains. So not all traders rush to fill their portfolios with dollar-denominated assets, despite the more favorable domestic interest rates. The enormously liquid, enormously high- volume, enormously volatile foreign exchange markets settle at the point where greed and fear balance. Thus we say the real exchange rate e is equal to the average foreign exchange trader’s opinion $\epsilon_o$ of where the exchange rate ought to settle and would settle if there were no interest rate differentials, minus a parameter $\epsilon_r$ times the interest rate differential between foreign and domestic real interest rates $r^f$ and $r$:

$\epsilon = \epsilon_o + \epsilon_r(r^f - r)$

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 s r will be and the larger will be the effect of a given interest rate differential on the exchange rate.

Remember: The exchange rate is the value of foreign currency and goods. If foreign currency becomes more valuable, the exchange rate rises; if domestic 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 $\epsilon$.

A depreciation or devaluation of the dollar is a rise in the value of the exchange rate $\epsilon$.

You may have trouble remembering this—most economists do. Why? Because "de" is an English prefix borrowed from the Latin whose original meaning is to become lower or subservient. Remember: when the home currency—for most of you, that is the dollar—gets more valuable, the value of the exchange rate is falling. **The exchange rate is the value of foreign currency and goods.

Our equations for net exports:

$NX = GX - IM = x_fY^f + x_{\epsilon}{epsilon} - im_yY$

and for the exchange rate

$\epsilon = \epsilon_o- \epsilon_r(r^f - r)$

We can combine them and get the trade balance:

$NX = \left(x_fY^f - im_yY\right) + x_{\epsilon}\epsilon_o + \left(x_{\epsilon}\epsilon_rr^f x_{\epsilon}- \epsilon_rr\right)$

as a function of three sets of variables:

1. prosperity—national income abroad $Y^f$ and at home $Y$
2. foreign exchange speculators' optimism or pessimism $\epsilon_o$
3. interest rates abroad $r^f$ and at home $r$.

Gross exports depend positively on foreign real GDP and on the real exchange rate. Imports depend positively on domestic real GDP. The difference between gross exports and imports is net exports, which is the fourth and last component of aggregate demand.

In turn, the exchange rate depends on a number of factors, the most important of which is the difference between domestic and foreign real interest rates. The higher the domestic real interest rate or the lower foreign real interest rates, the lower are the nominal and real exchange rates. The most important df the other factors that affect the real exchange rate is foreign currency speculators’ confidence.

6.3.3.1 Exchange Rate Overreaction and Diagnostic Expectations

We will usually take the value for $\epsilon_r$, the sensitivity of the exchange rate to the real interest rate differential, to be 10: a change in the interest rate differential induces a ten times larger swing in the value of the real interest rate. This would be sensible if foreign exchange speculators had good reason to believe that interest differentials and the exchange rate value they supported had a one-in-ten chance of returning to its fundamental value in a year. If so, then the market would be "efficient" in the sense that bets on the foreign exchange market would not be no-brainers. If you bet on the foreign exchange market you would then have nine chances in ten of collecting the interest rate differential $r^f - r$ over the next year, and one chance in ten of losing your shirt and receiving: $-(\epsilon - \epsilon_o)+ (r^f - r)$. That bet would not be an especially good one (and taking the other side of that bet would not be an especially good one) only if $\epsilon_r = 10$. And economists like to believe that markets are "efficient" in this sense.

In fact, it is easy to believe that exchange rate differentials reverse themselves more frequently than once every ten years on average: once every five appears to be a better rule of thumb:

This is only one of many pieces of information that financial markets overreact, and are not so much "efficient" with "rational expectations", but rather excessively volatile with what Nicola Gennaioli and Andrei Shleifer call "diagnostic" beliefs in their book 2018 book A Crisis of Beliefs: Investor Psychology and Financial Fragility (Princeton University Press). Think of financial markets not so much as keen-eyed rational accountants but as, rather, triage nurses in a hospital emergency room, grabbing onto the most salient feature of the case in front of them and then using that as a diagnosis to guide all treatment.

### 6.4 Conclusion

This chapter has focused only on the building blocks of the analysis. Putting the blocks together and determining the division of real GDP between its four components are tasks reserved for the next chapter. Moreover, recall that this chapter has presented only a snapshot view of the flexible-price economy. It has not discussed the impact of changes in policy and in the economic environment on economic growth. That was done in Chapters 4 and 5 (refer to them to analyze how changes in investment spending ultimately affect productivity). This chapter has ignored the nominal financial side of the economy—money, prices, inflation, interest rates, and nominal exchange rates—entirely.

Last, but not least, the flexible-price analysis of this part, Part III, is itself not a complete analysis of even the real side of the economy. It needs to be supplemented by the analysis of what happens in the short run when prices are sticky. That analysis is carried out in Part IV.

## Catch Our Breath¶

Building Blocks of the Flexprice Model: https://www.icloud.com/keynote/0qPkVy4AgrnNRIMq3I7HCoN-w

# Building Blocks of the Flexprice Model¶

### Flexible Price Macroeconomics¶

In this part we shift our point of view and take a "snapshot" of the economy, looking at it over such a short period that its productive resources are fixed but such a long period that wages and prices are fully flexible:

• The "classical" assumption
• Why make this “classical” assumption?
• As a baseline and a benchmark
• If the economy does not suffer big shocks for a while (five years?), it may apply

In this analysis, the key questions are:

• What are the economic forces that keep real GDP at its equilibrium value?
• And in an economy with flexible wages and prices what determines the division of real GDP among:
• consumption spending,
• investment spending,
• government purchases, and
• net exports?

Part 3 contains three chapters. Chapter 6 assembles the building blocks. It analyzes the determinants of the components of spending that make up GDP. The answers to the questions above are the same whether prices are flexible (Part 3) or sticky (as they will be in Part 4). So our building blocks form the basis for both our long-run and our short-run stories.

In Chapter 7 these building blocks are put together. Chapter 7 demonstrates how to use the flexible-price model to analyze the composition of real GDP, and how a flexible-price macroeconomy reacts to disturbances and shocks.

Chapter 8 turns the focus of attention from production to the price level. It performs the straightforward task of analyzing the determinants of the price level and inflation in the flexible-price model.

## The Model: Building Blocks¶

• Consumption function
• Investment demand
• Government sector
• International sector:
• Exports and imports
• Exchange rates

### Production Function¶

• (Gross or Net) Domestic Product; National Income
• K, L, E are fixed

• $Y^* = F\left(K, L, E\right) = K^{\alpha}\left(LE\right)^{1-\alpha}$ (Note: "*" means something different here than "BGP value")

### Labor Demand¶

• Suppose a typical firm owns one unit of capital...

• $Y_{firm} = F\left(1, L_{firm}, E\right)$

• $MPL = \frac{dY_{firm}}{dL_{firm}} = \frac{(1-\alpha)E^{1-\alpha}}{{L_{firm}}^{\alpha}}$

• Firm equilibrium: profit maximization:

• $\frac{w}{p} = \frac{(1-\alpha)E^{1-\alpha}}{{L_{firm}}^{\alpha}}$

• ${L_{firm}}^{*} = \left[{(1-\alpha)E^{1-\alpha}}\left(\frac{P}{W}\right)\right]^\left(\frac{1}{\alpha}\right)$

### Labor Market Equilibrium¶

Labor supply equals labor demand

• $L = K{L_{firm}}^*$

• $L = K\left[{(1-\alpha)E^{1-\alpha}}\left(\frac{P}{W}\right)\right]^\left(\frac{1}{\alpha}\right)$

• $\frac{W}{P} = {(1-\alpha)E^{1-\alpha}}\left(\frac{K}{L}\right)^{\alpha} = (1-\alpha)\left(\frac{Y}{L}\right)$

How does the economy get to equilibrium?

• if W/P is low, firms hire more...

• if W/P is high, firms fire...
• if there are (excess) unemployed workers, W/P drops...

• if people regard themselves as overwored, W/P rises...

• This equilibrium is a full employment equilibrium

### Spending on Domestically-Produced Goods¶

Aggregate demand

• Total spending, planned expenditure, aggregate demand
• AD = C + I + G + NX

Four components

• Or three components and a balancing item

• C: consumption spending by households

• I: investment spending by businesses

• G: government purchases of goods and services

• NX = GX - IM: net exports

Full employment equilibrium

• C + I + G + NX = AD = Y = Y*

### The Consumption Function¶

Household decisions:

• Net taxes: $T = tY$

• Disposable income: $Y^d = Y - T = (1-t)T$

• Consumption, savings, disposable income, taxes: $C = Y^d - S^p = Y - T - S^p$

The consumption function:

• $C = c_o + {c_y}Y^d = c_o + {c_y}(1-t)Y$

• Baseline consumption: $c_o$

• The marginal propensity to consume: $MPC = \frac{dC}{dY^d} = c_y$

• Other terms:

• Wealth terms in consumption?
• Income terms in consumption?

### Investment Spending¶

The investment function

• $I = I_o - {I_r}r$

• The real interest rate: $r = i + \rho - \pi$

• The nominal risky interest rate: $i + \rho$

• The nominal safe interest rate: $i$

• The inflation rate: $\pi = \frac{dP}{dt}$

• The investment accelerator version: $I = I_o - {I_r}r + {I_y}Y$

The stock market and investment

• The value of the stock market: $V = \frac{D}{r - (n + g)}$

• The Tobin's Q version of the investment function: $I = I_o + I_{q}\left(\frac{V}{B}\right)$

The peculiar role of inventories

• 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...

### Government Purchases¶

• Government purchases of goods and services (including wages of government workers): $G$
• The government surplus (or deficit): $DEF = G - T = G - tY$

The international sector

• Net exports: $NX = GX - IM$

• Gross exports: $GX = x_fY^f + {x_{\epsilon}}{\epsilon}$

• Foreign economic product: $Y^f$

• The real exchange rate: $\epsilon = \frac{eP^f}{P}$
• The nominal exchange rate—the dollar value of foreign currency: $e$

• The foreign price level $P^f$

• Imports: $IM = im_yY$

#### Real Exchange Rate (Value of Foreign Goods/Currency) Determination¶

• $\epsilon = {\epsilon}_o + {\epsilon}_r\left(r^f - r\right)$
• Foreign real interest rate: $r^f$

• Baseline real exchange rate: ${\epsilon}_o$
Elasticity of the exchange rate to interest rate differentials: ${\epsilon}_r$

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.

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.

I will try to say "the exchange rate—the value of foreign currency/goods" whenever I can...

### Recap: Pieces of the Flex-Price Model¶

• Output equal production function potential: $Y = Y^* = F(K, L, E)$

• The real wage adjusts to give us full employment: $\frac{W}{P} = {(1-\alpha)E^{1-\alpha}}\left(\frac{K}{L}\right)^{\alpha} = (1-\alpha)\left(\frac{Y}{L}\right)$

• The consumption function: $C = c_o + {c_y}(1-t)Y$

• Investment spending: $I = I_o - {I_r}r$

• Government purchases: $G$

• The international sector: $NX = GX - IM = x_fY^f + {x_{\epsilon}}{\epsilon} - im_yY$

• Exchange rate—the value of foreign currency—determination: $\epsilon = {\epsilon}_o + {\epsilon}_r\left(r^f - r\right)$

• The full-employment national income identity: $Y^* = Y = AD = C + I + G + NX$