please answer the whole question, thx

2. (32 pts) Imagine a market with a monopoly in a small country. Govern- ment decides to fight the high prices of the monopolist allowing the entry of a fringe of price taking firms. Market demand is Q = 10 -p, the monopolist can produce at a constant marginal cost c = 2 and fringe is known to have a suply curve Qs = p - 2. a. (8 pts) Find the price the monopolist was setting and the Government decided to fight. Find the quantity sold at this price and the welfare loss. Max (p-2)(10-p) gives py = 6, QM = 4 and WL = (10-6)(10 -6) = 8. b. (7 pts) Faced with entry of the fringe the monopolist behaves as a domi- nant firm. Compute the new optimal price and quantity sold by the dominant firm. Draw a diagram of the market and represent the old monopolist and the new dominant firm equilibrium. Residual demand is QR = 10 -p - (p - 2) = 12 - 2p. Max (p -2)(12 - 2p) gives p= 4 and Q" = 4. Graph is standard. c. (6 pts) What is the quantity sold in the market by the fringe? What is its market share? QS =4-2 = 2 and Q = QD +Qs =4+2 -6, so the fring market share is SF = = = 0.33. d. (5 pts) What is the producer surplus of the fringe? (notice that the cost of production of the firnge is different from the cost of the dominant firm). Variable cost of the fringe is the area below its supply curve: VC = (2 - 0) (2 + 4) = 6, and hence PSF = R- VC =4 x 2 -6 =2. e. (6 pts) Somebody argues that there is a loss in productive effiency because of the higher cost of the production carried out by the fringe. Government asks you to show in response that total welfare has increased. Why welfare increases if there is a loss in effiency? CSD = (10 -4) (10 - 4) = 18 and CSM = (10 -6)(10 -6) = 8. On the other hand PSP - (4-2)4 - 8, PSF = 2 (see above) and PSM = (6-2)4 = 16. Hence AW = ACS +APS = (18 -8) + (8+2-16) = 10 -6 = 4. Because the gains in allocation efficiency are greater than the looses in productive efficiency