# Week 3 chapter notes

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Chapter 7 Economic Growth I: Capital Accumulation and Population Growth
Notes
x differences in income must come from differences in capital, labour, and technology
x Solow growth model Æ a theory of economic growth in per-capita income; a model showing how saving, population growth,
and technological progress determine the level of and growth in the standard of living
7.1 The Accumulation of Capital
x the Solow growth model is designed to show how growth in the capital stock, growth in the labour force, and advances in
technology interact in an economy, and how they affect a nation’s total output of goods and services
The Supply and Demand for Goods
x the supply and demand for goods play a central role in the Solow model
x the supply of goods in the Solow model is based on the production function, which states that output depends on the capital stock
and the labour force: Y = F(K, L)
x the Solow growth model assumes that the production function has constant returns to scale (CRTS), which is considered realistic
x production functions with CRTS allow the analysis of all quantities in the economy relative to the size of the labour force
x by letting z = 1/L: Y / L = F(K / L, 1)
x this equation shows that the amount of output per worker Y / L is a function of the amount of capital per worker K / L
x the assumption of CRTS implies that the size of the economy—as measured by the number of workers—does not affect the
relationship between output per worker and capital per worker
x because size of economy doesn’t matter, y = Y / L, k = K / L, and f(k) = F(k, 1) and production function is written as: y = f(k)
x the slope of the production function shows how much extra output a worker produce when given an extra unit of capital
x this amount is the marginal product of capital, MPK, shown as: MPK = f(k + 1) – f(k)
x as amount of k increases, production function becomes flatter, indicating that production function exhibits diminishing MPK
x when k is low, average worker has only little k to work with, so extra unit of k is very useful and produces lot of additional
output; on other hand, when k is high, average worker already has lot of k, so extra unit increases production only slightly
x the demand for goods in the Solow model comes from consumption and investment
x in other words, output per worker y is divided between consumption per worker c and investment per worker i: y = c + i
x this equation is the per-worker version of the national accounts identity for the economy
x the Solow model assumes that each year people save a fraction s of their income and consume a fraction (1 – s)
x this idea can be expressed with the following consumption function: c = (1 – s)y, where s is saving rate between 0 and 1
x this implies for investment: y = (1 – s)y + i : i = sy
Growth in the Capital Stock and the Steady State
x at any moment, k is key determinant of economy’s output, but k can change over time, and these can lead to economic growth
x in particular, two forces influence the capital stock—(1) investment: expenditure on new plant and equipment causing k to rise;
and (2) depreciation: wearing out of old k causing k to fall
x since, i = sy and y = f(k), investment per worker as a function of k per worker is: i = s f(k)
x this equation relates the existing stock of capital k to the accumulation of new capital i
x to incorporate depreciation, the depreciation rate is signified by / and the amount of capital that depreciates each year is /k
x change in capital stock = investment – depreciation Æ ûk = i – /k Æ ûk = s f(k) – /k
x the higher the k, the greater the amounts of output and investment, but also the greater the amount of depreciation
x there is a single capital stock k* at which the amount of investment equals the amount of depreciation
x if the economy finds itself at this level of the capital stock, the capital stock will not change because the two forces acting on it—
investment and depreciation—just balance; which means that k* the steady-state level of capital
x steady-state Æ a condition in which key variables are not changing
x the steady-state is significant for 2 reasons—(1) an economy at the steady state will stay there; and (2) an economy will reach the
steady state level of capital if it is not at the steady state level of capital already
x the steady state represents the long-run equilibrium of the economy
x if the level of investment exceeds the amount of depreciation, then, over time, the capital stock will rise and will continue to
rise—along with output f(k)—until it approaches the steady state k*
x if the level of investment is less than depreciation, then, over time, the capital stock will fall, approaching the steady state level
x once k reaches the steady state, investment equals depreciation, and there is no pressure for k to increase or decrease
How Saving Affects Growth
x if the saving rate is high, the economy will have a large capital stock and a high level of output in the steady state
x if the saving rate is low, the economy will have a small capital stock and a low level of output in the steady state
x higher saving leads to faster growth in the Solow model, but only temporarily
x an increase in the rate of saving raises growth until the economy reaches the new steady state
x if economy maintains high saving rate, it will also maintain large k and high y, but it won’t maintain high rate of growth forever
x policies that alter the steady-state growth rate of income per person are said to have a growth effect by contrast, a high saving
rate is said to have a level effect, because only the level of income per person—not its growth rate—is influenced by the saving
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## Document Summary

Chapter 7 economic growth i: capital accumulation and population growth. N differences in income must come from differences in capital, labour, and technology. Solow growth model a theory of economic growth in per-capita income; a model showing how saving, population growth, and technological progress determine the level of and growth in the standard of living. Y = f(k, l) y = c + i. Y / l = f(k / l, 1) Growth in the capital stock and the steady state. N when choosing a steady state, the policymaker"s goal is to maximize the well-being of the individuals who make up the society. The transition to the golden rule steady state. N when k exceeds golden rule level, reducing saving is good policy because it increases consumption at every point in time. N when the economy begins with less capital than in the golden rule steady state, the policymaker must raise the saving rate.

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