Consider a Solow growth model with a human capital augmented production function Y₁ = AK; HN-- Suppose that both physical and human capital are accumulated with constant savings rates sx and Sir respectively and depreciate at the common rate 8, that is K+1K₁ = SKY₁ - 8K, and H₁+1H₁ = SKY₁ - 8H, There is no growth in productivity A or raw labor N. Suppose A = 1, a = B = 1/4, SK = sur = 0.12 and 8 = 0.06. Let y = Y/N, k = K/N and h = H/N denote output per worker, physical capital per worker, and human capital per worker respectively. Let = h/k denote the intensity of human capital relative physical capital. Calculate y, k, h and dp in steady state. (b) How does steady state output per worker in this economy compare to the steady state output per worker of the analogous Solow model without human capital (i.e., with Y, AK N- and A = 1, a = 1/2, s = 0.12 and 8 = 0.06. Explain the differences. Now consider the case = 1/4 and ß= 3/4 with all the other parameters as in part (a) above. Explain why this version of the Solow growth model can exhibit endogenous growth. Calculate the long run growth rate of output per worker. (d) Assume the same production function as in part (c) but now, suppose the savings rate in human capital increases to s= 0.18. Would this increase or decrease the long run growth rate o output per worker? Explain.
Consider a Solow growth model with a human capital augmented production function Y₁ = AK; HN-- Suppose that both physical and human capital are accumulated with constant savings rates sx and Sir respectively and depreciate at the common rate 8, that is K+1K₁ = SKY₁ - 8K, and H₁+1H₁ = SKY₁ - 8H, There is no growth in productivity A or raw labor N. Suppose A = 1, a = B = 1/4, SK = sur = 0.12 and 8 = 0.06. Let y = Y/N, k = K/N and h = H/N denote output per worker, physical capital per worker, and human capital per worker respectively. Let = h/k denote the intensity of human capital relative physical capital. Calculate y, k, h and dp in steady state. (b) How does steady state output per worker in this economy compare to the steady state output per worker of the analogous Solow model without human capital (i.e., with Y, AK N- and A = 1, a = 1/2, s = 0.12 and 8 = 0.06. Explain the differences. Now consider the case = 1/4 and ß= 3/4 with all the other parameters as in part (a) above. Explain why this version of the Solow growth model can exhibit endogenous growth. Calculate the long run growth rate of output per worker. (d) Assume the same production function as in part (c) but now, suppose the savings rate in human capital increases to s= 0.18. Would this increase or decrease the long run growth rate o output per worker? Explain.
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Transcribed Image Text:Consider a Solow growth model with a human capital augmented production function
Y, = AK" H N-a-
%3D
Suppose that both physical and human capital are accumulated with constant savings rates sx and
Sy respectively and depreciate at the common rate 8, that is
K+1 - K, = sKY, - 8K,
and
H1 - H, = SKY, - SH,
There is no growth in productivity A or raw labor N.
"Suppose A = 1, a = ß = 1/4, sx = Sn = 0.12 and ô = 0.06. Let
(a)
y = YIN, k = KIN and h = HIN denote output per worker, physical capital per worker, and
human capital per worker respectively. Let = hlk denote the intensity of human capital relative to
physical capital. Calculate y, k, h and o in steady state.
(b) .
output per worker of the analogous Solow model without human capital (i.e., with Y, = AK" N-
and A = 1, a = 1/2, s 0.12 and ô = 0.06. Explain the differences.
How does steady state output per worker in this economy compare to the steady state
* I Now consider the case a = 1/4 and ß = 3/4 with all the other parameters as in part
(c
(a) above. Explain why this version of the Solow growth model can exhibit endogenous growth.
Calculate the long run growth rate of output per worker.
(d)'
human capital increases to sH = 0.18. Would this increase or decrease the long run growth rate of
Assume the same production function as in part (c) but now, suppose the savings rate in
output per worker? Explain.
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