The Green Company produces chemicals in a perfectly competitive market. The tota

Question

The Green Company produces chemicals in a perfectly competitive market. The total cost is given by C- 100+4Q+Q2 Write down an equation for the firm's supply curve in terms of price P. a. bal fims in this iduatry write w a eor the industy'" supply curve in terms of price P Suppose the market demand curve is given by: Q-1280-20P. Find the market price in the short run. How many units will each firm supply at this price? The market? Find the firm's profit. c. d. Complying with more stringent environmental regulations increases the firm's fixed cost from S100 to $144. Would this affect the firm's output? Profit? Its Supply curve? What is the equilibrium price in the long-run? e.

Explanation / Answer

a). Solution :- C = 100 + 4Q + Q2

Marginal cost (MC) = 4 + 2Q

Price (P) = 4 + 2Q (Marginal cost = Price for the perfectly competitive firm).

Conclusion :- P = 4 + 2Q (Supply curve equation)

b). Solution :- Industry supply curve equation is as follows :-

P = 40 * (4 + 2Q)

P = 160 + 80Q

Conclusion :- P = 160 + 80Q (Industry supply curve equation)

c). Solution :- Q = 1280 - 20P

20P = 1280 - Q

Divide the above equation by 20.

P = 64 - 0.05 Q (Inverse market demand curve equation)

  P = 160 + 80Q (Industry supply curve equation)

Equating inverse market demand curve equation and industry supply curve equation,

64 - 0.05 Q = 160 + 80Q

(-) 80Q - 0.05Q = 160 - 64

(-) 80.05Q = 96

Q = (-) 96 / 80.05

Q = (-) 1.20 Units (Units can not be in negative, accordingly, ignore negative sign.)

P = 64 - 0.05 * 1.20

P = 64 - 0.06 = $ 63.94 (approx).

Conclusion :- Market price in short-run = $ 63.94, Quantity of product supplied by each firm = 1.20 units.

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