Use b as the exponent for physical capital, and c as the exponent for human capital. Assume that b = 0.25 and c = 0.60. Further assume that per person income of a rich country is 10 times that of a poor country.
-Refer to the information above.What is the approximate value of the multiple of combined physical and human capital that the rich country must have in order to produce 10 times the output per person of the poor country?
A)12
B)25
C)100
D)1000

Question

Quizplus · Accepted Answer

The correct answer is A.The production function is given by:Y = AK^bL^cwhere Y is output, A is a constant, K is physical capital, L is human capital, b is the exponent for physical capital, and c is the exponent for human capital.We are given that b = 0.25 and c = 0.60. We are also given that the per person income of a rich country is 10 times that of a poor country. This means that:Y_rich/Y_poor = 10Substituting the production function into this equation, we get:A_richK_rich^bL_rich^c / A_poorK_poor^bL_poor^c = 10Since A, K, and L are all positive, we can divide both sides of this equation by A_poorK_poor^bL_poor^c to get:(K_rich/K_poor)^(b) * (L_rich/L_poor)^(c) = 10Substituting b = 0.25 and c = 0.60 into this equation, we get:(K_rich/K_poor)^(0.25) * (L_rich/L_poor)^(0.60) = 10This equation tells us that the multiple of combined physical and human capital that the rich country must have in order to produce 10 times the output per person of the poor country is:(K_rich/K_poor)^(0.25) * (L_rich/L_poor)^(0.60) = 10We can solve this equation for K_rich/K_poor to get:K_rich/K_poor = 10^(1/0.25) = 10^4 = 10000Therefore, the approximate value of the multiple of combined physical and human capital that the rich country must have in order to produce 10 times the output per person of the poor country is 10000.

Use B as the Exponent for Physical Capital, and C