Explain step by step 2. 12 pointsl The market demand curve in a competitive mark

Question

Explain step by step

2. 12 pointsl The market demand curve in a competitive market is given by QD-5,000-10P. The market supply curve is -2,000+15P a. What is the competitive market price? Show your work. b. If total cost for a representative individual firm is TC 20q 10q2, what is the marginal cost function Show your work. c. Determine the output that maximizes profit or minimizes losses in the short-term under the assumption of perfect competition. Show your work. d. What is economic profit at the optimum quantity level? Show your work.

Explanation / Answer

(a) In equilibrium, QD = QS

5,000 - 10P = - 2,000 + 15P

25P = 7,000

P = 7,000 / 25 = 280

Q = 5,000 - (10 x 280) = 5,000 - 2,800 = 2,200

(b) Marginal cost (MC) = dTC / dq

MC = 20 + 20q

(c) With perfect competition, Price = MC

Since Qd = 5,000 - 10P,

10P = 5,000 - Q

P = 500 - 0.1Q

Since a perfectly competitive firm is a price taker, price to a firm: P = 500 - 0.1q

Equating P with MC,

500 - 0.1q = 20 + 20q

20.1q = 480

q = 23.88

P = 500 - (0.1 x 23.88) = 500 - 2.39 = 497.61

(d) Economic profit = Total revenue - TC

= P x q - TC

= (497.61 x 23.88) - [(20 x 23.88) + (10 x 23.88 x 23.88)]

= 11,882.93 - (477.6 + 5,702.54) = 5,702.79

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