Question

Suppose that the production function for the economy is Y = AK0.25L0.75, A = 2, K = 100,000, and L = 60,000. What are the values of real GDP, the real wage, and the real rental cost of capital? Show this data using graphs of the aggregate production function, the aggregate capital market, and the aggregate labor market. Really need help on this ASAP!!

Answer 1

Consider the given problem here the production function is given by.

=> Y = A*K^0.25*L^0.75, where “A=2”, “K=100,000” and “L=60,000”.

=> Y = 2*(100,000)^0.25*(60,000)^0.75 = 2*(17.78)*(3,833.66) = 136,324.95,

=> Y = 136,324.95, be the production of the economy as a whole.

Now, given the production function “Y = 2*K^0.25*L^0.75”, the “MPL” and “MPK” are given by.

=> MPL = 2*K^0.25*0.75*L^(-0.25) = 2*0.75*(K/L)^0.25, => at the equilibrium the real wage must be equal to “MPL”,

=> W = MPL = 2*0.75*(100,000/60,000)^0.25 = 1.5*(10/6)^0.25.

=> W = 1.7, => the real wage is given by “W=1.7”.

Similarly, the real rental rate is given by, “R = MPK”, => R = 2*0.25*(L/K)^0.75.

=> R = 2*0.25*(L/K)^0.75 = 0.5*(60,000/100,000)^0.75 = 0.5*(6/10)^0.75 = 0.5*(0.6)^0.75

=> R = 0.34, be the real rental rate. Consider the following fig shows the production function.

Now, the following two fig shows the "labor market" and "Capital Market".

and

So, here the equilibrium real wage and real rental rate are given by, "W=1.7" and "R=0.34".