Question

6. There are two firms in a market with marginal cost functions given by MC:(9) = 59 MC2(q) = q. Market demand is given by D(p) = 20 - 2p. (a) Obtain the competitive equilibrium output and price. Calculate consumer surplus and each firm's producer surplus. (b) Derive the monopoly price when only firm 1 operates. Calculate consumer surplus and each firm's producer surplus. (c) Derive the monopoly price when only firm 2 operates. (d) Now assume that a monopolist owns two plants with marginal costs MC(q), MC2(9) given above. Obtain the monopoly price and output.

Answer 1

(2) Fiart market: Pa mc is the condition & cal = 20-21 2p= 20-ų (p= 10-16 CS=05XBXH = 0.5x (10-4) (12) | = 6.5 x 6 x 12 = 0.5872 = 136 10-1B = 134 20-8 = ? 60-36=20 60 =50 18 = 12 P = 10-12 = 10-6 = 4 Second Market Pa mc 10_0.50 =ą 10 = 1.50 Ps= 0.5XBXH = 0.5(4-0) (12) = 6-5X4X12 = 0.58 48 = 24 Tols=0.5XBXH = 0.5610-bb) (6:66) = 11.12] 8 = 10 Ps= 0.5XBXH 7 = 0.5 x 6.66% 6.66 " = [6.66 P= 10-146 66 = [6.66 - [22.17

CS = 10.5X Clu-1:25) x7.5 P = 10-18 TR= (10-1B) x = 108 - 26 MR = d (108-16) 1 l -144.06 ) Ps= 7.5x25x0.5 + 7.5x3.75 = 37.5 = 10 & Ma=mca 10-B = 18 30-38 = 4 30 = 48 8=30 P= lo-0.5x7.5 = 6.25) ( MR=mc₂ 10-8 = 9 lo= 20 (8=0.5x2.5x5 - 6.25 7. 5 t 5t Ps= 5x580.5t 3 5 MR=105 7=5 Pa 10-0.5x5 = 7.5

a 7 Portal MC, x = 3mc t mc B = AMC MG = -a MA = мс. 10-8 = 0 40 - 418 = 8 40 =50 8 = 46 p= 10-18 = 10-248 - to - 4 1 = 6