Question

Problem 2

Suppose that an economy’s production function is Cobb- Douglas with parameter = 0.3.

c. Suppose that a gift of capital from abroad raises the capital stock by 10 percent. What happens to total output ( in percent)? The rental price of capital? The real wage?

d. Suppose that a technological advance raises the value of the parameter A by 10 percent. What happens to total output ( in percent)? The rental price of capital? The real wage?

Answer #1

answer c

*Y _{1} =
AK^{0.3}L^{0.7},
Y_{2} =
A(1.1K^{0.3})L^{0.7}*

*Y _{2} /
Y_{1} = (1.1)^{0.3} = 1.029*

*(R/P) _{1} = MPK =
0.3AK^{-0.7}L^{0.7},
(R/P)_{2} =
0.3A(1.1K^{-0.7})L^{0.7}*

*(R/P) _{2} /
(R/P)_{1} = 0.935*

*(W/P) _{1} = MPL =
0.7AK^{0.3}L^{-0.3},
(W/P)_{2} =
0.7A(1.1K^{-0.7})L^{-0.7}*

*(W/P) _{2} /
(W/P)_{1} = 1.029*

*Thus output rises by 2.9%,
rental rates fall by 6.5%, and wages rise by 2.9%*

answer d

*Y _{1} =
AK^{0.3}L^{0.7},
Y_{2} =
A(1.1K^{0.3})L^{0.7}*

*Y _{2} /
Y_{1} = (1.1)^{0.3} = 1.10*

*(R/P) _{1} = MPK =
0.3AK^{-0.7}L^{0.7},
(R/P)_{2} =
0.3A(1.1K^{-0.7})L^{0.7} *

*(R/P) _{2} /
(R/P)_{1} = 1.10*

*(W/P) _{1} = MPL =
0.7AK^{0.3}L^{-0.3},
(W/P)_{2} =
0.7A(1.1K^{-0.7})L^{-0.7} *

*(W/P) _{2} /
(W/P)_{1} = 1.10*

**Everything goes up by 10 %**

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