There are 2 firms in the market and each of them plans the production as Q =^K1/
ID: 1215367 • Letter: T
Question
There are 2 firms in the market and each of them plans the production as Q =^K1/3L^I/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)^1/2 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) Since K = 8, supply relation is the production function with K = 8:
Q = (8)1/3L1/3 = 2 x L1/3
(2) Labor is demanded upto the point where
Output price (P) x MPL = Wage rate
MPL = dQ / dL = (2/3) / L2/3
So,
P x [(2/3) / L2/3]= 8
P x [1 / (3 x L2/3)] = 4
(3)
Since K = 8, capital is fixed and labor is the only variable factor. So, total variable cost (TVC) is the total wages cost:
TVC = W x L = 8L
(4)
Total cost, TC = WL + RK = 8L + (0.5 x 8) = 8L + 4
(5)
Since Q = 2 x L1/3,
L = Q3 / 8
TC = 8 x (Q3 / 8) + 4 = Q3 + 4
Cost of producing 1 more unit = Marginal cost (MC)
MC = dC / dQ = 3Q2
Note: First 5 sub-questions are answered.
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