Question

consider a market with inverse demand curve p=400-4Q.

costs per firm are given by C(q)= 16+10q+q^2

a) find the minimum efficient scale output level

b) in a competitive market , how many firms will be active in the long-run

c) suppose we have a cournot oligopoly with n firms . determine output of each firm and the equilibrium price

d) find the long run equilibrium number of firms if the market is a cournot oligopoly and entry occurs until profit per firm is zero

Answer 1

2 4 ) P=400-40, 6(9)= 16 +109 +92090 a) at MES, AG is Minimum AC=C/9 = 16/9 + 10 + q dace = -16.2 +4 =0, 9-4. Ang b.) In long run, P= Min Ac= 16 +10+4=$18 then total MKE olp demanded, at p=18 18= 400- 40 Q = 400-18)/4 = 95.5 , each from puro duces, 9=4 then Number of firms n= Qla = 95.5/4 = 23.875 ~ 24 firms And

c.) Cournot game, n firms, Q = + 2q = 4 + Q - V then To= pan-cow) = (400 - 494 - 48-i) W - 16-10 -4² I = (400 - 4Q i) W - 4002-16-104 qi² = (390-4Q-i) W - 590²-16. then Bri & ani = (390-4Q-1) - 100 =0. OU Y = 39- ,4 Qi as it is a symmetric Eqm, where q i = q ti. Q-2 = (n-1)q q= 39 - . 4 (n-1) q q=39- .4nq + - 49 .69 to An q = 39 19= 39.6+040). each from op - then Q = nq = 39n ang 706784n)

80 P = 400 4x39 (06 to 40) - 400 - 1560 To6 to 40) d.) LR Eq m * 8o when profit per from is zero, n î To= pq - Cac) P. - (940 +.160n-156n) = @40+4n) | (6 to 40) (66to4n) T= (240 +40) «39 - 16-10x39. . - (39) ² (o6to4n) 2 (o6taan) (66to40)2 => (240 +40) 39 - 16 (067o4n) 2 - 390 (56+o4n) —399 = 0. 8o. n= 53 firms Ang