Let P=P(K,L) represent the total production P of an economic system as a function of the amount of labor L and the capital investment K. Then
The partial derivative of PL= ∂P/∂L is the rate at which production changes with respect to the amount of labor, and is called the marginal product of labor;
The partial derivative of PL= ∂P/∂K is the rate at which production changes with respect to the capital, and is called the marginal product of capital.
Economists Cobb and Douglas modeled the total production in the American economy from 1899 to 1922 with the function P=1.01L^(0.75)K^(0.25) where L is the amount of labor and K is the capital investment.
A. Find the marginal product of PL=∂P/∂L
B. Find the marginal product of PK=∂P/∂K
I tried solving this and I got 0 for both answers but it is wrong and I have no idea how to figure this out.
Please help me out!
Thank you so much.
The partial derivative of PL= ∂P/∂L is the rate at which production changes with respect to the amount of labor, and is called the marginal product of labor;
The partial derivative of PL= ∂P/∂K is the rate at which production changes with respect to the capital, and is called the marginal product of capital.
Economists Cobb and Douglas modeled the total production in the American economy from 1899 to 1922 with the function P=1.01L^(0.75)K^(0.25) where L is the amount of labor and K is the capital investment.
A. Find the marginal product of PL=∂P/∂L
B. Find the marginal product of PK=∂P/∂K
I tried solving this and I got 0 for both answers but it is wrong and I have no idea how to figure this out.
Please help me out!
Thank you so much.
-
A)
diff(1.01*L^.75*K^.25, L) = 0.7575*K^0.25/L^0.25
B)
diff(1.01*L^.75*K^.25, K) = 0.2525*L^0.75/K^0.75
diff(1.01*L^.75*K^.25, L) = 0.7575*K^0.25/L^0.25
B)
diff(1.01*L^.75*K^.25, K) = 0.2525*L^0.75/K^0.75