Please take a look at those two questions 2. Consider a competitive firm, which
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Question
Please take a look at those two questions
2. Consider a competitive firm, which takes prices as given. There are two factors used to produce a product. The amount of capital is fixed at 10 units. Suppose that the marginal product of labor (while capital is held fixed) is given by MPL-50-L where L is the labor input. Suppose that the wage rate is equal to 40 while the rental rate is 50. The output price is equal to 2 (a) What is the fixed cost? (b) What is the relationship between marginal cost and marginal product of labor when labor is the only variable input? Determine the marginal cost in terms of the labor input. (c) What is the amount of labor the firm wants to hire? (d) What is the resulting total cost? (e) (bonus) What is the total revenue? What is the short-term profit? If the short-term profit is positive, how would the number of firms in the industry change?Explanation / Answer
2). Consider the given problem here the marginal product of labour is given below.
=> MPL = 50 – L, we have also given W=40 and R=50.
a).
In the given problem there are 2 inputs “K” and “L”, so the cost function is given by, “C=RK + WL.
So, here K is fixed at “10”, => fixed cost is “RK=50*10=500”.
b).
As we know that the marginal cost is the additional change in “cost” due to additional increase in “output”, mathematically MC=dC/dQ.
So, here “Cost” function is given by, “C=R*K + W*L”, => dC/dQ = W*dL/dQ = W*[1/MPL].
=> MC = W*[1/MPL] = W*[1/(50 – L)], is the MC interms of “L”.
c).
So, under “”Perfect Competition” a firm will determine the optimum choice of “Q” by “P=MC” condition, here P=2.
=> P=MC, => W*[1/(50 – L)] = 2, => 40/2 = 50 – L, => 50 – L = 20, => L = 50 – 20 = 30, => L=30.
So, the optimum labor hiring is “L=30”.
d).
So, the “total cost” function is given by, C=W*L + R*K = 40*30 + 50*10 = 1200 + 500 = 1,700. So, the total cost is “1,700”.
e).
Now, “TR” is the product of “Price” and “quantity”, here P=2, now we need to fig out Q. Now, the total production is the area under the MPL curve up to L, at L=30 MPL=50-L=20.
=> Q = (1/2)*(50 – 20)*30 + 30*20 = 15*30 + 600 = 450 + 600 = 1,050.
So, the TR = P*Q = 2*1,050 = 2,100.
=> So, the short-term profit is, “TR – TC = 2,100 – 1,700 = 400 > 0.
Now, since SR profit is positive, => new firm have an incentive to enter into the industry and get positive profit. So in the LR new firms will enter into the industry.