Question

1. Let the production function beq(: capital, L: labor), the unit prices of capital and labor ba both SI 28 (a) Find the cost function. (b) If the firm with this production function is in a competitive market and the market price is $12, how many units of products should the firm produce? -6 2. (a) Let the cost function be C(ą)-F+mq (i) Is there economies of scale? (i) If market price is equal to margiial cost, can the firm make profit? ho (b) Let the cost function be C(qi, q-F+qi+q. (i) Is there economies of scope? (i) If market prices are equal to mdrginal costs, can the firm make profit? 1+ 3. Consider a market with 2 identical firms. Each firm has cost function c(q) q. The market demand is p-100-q () Find the market equilibrium, price elasticity of demand at the equilibrium, and each firm's profit if firms choose output simultan equilibrium and sach firm's profit if the two firms choose output to m (ii) Find the if the two firms choose output to maximi joint profit. (ii) What is the percentage c in the profit of éach firm from (i) to (p? 4. (a) There is only one firm in a market. This firm has 100 plants, each produces according to cost function c(q)"92. The market demand is P = 18-1 Find theprice, output and profit. 100 (b) If each plant in (a) is now controlled by different owners and they behave competitively, find the market price and market output (c) How much is the deadweight loss in (a)? (d) If the firm in (a) sells 40 plants to 40 different firms and these 40 firms behave competitively, find the market equilibrium, profit of each firm, consumers' surplus, and welfare. s. Consider a competitive market with identical firms. Each firm has a cost function with average cost AC(ą)-(q-2) +5. The market demand is p 8- (o) Find the deadweight loss if there are 100 fims in the market. ya18 (b) How many additional firms are needed to achieve market efficiency? Why these additional firms are interested in this market? s0 (c) After the additional firms in (b) have entered the market, a firm with cost function c(g) q also enter the market. What will be the equilibrium price and output level? 6. Consider a market with two identical firms. Each firm has a cost function c(a)-100+20q. The market demand is p-200-g. Find the market price, each firm's output and profit, consumers' surplus, and DWL if (a) cartel, (b) Cournot model, (c) Stackelberg model, (d) Bertrand model. 7. Let the cost function of a monopolist be c(ą)-100+20g. Find the market equilibrium, price elastici of demand at the equilibrjum, profit, and DWL if almarket demand is p-100-4"--ho. (b) market demand is q-120-2p 1.s 2 40D, S. There are two identical firms in the market. Each firm has cost function c(a)-24q and the market demand is p-60-q. The two firms are considering whether to produce at cooperative output level (cartel) or to set output level non-cooperatively (Cournot) (a) Find each firm's profit if () both firms choose to co-operate; P3b. 14 both firms choose not to co-operate one firm chooses to co-operate but another firm chooses not to co-operate. (b) Based on (a), find the market equilibrium if the firms set output levels simultaneously Customers are uniformly located along a street with unit length ( the left end is 0 and the right end is 1). Each of them wants to buy one unit of a good. The transportation cost of customers is c dollars per
4、5and 6 thanks

Answer 1

Answer 4. c(q)= q² , so the total cost function= 100q²

the market demand is, p= 18-q/100

so here, monopoly has its profit at MR=MC

dc(q)/dq= 200q= MC

MR= A-2BQ

MR=18-2q/100

so, MR=MC

2q= 18-2q/100

q= 9-2q/200

q+2q/200=9

202q/200=9

q_m=1800/202

q_m=8.910

p=9.089

c) For deadweight loss we have to calculate Qc

which is , MC=demand curve

2q=18-q/100

2q+q/100=18

201q/100=18

q_c=1800/201

q_c=8.955

DWL=1÷2 (P - MC) (Qc - Qm)

DWL= 1/2 (9.089-17.821)(8.955-8.910)

DWL=1/2*(-8.732)*(0.045)

=-0.19647

b) it can be solved by perfectly competetive market equillibrium condition by taking the number of firms=100