If the price of the output good is 4, the price of factor 1 is 2, and the price
ID: 1201007 • Letter: I
Question
If the price of the output good is 4, the price of factor 1 is 2, and the price of factor 2 is 3, find the profit-maximizing amount of factor 1, the profit-maximizing amount of factor 2, and the profit-maximizing output. A firm has two variable factors and a production function, Q = x^1/2_1 x^1/4_2 The price of its output is 4. Factor 1 receives a wage of w_1 and factor 2 receives a wage of w_2. For question 2 and 3, solve the amounts of factors 2 and 3 that maximize the firm's profits as a function of w_1and w_2. For question 4, find the equation of supply function. Write down a function that states the firm's profit. What is the factor demand function for x_1? What is the factor demand function for x_2? What is the supply function?Explanation / Answer
17) Profit function for any firm is the difference of TR and TC
Profit = TR - TC
= PQ - C(Q)
= 4x1/2x1/4 - w1x1 - w2x2
18) Demand function of a factor has the value of marginal product of labor equal to its wage rate:
VMP(x1) = w1
4*(2(x2)1/4/(x1)1/2) = w1
x1 = 4(x2)1/4/(w1)2
Hence the demand function of x1 = 4(x2)1/4/(w1)2
The MRTS equal to price condtion will yield x1 = 2x2w2/w1
19)
Demand function of a factor has the value of marginal product of labor equal to its wage rate:
VMP(x2) = w2
x2 = (x1)2/3/w14/3