5) manufacturing. This market in the United States is a mature market with a lar

Question

5) manufacturing. This market in the United States is a mature market with a large number of buyers and sellers and can be characterized as a perfectly competitive market. The demand curve is defined by: Your firm produces an alloy used for second generation P = 200-0.25C The supply curve is defined as P = 25 +0.75Qs a) Solve for the total market quantity and equilibriurn price for the alloy As an analyst for this firm, you have been tasked to solve for the ideal level of production that will ensure that the firm will be producing at a maximum level of profit. Your fixed costs are at $57 and total variable costs are: TVC = Q + Q2 b) Confirm that the ideal production level that you arrived at above is a maximum. How much market share do you anticipate having? Your firm decides to expand into an overseas market where you are going to be the sole producer of this alloy. The demand curve for this market is P500 0.15QD c) Wha t will be your level of output under this scenario assuming that your rm's objective is to maximize profit? How do your results under this fi scenario differ from the one above? Is this what you expected? Why or why not? Who benefits and who suffers from these differences?

Explanation / Answer

(a) In market equilibrium, QD = QS

200 - 0.25Q = 25 + 0.75Q

Q = 175

P = 200 - (0.25 x 175) = 200 - 43.75 = 156.25

(b) Total cost (TC) = Fixed cost (FC) + TVC = 57 + Q + Q2

Marginal cost (MC) = dTC / dQ = 1 + 2Q

Firm maximizes proft by equating Price with MC:

156.25 = 1 + 2Q

2Q = 155.25

Q = 77.63

Market share = Firm output / Market output = 77.63 / 175 = 0.44 = 44%

Profit (Z) = TR - TC

TR = P x Q = 200Q - 0.25Q2

Z = 200Q - 0.25Q2 - 57 - Q - Q2 = - 1.25Q2 + 199Q - 57

For a maximum,

First order condition is dZ/dQ > 0.

dZ/dQ = - 2.5Q + 199 = - 2.5 x 77.63 + 199 = - 155.26 + 199 = 4.74 > 0

Second order condition: d2Z/dQ2 < 0

d2Z/dQ2 = - 2.5 < 0

Therefore, profit is maximum.

(c) In this case profit is maximized when Marginal revenue (MR) equals MC.

Total revenue (TR) = P x Q = 500Q - 0.15Q2

MR = dTR/dQ = 500 - 0.3Q

Equating with MC,

500 - 0.3Q = 1 + 2Q

2.3Q = 499

Q = 216.96

P = 500 - (0.15 x 216.96) = 500 - 32.54 = 467.46

Price is higher as well as quantity is higher compared to competitive equilibrium. This is because the demand curve is higher than the demand curve in competitive market, leading to both higher price and quantity.

Since price is higher than competitive outcome, consumers will lose as consumer surplus will fall, and producers will benefit as producer surplus will rise.

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