5. (15 points) Suppose the total cost for a given firm is characterized by the f

Question

5. (15 points) Suppose the total cost for a given firm is characterized by the following equation: TC = 492 + 49 + 10 (marginal cost is given by MC = 89 +4). The firm operates on a perfectly competitive market with demand given by Pd 100- 2Q, where Q total quantity of production on this market. Assume thatl the firms on this market are identica.e. having the same total cost function ·Suppose the firm produces q = 4 Given that it behaves rationally in the short-run, what is the number of firms in the market? (Hint: Q = ng, where n-number of firms in the market.) ·Suppose the firm produces q = 1 . In the long run, what is the number of firms in the market? (Hint: look at the properties of long-run equilibrium.)

Explanation / Answer

1) If firm produces 4 units and acts rationally then it must be producing 4 units at point where MR meets MC.

MC at q = 4; MC = 8(4)+4 = 32+4 = 36

Thus MR = 36

And we know that under perfect competition, MR = price.

P = 100-2Q

36 = 100-2(Q)

Q = 64/2 = 32

Thus total output in industry is 32 units. As every firm produces equally then

Number of firms = Q/q = 32/4 = 8

There are 8 firms.

2) Under long run, there is no super normal profit, that is

TR = TC

If firm produces 1 unit, then TC = 4+4+10 = 18

TR = 18

and also TR = q*P

18 = 1*P

P = $18

now put this value into demand function

18 = 100-2Q

Q = 82/2 = 41

And hence,

number of firms = Q/q = 41/1 = 41 firms.

Related Questions

Navigate

• Browse (All)
• Browse 5
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.