Consider the following production function: Y; = AKSH!-"L %3! where K; is capital, H;is human capital, Leis the amount of workers and A is the (constant) level of technology. • (1) Does this production function satisfy all the neoclassical properties. Discuss the meaning of each property INTUITIVELY. Imagine that parents invest in the human capital of their children up to the point where the MARGINAL PRODUCT OF PHYSICAL CAPITAL, Kr, is equal to the MARGINAL PRODUCT OF HUMAN CAPITAL, H:. • (ii) What is the relation between Krand H:? Use this relation to write down total output as a function of Kronly. Imagine that the number of people in this economy, N, is different from the number of workers because some people do not work. Let =be the number of workers per capita (the fraction of the population that works). Let y, be output per capita and k = be capital per capita. Finally, let n be the rate of population growth and Y be the growth rate of labor. Ne
Consider the following production function: Y; = AKSH!-"L %3! where K; is capital, H;is human capital, Leis the amount of workers and A is the (constant) level of technology. • (1) Does this production function satisfy all the neoclassical properties. Discuss the meaning of each property INTUITIVELY. Imagine that parents invest in the human capital of their children up to the point where the MARGINAL PRODUCT OF PHYSICAL CAPITAL, Kr, is equal to the MARGINAL PRODUCT OF HUMAN CAPITAL, H:. • (ii) What is the relation between Krand H:? Use this relation to write down total output as a function of Kronly. Imagine that the number of people in this economy, N, is different from the number of workers because some people do not work. Let =be the number of workers per capita (the fraction of the population that works). Let y, be output per capita and k = be capital per capita. Finally, let n be the rate of population growth and Y be the growth rate of labor. Ne
Chapter1: Making Economics Decisions
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Transcribed Image Text:Problem 4
Consider the following production function:
Y, = AKÇH!-"L
where Kr is capital, H;is human capital, Leis the amount of workers and A is the (constant) level of technology.
• (1) Does this production function satisfy all the neoclassical properties. Discuss the meaning of each property INTUITIVELY.
Imagine that parents invest in the human capital of their children up to the point where the MARGINAL PRODUCT OF PHYSICAL
CAPITAL, K, is equal to the MARGINAL PRODUCT OF HUMAN CAPITAL, H:.
2
• (ii) What is the relation between K:and H:? Use this relation to write down total output as a function of Kronly.
Imagine that the number of people in this economy, Nr, is different from the number of workers because some people do not work.
Let l
=4 be the number of workers per capita (the fraction of the population that works). Let y;
ミ
be output per capita and
be capital per capita. Finally, let n be the rate of population growth and y, be the growth rate of labor.
(ii) Using the "effective production function" you derived in (b), write down output per capita, yt, as a function of capital per
capita, k, labor per capita, I, the level of population Nr, and the level of technology, A.
Following Solow and Swan, assume there is no government and no net exports, that the depreciation rate of capital is the constant
8 > 0 and the savings rate is constant 0 <s< 1.
(iv) DERIVE the fundamental equation of Solow-Swan. How does the growth rate of capital depend on employment per
person, l:? Explain intuitively.
(v) Does the equation of the growth rate of capital depend on the growth rate of population, n, or the growth rate of
employment? Explain intuitively.
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