%%javascript
IPython.OutputArea.prototype._should_scroll = function(lines) {
return false;}
We have just stormed through chapter 6—the building blocks of the business cycle model chapter:
Now we will move on to chapter 7: Equilibrium in the flexprice business cycle model
Three prices: W/P, P, r
Move to a different form of the national income identity
$ Y = C + I + G + NX $
$ Y - C - T - NX = I + (G-T) $
$ (Y - C - T) - NX + (T-G) = I $
$ S_p + S_f + S_g = I $
We have not just an equation: we have a process
$ S_p(Y, t) + S_f(\epsilon, ...) + S_g = I(r) $
The private savings function
$ Y - C - T = S_p $
$ Y - (c_o + c_y(1-t)Y) - T = S_p $
$ Y - (c_o + c_y(1-t)Y) - tY = S_p $
$ (1 - c_y - t + c_{y}t)Y - c_o = S_p $
Government savings
$ S_g = T - G = tY - G $
Foreign Savings
$ S_f = - NX = IM - GX $
$ S_f = im_{y}Y - x_fY^f - {x_{\epsilon}}{\epsilon} $
$ S_f = im_{y}Y - x_fY^f -$
$ {x_{\epsilon}}\left({\epsilon}_o + {\epsilon}_r\left(r^f - r\right)\right) $
Investment
$ I = I_o - {I_r}r $
$ {\Delta}Y = 0 $
$ {\Delta}C = {\Delta}c_o + {c_y}(1-t){\Delta}Y $ :: consumption
$ {\Delta}I = {\Delta}I_o - {I_r}{\Delta}r $ :: investment
$ {\Delta}G $ :: government
$ {\Delta}NX = x_f{\Delta}Y^f + {x_{\epsilon}}{\Delta}{\epsilon} - im_y{\Delta}Y $ :: international
$ {\Delta}\epsilon = {\Delta}{\epsilon}_o + {\epsilon}_r\left({\Delta}r^f - {\Delta}r\right) $ :: exchange rate
$ {\Delta}G = {\Delta}G $
$ {\Delta}Y = 0 $
$ {\Delta}S_p + {\Delta}S_f + {\Delta}S_g = {\Delta}I $
$ {\Delta}S_p + {\Delta}S_f - {\Delta}G = {\Delta}I $
$ {\Delta}S_p = (1 - c_y - t + c_{y}t){\Delta}Y - {\Delta}c_o = 0 $
$ 0 + {\Delta}S_f - {\Delta}G = {\Delta}I $
$ {\Delta}S_f = im_{y}{\Delta}Y - x_f{\Delta}Y^f - {x_{\epsilon}}\left({\Delta}{\epsilon}_o + {\epsilon}_r\left({\Delta}r^f - {\Delta}r\right)\right) $
$ {\Delta}S_f = x_{\epsilon}{\epsilon}_r{\Delta}r $
$ {\Delta}I = {\Delta}I_o - {I_r}{\Delta}r $
$ 0 + x_{\epsilon}{\epsilon}_r{\Delta}r - {\Delta}G = -{I_r}{\Delta}r $
$ -{\Delta}G = -\left({I_r} + x_{\epsilon}{\epsilon}_r\right){\Delta}r $
$ {\Delta}r = \frac{{\Delta}G}{{I_r} + x_{\epsilon}{\epsilon}_r} $
$ {\Delta}I = -I_{r}{\Delta}r = \frac{-I_{r}{\Delta}G}{{I_r} + x_{\epsilon}{\epsilon}_r} $
$ {\Delta}GX = {\Delta}NX = -{x_{\epsilon}}{\epsilon}_r{\Delta}r = \frac{-{x_{\epsilon}}{\epsilon}_{r}{\Delta}G}{{I_r} + x_{\epsilon}{\epsilon}_r} $
$ {\Delta}I + {\Delta}GX = -{\Delta}G $
$ {\Delta}I = {\Delta}I_o - I_r{\Delta}r $ :: investment
$ {\Delta}Y = 0 $ :: full employment is maintained
$ {\Delta}S_p + {\Delta}S_f + {\Delta}S_g = {\Delta}I $ :: flow-of-funds
$ {\Delta}S_g = t{\Delta}Y - {\Delta}G = 0 $ :: government savings
$ {\Delta}S_p + {\Delta}S_f + 0 = {\Delta}I_o - I_r{\Delta}r $ :: it's a zero...
$ {\Delta}S_p = (1 - c_y - t + c_{y}t){\Delta}Y - {\Delta}c_o = 0 $ :: pvt dom svgs
$ 0 + {\Delta}S_f + 0 = {\Delta}I_o - I_r{\Delta}r $ :: it's a zero
$ {\Delta}S_f = im_{y}{\Delta}Y - x_f{\Delta}Y^f - x_{\epsilon}{\Delta}{\epsilon}_o - {x_{\epsilon}}{\epsilon}_r\left({\Delta}r^f - {\Delta}r\right) $ :: foreigners
$ {\Delta}S_f = 0 - 0 - 0 - x_{\epsilon}{\epsilon}_r\left(0 - {\Delta}r\right) $ :: one term nonzero
$ x_{\epsilon}{\epsilon}_r{\Delta}r = {\Delta}I_o - I_r{\Delta}r $ :: flow-of-funds
$ \left(I_r + x_{\epsilon}{\epsilon}_r\right){\Delta}r = {\Delta}I_o $
$ {\Delta}r = \frac{{\Delta}I_o}{I_r + x_{\epsilon}{\epsilon}_r} $ :: Change in r
$ {\Delta}I = {\Delta}I_o - I_r{\Delta}r = {\Delta}I_o - \frac{I_r{\Delta}I_o}{I_r + x_{\epsilon}{\epsilon}_r} = \frac{x_{\epsilon}{\epsilon}_r{\Delta}I_o}{I_r + x_{\epsilon}{\epsilon}_r} $ :: Change in I
$ {\Delta}GX = - {\Delta}S_f - x_{\epsilon}{\epsilon}_r{\Delta}r = -\frac{x_{\epsilon}{\epsilon}_r{\Delta}I_o}{I_r + x_{\epsilon}{\epsilon}_r} $ :: Change in GX
$ {\Delta}S_p + {\Delta}S_f - {\Delta}G = {\Delta}I $
$ {\Delta}S_p = (1 - c_y - t + c_{y}t){\Delta}Y - {\Delta}c_o = 0 $
$ 0 + {\Delta}S_f - {\Delta}G = {\Delta}I $
$ {\Delta}S_f = im_{y}{\Delta}Y - x_f{\Delta}Y^f - {x_{\epsilon}}\left({\Delta}{\epsilon}_o + {\epsilon}_r\left({\Delta}r^f - {\Delta}r\right)\right) $
$ {\Delta}S_f = x_{\epsilon}{\epsilon}_r{\Delta}r $
$ {\Delta}I = {\Delta}I_o - {I_r}{\Delta}r $
$ 0 + x_{\epsilon}{\epsilon}_r{\Delta}r - {\Delta}G = -{I_r}{\Delta}r $
$ -{\Delta}G = -\left({I_r} + x_{\epsilon}{\epsilon}_r\right){\Delta}r $
$ {\Delta}r = \frac{{\Delta}G}{{I_r} + x_{\epsilon}{\epsilon}_r} $
$ {\Delta}I = -I_{r}{\Delta}r = \frac{-I_{r}{\Delta}G}{{I_r} + x_{\epsilon}{\epsilon}_r} $
$ {\Delta}GX = {\Delta}NX = -{x_{\epsilon}}{\epsilon}_r{\Delta}r = \frac{-{x_{\epsilon}}{\epsilon}_{r}{\Delta}G}{{I_r} + x_{\epsilon}{\epsilon}_r} $
$ {\Delta}I + {\Delta}GX = -{\Delta}G $
Real GDP:
Real GDP per Worker:
Investment as a Share of Potential GDP:
Consumption as a Share of Potential GDP:
Gross Exports as a Share of Potential GDP:
Imports as a Share of Potential GDP:
Net Exports as a Share of Potential GDP:
Nominal Short-Term Safe Rate:
Long-Term Real Safe Rate:
Long-Term Risky Real Rate:
Real Exchange Rate (Value of Foreign Goods/Currency):
Real GDP
Real GDP per Worker
Investment Spending as a Share of Potential GDP
Personal Consumption Expenditures as a Share of Potential GDP
Gross Exports
Gross Imports
The Trade Balance
Short-Term Safe Nominal Interest Rate: Treasury Bills
Long-Term Safe Real Interest Rate
Long-Term Risky Real Interest Rate
Real Exchange Rate
Price Level
Inflation Rate
Balanced-growth path: The path toward which total output per worker tends to converge, as the capital-output ratio converges to its equilibrium value.
Capital intensity: The ratio of the capital stock to total potential output, K/Y, which describes the extent to which capital, as opposed to labor, is used to produce goods and services.
Divergence: The tendency for a per capita measurement such as income or standard of living in various countries to become less equal over a period of time.
Demographic transition: A period in history which sees first a rise and then a fall in birth rates and a sharp fall in death rates as material standards of living increase above "subsistence" levels.
Efficiency of labor: The skills and education of the labor force, the ability of the labor force to handle modern technologies, and the efficiency with which the economy's businesses and markets function.
Industrial Revolution: The transformation of the British economy between 1750 and 1850 when, due to technological advances, largely handmade production was replaced by machine-made production.
Long-run economic growth: The process by which productivity, living standards, and output increase.
Malthusian age: A period in which natural-resource scarcity limits any gains from increases in technology; a larger population becomes poor and malnourished, lowering their standard of living, and ultimately lowering population growth to near zero.
Patent laws and copyrights: Laws designed to encourage invention and innovation by providing the right to exclude anyone else from using a discovery (patent) or intellectual property (copyright) for a period of years.
Productivity growth: The rate at which the economy's full-employment productivity expands from year to year as technology advances, as human capital increases, and as investment increases the economy's physical capital stock.
Productivity growth slowdown: The period from 1973 to about 1995 when the rate of productivity growth in the United States and other economies suddenly slowed, for still mysterious reasons.
Saving rate: The share of total GDP that an economy saves, s, equal to the sum of household, government, and foreign saving divided by total output.
# keep output cells from shifting to autoscroll: little scrolling
# subwindows within the notebook are an annoyance...
# set up the environment by reading in every library we might need:
# os... graphics... data manipulation... time... math... statistics...
import sys
import os
from urllib.request import urlretrieve
import matplotlib as mpl
import matplotlib.pyplot as plt
from IPython.display import Image
import pandas as pd
from pandas import DataFrame, Series
from datetime import datetime
import scipy as sp
import numpy as np
import math
import random
import seaborn as sns
import statsmodels
import statsmodels.api as sm
import statsmodels.formula.api as smf
# report library versions...
%matplotlib inline
# put graphs into the notebook itself...
# graphics setup: seaborn-whitegrid and figure size...
plt.style.use('seaborn-whitegrid')
figure_size = plt.rcParams["figure.figsize"]
figure_size[0] = 12
figure_size[1] = 9
plt.rcParams["figure.figsize"] = figure_size
(A) If we want to account for the cross-country pattern of prosperity in the world today in income per capital and productivity, we need to be thinking primarily about:
(B) The Malthusian framework breaks the expectation that human ingenuity will always and rapidly lead to rising standards of living and productivity levels over time because:
(C) A Solow growth model analysis based on improving incentives for investment raising the capital-output ratio is relevant at a time horizon:
(D) SHORT ANSWER: Why do you think it has proven so much easier to spread around the world knowledge about how to obtain good public health than knowledge about how to obtain frontier levels of economic activity?
We study business cycles because:
The consumption function:
In the flexible price model: