Assuming demand function is Qd = 850 - 5P Suppose there are 100 firms in a perfe

Question

Assuming demand function is Qd = 850 - 5P

Suppose there are 100 firms in a perfectly competitive industry. Suppose that an individual firm's cost function is given by C(q) = 2q2 + 2q + 32 (c) Illustrate the short-run equilibrium for a representative firm and the industry (d) Determine the consumers' and producers' surpluses at the equilibrium. (e) Explain what you would expect to happen to market price and output in this industry as we move to the long run. Explain what you would expect to happen to firm output and profits as we move to the long run.

Explanation / Answer

C. P = 850/5 - 1/5Q

P = 170 - 0.2Q

Q = nq where n is number of firms and q in firm 's output.

Q = 100*q

P = 170 - 20q

Mc = dTc/dq

Mc = 4q +2

Under perfect competition price is same as marginal revenue which is equal to marginal cost at equilibrium.

170- 20q = 4q +2

24q = 168

q = 7

Q = 100*7=700

P = 170 - 20*7

P = 170 - 140 = 30

D. Consumer surplus = area of triangle whose base is quantity and height is difference between maximum willingness to pay and price.

Cs = 1/2 * (170-30) * 700

Cs = 1/2 * 40*700 = 14000

Ps = area of triangle whose base is equilibrium quantity and height is price.

Ps = 1/2 * 30 *700 = 10500

E. In Long run firm's profits are zero.

Price remain same as 30 in Long run.

Long run output is determined at the minimumypoint of average cost curve which is same as marginal cost in Long run.

2q +2+32/q = 4q +2

32/q = 2q

q = 16

q = 4

In long run firm's output will decrease from 7 to 4..

Similarly, industry's output will also decrease from 700 to 400.

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