Question

Question 2: Firm Heterogeneity Suppose that the demand curve is given by: Q = S(1/n - (P-P), where P=5,= 100, b = 0.1 and n = 10. Let us consider various firms with different marginal costs. (a) Derive the marginal revenue curve for the firm (MR(Q)). (b) Consider a firm with marginal cost c=3. What quantity does it produce in equilibrium? (c) Suppose that the country opens to trade. As a result, in the new equilib- rium we now have: S=200, n = 20 and P = 4. Does that firm (c= 3) increase its production Q? Explain. (d) Answer questions (b) and (c) for the firms with marginal costs c= 2 and c= 4. Explain the difference between the answers.

Answer 1

a.= Q=S(1/n-b(P-P*))

Q=100(0.1-0.1P+0.5)

Q=60-10P

R=P.Q

R=60P-10P^2

MR=60-20P

MC=3

Equilibrium condition=MR=MC

60-20P=3

57=20P

P=2.85

Q*=31.5

c. 200(0.05-0.1(P-4))

Q=90-20P

R=90P-20P^2

MR=90-40P

MC=3

MR=MC

90-40P=3

87=40P

P=2.175

NO firm will not produce

d. MC =4

MR=60-20P

MR=MC

60-20P=4

56=20P

P=2.8

Q*=28

60-10P=2

58=10P

P=5.8

Q*=2

MR=90-40P

MC=2

88=40P

P=2.2

Q*=68