Can somebody please help me with this! Thanks! There are 2 firms in the market a
ID: 1215429 • Letter: C
Question
Can somebody please help me with this! Thanks!
There are 2 firms in the market and each of them plans the production as Q = K1/3L1/3, where K. is capital and L labor. Given K=8, capital rental rate R=0.5, and wage W=8, answer the following questions if the market demand function is Q = (P+2),/2 What is the supply relation by a firm? What is the labor demand relation by a firm? Can you derive the variable cost of a firm? What is the total cost of a firm? What is the cost of producing more units of good? In equilibrium, what is the supply function of a firm? What is the total supply function of the economy? What is the equilibrium price for goods? What is the equilibrium quantity of goods? How much labor will a firm demand? What is the revenue of a firm?Explanation / Answer
1. Q = K^1/3L^1/3 , Putting K = 8
Q = 2L^1/3
2 Q = K^1/3L^1/3 , Putting K = 8
Q = 2L^1/3
L = 1/8*Q^3 is labour demand
3 Variable Cost = W*L = 8*1/8*Q^3 = Q^3
4 TC = WL + RK = Q^3 + 0.5*8 = 4 + Q^3
5 MC = dTC/dQ = 3Q^2
6 Suply Function, P = 3Q^2
7 Suply Function of Economy, P = 3/4Q^2
8 Qq = Qs , (P+2)^1/2 = 2(P/3)1/2
P + 2 = 4/3P
1/3P = 2
P = 6
9 Q = P^2 - 2 = 2*(2)^1/2
Q = 2.82
10 L = 1/8*Q^3 = (1/8)*(2.82)^(3)
L = 2.80
11 TR = P*Q = 6*2.82 = 16.92
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