For each firm within an industry, T = X(X - 1)^2 + 25X; where T is the long-run

Question

For each firm within an industry, T = X(X - 1)^2 + 25X; where T is the long-run cost of the firm, and X is the firm's level of output. For the industry as a whole, Y = 34 - p; where Y is total consumer demand for the industry's product, and p is the price of this product. Assuming first that the industry is a monopoly, find the values of X, Y, p and pi; where pi is the firm's level of profits (pX - T). Assuming next that all barriers to entry are eliminated to make the industry perfectly competitive, find the new value of each of the four variables (X, Y, p and pi) calculated in part A, and determine the new number of firms in the industry. Estimate the difference in consumer surplus between parts A and B.

Explanation / Answer

A. When at monopoly X will be equal t Y

R = P*Q = (34-X) * X so MR =dR/dX = MR = 34-2X

TC = x^3-2X^2+26X

Now MC = dTC/dX = 3X^2-4X+26

MC=MR so 3X^2-2X-8=0

So X=Y=2

p =34-2 = 32

T = 2+50 = 52

Profit = 32*2-52 = 12

b) ATC = T/X = X^2+23X+1 So for the firms optimal output

MC = ATC i.e. 3X^2-4X+26 = X^2+23X+1 = p

so 2X^2-27X+25

So X=1 Substituting value of X in MC equation we get p=25

Y = 34-25 = 9

no of firms = Y/X = 9

and profit = 25*1-25 = 0

C. In part A Consumer surplus = 0.5*(34-32)*2 = 2 in part B Consumer surplus = 0.5*(34-25)*9 = 40.5

So consumer surplus increased by 38.5

In part A producer surplus = 0.5*(32)*2 = 32 in part B Producer surplus = 0.5*(25)*9 = 112.5

So consumer surplus increased by 80.5

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