3. Suppose there are ten identical firms in an industry. The cost function for each firm is: 1 c(y) = y² + wy where y is the firm's output of the homogenous good, and where w is the wage rate of workers in the industry. Suppose further that w = 1.9Qs, where Qs denotes total industry output. (a) Find the industry supply function assuming symmetry. (b) Suppose market demand is QD = 6 p, where p is the output price. Find the price, market quantity, wage rate, and total surplus in equilibrium. (c) Now suppose that the government imposes a unit excise tax of $1. What happens to the equilibrium price, market quantity, and total surplus in this case?
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- A market consists of a dominant firm and a number of fringe firms. The followings are the information about these firms. Total market demand: QALL=300 – (2.5) P The competitive fringe supply function (total): QF=2P-12 The dominant firms marginal cost function: MC = 12 + (1⁄2) QD. a) What is the equilibrium price set by the dominant firm? b) How much will the competitive fringe supply to the market at the price found in question (a)? Show the answers graphically.Consider an imperfectly competitive service provider, Muscat Automotive Repair Services (MARS), whose total cost of production is C = 30Q +0. 165Q2. Also, MARS faces two different market segments, A and B, whose demands can be linearly expressed as QA = 240 − PA and QB = 120 − 0.5PB . (Hint: the marginal cost is the slope of the total cost function). 4. If MARS decides to segment the market in accordance with the demands of groups A and B, find the profit-maximizing prices and quantities (PA, QA) and (PB, QB).5. What is the value of the consumer surplus for each group A and B, under this segmentation strategy?6. Draw the situation described in (4) and (5) above, clearly showing each group’s profitmaximizing price and quantity, and the areas that correspond to their consumer surpluses.7. Verify the inverse elasticity rule under each of the scenarios described (1) and (4) above.Market Failures in Imperfect Competition Efficiency in exchange is satisfied with the equality between MRS and price ratios of the goods. Efficiency in production is satisfied with the equality between MRTS and the price ratios of factor markets (labor and capital; hence, wage and rent). Efficiency in product mix is normally not satisfied under imperfect competition because MRS is not equal to MRT. Answer the following: a. If there is an imperfect competition in both the goods market (X and Y), say that Px/Py is both under monopoly, is it possible for economic efficiency to be reached? How? Explain in words and mathematically. b. If there is an imperfect competition in both the two factor market (L and K), say that w/r or Pl/Pk is both under monopoly, is it possible for economic efficiency to be attained? How? Explain in words and mathematically.
- a) when w1 = 8 and w2 = 9, derive the supply function y(p) for Pot & Gold Inc b) Suppose that Pot & Gold Inc has to pay a quasi-fixed cost of $50. When w1 = 8 and w2 = 9, derive the supply function y(p) for Pot & Gold Inc1. Let a firm’s cost function be c(y1, y2) = F + αy1y2 + y21 + y22, where α is some constant.a) What restriction on α is required to guarantee that this cost function exhibits economies ofscope?b) What restriction on α is required to guarantee that this cost function exhibits cost complementarities in both goods? Note that you’ll need to verify cost complementarities for y1 andy2.2. Given the industry demand function X(p) = 100 − 2p, consider the following scenarios:• The market is a perfectly competitive market. Assume there are identical firms with marginalcost of 12 in this perfectly competitive market.• The market is dominated by one monopolist with a marginal cost of 12. This monopolist isable to achieve 1st degree pricing.• The market is dominated by one monopolist with a marginal cost of 12, but the monopolistis able to achieve only 2nd degree pricing. Assume the menu offers only 2 choices:(Q∗1 = 30, p∗1 = 35), and (Q∗2 = 60, p∗2 = 20).• The market is dominated by one monopolist…PakMonoG’s inverse demand function is P = 100 – 2Q and cost function is TC = 10 + 2Q, where Q is quantity in units and P price in PKR. Determine the profit-maximizing price, quantity and profit (or loss) of PakMonoG. If we were to compare PakMonoG with a perfect competitive firm in the market, are there differences in characteristics of the two structures? What are welfare implications? Is total societal welfare of the firm higher or lower than that of a competitive firm?
- 1. Imagine that there is an industry for a particular product where the demand for this product is given by P = 100-X. There are two factors of production, capital K and labor L; the price of each will be $1 throughout. The firms all have identical technology, which is given by a fixed coefficients production function: where Y is the level of output and a is some constant from (0, 1). Each firm has fixed costs of 16. (a) Suppose there are precisely six firms in this industry; they can exit if they are unprofitable, but no firms can enter. What is the long-run equilibrium in this case? (Even though there are only six firms, they all entertain competitive conjectures about their effect on various prices.) (b) Suppose there is free entry into this industry. What is the long-run equilibrium? 2. Suppose one firm in a general equilibrium economy has a technology with free disposal Prove that Walrasian equilibrium prices are nonnegative.Signaling. There are two firms, A and B. There are two time periods, 1 and2. There is one commodity, that can be produced by both firms, at linear cost. So,if firm i has marginal cost i, then the cost of producing q units of the commodity is ciq. The inverse demand for the commodity, at any given moment, is 100 − 4Q,where Q is the aggregate supply at that moment.In period 1, firm A is alone in the market. Firm A’s marginal cost is determinedby Nature, either it is 10 or it is 2, each with probability 1/2. A knows it’s cost.Firm A produces some quantity in period 1 and firm B observes this. Betweenperiods 1 and 2, firm B decides to enter the market or not. After making thisdecision, B is told firm A’s cost. It is too late at this point for B to change itsaction.In period 2, if B is in the market, then A and B compete on quantity.(1) In words, what are the steps to solving this problem?(2) There are two possible quantity-competition games that happen in this game.Solve them both.(3) Now…A market consists of a dominant firm and a number of fringe firms. The followings are the information about these firms. Total market demand: QALL=300 – (2.5) P The competitive fringe supply function (total): QF=2P-12 The dominant firms marginal cost function: MC = 12 + (1⁄2) QD. a) What is the equilibrium price set by the dominant firm? b) How much will the dominant firm supply to the market at the price found in question (a)? Show the answers graphically
- Answer b and c Road Runner Co is a Pakistani manufacturer making Bicycles. It exports to two markets,Bangladesh and Sri Lanka. Demand for Bicycles in thesetwo markets is given by the following Functions: Bangladesh Q1 = 12 – P1 Sri Lanka Q2 = 8 – P2 Where Q1 and Q2 are respective quantities sold (in thousands) andP1 and P2 are the respective prices (in Pak. Rupees per unit) in the two markets. Total cost function is C = 5 + 2 (Q1+ Q2) a. Determine the company’s total profit function. Also, (i) What are the profit maximizing levels of price and output for the two markets? (ii) Calculate the marginal revenues in each market. b. Now consider two cases: (i) Company is effectively able to price discriminate in thetwo markets. What will be the total profits? (ii) Suppose the company does not engage in price discrimination. By charging thesameprice in the two markets what are the profit maximizing levels of price,output, and the total profits? c. Analyze,…A purely competitive firm has a single variable input L (labor), with the wage rate W0 per period. Its fixed inputs cost the firm a total of F dollars per period. The price of the product is P0. (a) write the production function, revenue function, cost function, and profit function of the firm. (b) What is the first-order condition for profit maximization? Give this condition an economic interpretation. (c) What economic circumstances would ensure that profit is maximized rather thatn minimized?Suppose both cooperatives are price-takers; with PG=12 and PF =10 being the market prices of gold and fish respectively. The cost of producing G units of gold is cg(G,x)=G2+(x−4)2; where x is the quantity of mercury effluent discharged into the dam. The cost of producing F units of fish is cF(F,x)= F2 + xF ; where cF(F,x) is an increasing function of x. a) Determine the profit maximizing level of gold output, profit and level of mercury effluent discharged into the dam. Comment and explain your results. b) What is the fishing cooperative’s profit maximizing level of fish output and profit? Explain your results. c) Suppose the two cooperatives were merged to operate as a single firm; determine the socially optimal level of gold and fish output, mercury effluent and profit. Explain, comment on and contrast your results with those obtained in a and b above. d) Suppose property rights to the dam water are created and assigned to the fishing cooperative. Does this induce efficiency and…