Macroeconomics
10th Edition
ISBN: 9781319105990
Author: Mankiw, N. Gregory.
Publisher: Worth Publishers,
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Question
Chapter 9, Problem 4PA
(a)
To determine
The constant capital-output ratio.
(b)
To determine
The constant share of capital and labor in the economy’s income.
(c)
To determine
The total capital income and total labor income.
(d)
To determine
The real rental price of capital and the real wage rate.
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Suppose that we modify the Solow growth model by allowing long-run technological progress. That is, suppose that z = 1 for convenience and that there is labor-augmenting technological progress, with a production function
Y =F(K,bN)
where b denotes the number of units of "human capital" per worker, and bN is "efficiency units" of labor. Letting b' denote future human capital per worker, assume that b' = (1 + f ) b, where f is the growth rate in human capital.
(c) In the real world, we usually consider education level as a proxy to human capital. To examine the theory, what suggestions can you make to growth economists? What are factors other than education can you think of that contribute to human capital?
Consider the following Solow growth model in which households save a constant fraction of their income. Let N be the population (also the labor force) in the current period. Assume that the population follows N′ = (1+n)N where N′ is the population in the future period, and n is the net population growth rate. Assume that the output is produced according to the production function Y = zF(K, N), where z is the total factor productivity, K is capital stock, and F(K, N) exhibits constant returns to scale. Capital depreciates at the rate d where 0 < d < 1. The capital stock changes over time according to K′ = (1 − d)K + I where I is the investment level.
(a) Derive the equation that determines the future capital-per-worker in competitive equilibrium. Here is some additional information for parts (5b), (5c), and (5d). Suppose that the economy is initially in steady state, and experiences a natural disaster (e.g. the recent quake and tsunami in Japan in 2011) that destroys some of the…
Consider the Solow model. Using suitable diagrams, compare the different dynamics for the levels and growth rates of capital per capita and output per capita following: (a) a new wave of immigration, (b) an increase in the saving rate, (c) a one-shot foreign investment which increase the size of the available stock of capital, (d) an important technological advance.
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