Question

Use the following information, where i and USA are countries, to answer the next two questions: Suppose Y_i = A_i[K_i^(.6)]*[L_i^(.4)], and Y_usa = A_usa[K_usa^(.6)]*[L_usa^(.4)], and if: y_i = Y_i/L_i, y_usa = Y_usa/L_usa, and k_i = K_i/L_i, and k_usa = K_usa/L_usa , and if (k_i)/(k_usa) = .25:

If we assume A_i = A_usa, then the predicted relative per capita real GDP, yi/y_usa, is (about):

a. .435, and the predicted per capita output of the U.S is 43.5% of that of country i

b. .57, and the predicted per capita output of the U.S. is about 57% of that of country i

c. .57, and country i's per capita output is about 57% of that of the U.S.

d. .435, and the predicted per capita output of country i is about 43.5% of that of the U.S.

Answer 1

Consider the given problem here the production function of two country are given by.

=> Yi = Ai*[Ki^0.6*Li^0.4], => Yi/Li = Ai*[Ki^0.6*Li^0.4]/Li, => yi = Ai*(Ki/Li)^0.6, => yi = Ai*ki^0.6, for the ith country.

=> Yusa = Ausa*[Kusa^0.6*Lusa^0.4], => yusa = Ausa*kusa^0.6, for the country “USA”.

=> yi/yusa = [Ai*ki^0.6]/[ Ausa*kusa^0.6] = (ki/kusa)^0.6, where “ki/kusa=0.25”.

=> yi/yusa = 0.25^0.6 = 0.4353, => yi = 0.4353*yusa, => “yi” is 43.5% of “yusa”.

=> So, here the correct option is “d”.