Question

If the incumbent can purchase new equipment: 1. he can either produce with the old equipment at marginal cost c =8, or 2 spend K = 5 for new equipment which cust its marginal cost to c = 6.

1. Market demand is given by p = 12 - Q. There are two firms: the incumbent firm (1) and the entrant firm (E). Incumbent moves first by choosing quantity q, from the interval [0,4]. The entrant observes q, and decides whether or not to enter and how much to produce if he enters (qe). There is no fixed cost of entry. If the entrant decides to stay out, his profit is zero and the incumbent enjoys a monopoly position. Suppose that both incumbent and entrant have identical marginal costs equal to c= 8.

Questions:

1. If the incumbent had purchased new equipment and anticipates entry, what quantity does he produce?

2. Will he enter the market?

3. What is the incumbent's payoff?

4. Will the incumbent choose to purchase new equipment in the first place?

Answer 1

Market demand, P= 12-0 Case I: When there is only single c=8, firm in comment, do T = PXQ - co = (12-0) Q - 80 ani - 12-20-8=0 12-8=20 [Q=2 P = 12-2 =10 T = 10x2 - 882 - 20-16 = $4 At stage 2, Case I, when there is entry of enterant, then we have a model ay stackelberg game. from 2 maximize their profit given the quantity of tiom I. 2 = (12-91-92) 92 – 892 - 1292-91 92-92 ² - 892 an = 12- 91 - 292 - 8 = 0 4-91 = 292 Best response 92-4-20 - bunction of fiom 2 2 Naw, at stage I fiom I try to maximize their profit. ni (12-91-92)9,- 891 - (12 - 91 -(4-2) 9. - 891

ni= 1291 - 9,² - (491-9; 2) - 891 d'ą - 12 - 291-(4-291) - 8 = 0 dar 12-291-2 +291-8=0 2 7 Q2 = 4.91 - 4 - 2 = 2 / Pe 12-91-92 = 12-2-1 = $9 Ti = 982 – 8X2 = 18-16 - $2 < 84 Az =(9- 8x1 = $9.8 = $1780 Case II: When Incumbent purchase new equibment TO=5+69... = Civen, q2 =4-91 11 = (12- 91 - 2 +91) 91 - (5 +69) = 1891 - 9,² + 9,2 – 5-69 ani = 10-291 + 91 - 6 = 0 14 = 91 2 . 091 & P = 12-4 = $8 in T = (884) – (5 +689) = 32-5-24 = $34 $4

6 he had do he had purchased how equipment, and anticipates enby then (Q = 9 units. 2. Eiherant can proo 3. Perant can produce o units. X2=0 in he is in different between entering or no entory Incumbent's payaff. If he anticipales entry, when c=8 » Ti= $2 When c=6 - Ti $3. when he is the single firm, T = $4. 9. To stop entry, he can choose the new equipment, bet if hers sure that Although, he is better off when he is a single biom, and C=8. but to give a threat to enterant, he must purchase new equipment since, A = $2 < $3 (with new equipment)
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