30 Apr change in the profit of each firm rom (1 (iii) What is the percentage 4. (a) There is only one firm in a market. This firm has 100 plants, each produces according to cos function c(q) q2 The market demand is p = 18-100 Find the price, output and profit. (b) If each plant in (a) is now controlled by different owners and they behave competitively, find th 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, fin the market equilibrium, profit of each firm, consumers’ surplus, and welfare. 5. Consider a competitive market with identical firms. Each firm has a cost function with average co ACa)-(-2)+5. The market demand is p 8-100 (a) Find the deadweight loss if there are 100 firmsinthe market y 18-56) (b) How many additional firms are needed to achieve market efficiency? Why these additional firn are interested in this market?包50 (c) After the additional firms in (b) have entered the market, a firm with cost function c(g)-q also ent 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(q)-100+20q. The mark demand is p-200-q. Find the market price, each firm’s output and profit, consumers’ surplus, a DWL if (a) cartel, (b) Cournot model, (c) Stackelberg model, (d) Bertrand model. 7. Let the cost function of a monopolist be c(a)-100+20q. Find the market equilibrium, price elastici ofdemand atthe equilibrium, profit, and DWL if (a) market demand is p-100-qo (b) market demand is q-120-2p Iyaa toD 2
1. Let the production function beq Kili (K: capital, L: labor), the unit prices of capital and labor be both $1. (a) Find the cost function. 2b (b) If the firm with this production function is in a competitive market an many units of products should the firm produce? d the market price is S12, how 2. (a) Let the cost function be C(g)-F+mq G Is there economies of scale? (ii) If market price is equal to marginal cost, can the firm make profit? (b) Let the cost function be C(qi, q)-F+itqa (i) Is there economies of scope? (ii) If market prices are equal to marginal 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. (i) Find the market equilibrium, price elasticity of demand at the equilibrium, and each firm’s profit if the two firms choose output simultaneously and non-cooperatively. T, T, 91,322 60 7-u (i) Find the arkot quilbrium and.gch fim’s polit if the two firms choose output to maximize their joint profit. I(こ言に「-25. T’=aL (iii) What is the percentage change in the profit of each firm. from (i) to (i)? 4.0% 4. (a) There is only one firm in a market. This firm has 100 plants, each produces according to cost
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