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- Inverse elasticity rule Use the first-order condition (Equation 15.2 ) for a Cournot firm to show that the usual inverse elasticity rule from Chapter 11 holds under Cournot competition (where the elasticity is associated with an individual firm's residual demand, the demand left after all rivals sell their output on the market). Manipulate Equation 15.2 in a different way to obtain an equivalent version of the inverse elasticity rule: pMCp=sieQ,p , where si=qi/Q is firm i's market share and eQp is the elasticity of market demand. Compare this version of the inverse elasticity rule with that for a monopolist from the previous chapter.Assuming you are the managing director of a firm that produces three goods: A, Band C. The price elasticity of demand for A is 1.2, for B it is 1.00 and for C it is 0.75.It is known that he firm is experiencing serious cash flow problems and you have toincrease total revenue as soon as possible. If you were in a position to set the pricesfor these goods, what would be your pricing strategy for each product1. Given the demand function Q = 500 − 3P − 2PA + 0.01Y where P = 20, PA = 30 and Y = 5000, find (a) the price elasticity of demand (b) the cross-price elasticity of demand (c) the income elasticity of demand.If income rises by 5%, calculate the corresponding percentage change in demand. Is the good inferior or superior? (d) A monopolistic producer of two goods, G1 and G2, has a total cost function TC = 5Q1 + 10Q2 where Q1 and Q2 denote the quantities of G1 and G2 respectively. If P1 and P2 denote the corresponding prices then the demand equations are P1 = 50 − Q1 − Q2 P2 = 100 − Q1 − 4Q2Find the maximum profit if the firm’s total costs are fixed at Gh100. Estimate the new optimal profit if total costs rise to Gh101.
- 2) The diagram below gives the demand for a new pharmaceutical in both the US and in India. Find the profit maximizing price and quantity in both markets assuming the firm can perfectly price discriminate between markets. In reality, what is one reason why the firm may NOT be able to price discriminate, instead preferring to charge a single price in both markets? Dus MC MC DassaSuppose Ford currently sells 250,000 Ford Mustangs annually. The unit cost of a Mustang, including the -delivery cost to a dealer, is $16,000. The current -Mustang price is $20,000, and the current elasticity of -demand for the Mustang is 21.5. a. Determine a profit-maximizing price for a -Mustang. Do this when the demand function is of the constant elasticity type. Do it when the -demand function is linear. b. Suppose Ford makes an average profit of $800 from -servicing a Mustang purchased from a Ford dealer. (This is an average over the lifetime of the car.) How do your answers to part a change?3. Call Your Aunt is a monopoly seller of deli sandwiches. In DC, the demand curve is p = 16 In Maryland, it is p y Marginal cost is 4. = 12 100 100 (i) Find the profit-maximizing prices under third-degree price discrimination. (ii) Find the profit-maximizing uniform price. (iii) Now 14 – By, where B is a positive constant. Without calculating the new profit-maximizing uniform price, explain whether it is higher or lower than in (ii). suppose that Call Your Aunt starts to sell in Virginia. The demand curve is p
- 2. Suppose the cost function for a monopoly is given by TC =F+c.q where TC is the total cost, F is the fixed cost and q is the output of the firm. The demand function for the monopoly is given by q = A-bP where A > 0 and b > 0. Find out the profit maximizing price, quantity, and profit for the monopoly. Also find out the expression for the marginal revenue of the monopoly as well as the elasticity of demand facing the monopoly.The Hevishus Corp. (HC) is a profit-maximizing company that owns the only cement factory in Charleston, South Carolina, and is the only seller of cement in that area; it also owns the only cement plant in Portland, Oregon, and is the only seller of cement there. 1. Its statistician-consultant has determined that the elasticity of demand for cement in Portland is -3.50 and in Charleston is -2.25, and HC has priced its cement in accordance with this information. In which city does it charge a higher price for cement? Explain. 2. The mayor of Portland has levied a $250,000 annual factory fee on any cement factory in the city. Though it is not happy about the fee, HC pays it and continues producing and selling cement in Portland. How will the fee affect the price of cement that HC sells in Portland? Explain.Consumer H Consumer L Limited $50 $25 Pro $175 $100 5.Refer to the above table of consumer valuations for two versions of a software product. If the manufacturer of the software product hopes to exercise second degree price discrimination, what should be the incentive compatible prices for the Limited and Pro versions of the software? Is second degree price discrimination profit maximizing?
- 5. Consider a software company which has considerable market power over one of its products. The company sells its products online so the marginal cost is practically zero. (a) Show that the profit maximizing price-quantity combination is at the point on the demand curve that the price elasticity of demand is equal to 1. (b) Suppose that the inverse demand function is given by p = a - bq. Show that unitary elasticity is at the mid-point of the curve.4. You are the manager of a monopoly, and your demand and cost functions are given by P= 200-20 and C(O) = 2,000 + 30, respectively. a. What price-quantity combination maximizes your firm's profits? b. Calculate the maximum profits. c. Is demand elastic, inelastic, or unit elastic at the profit-maximizing price-quantity combination? d. What price-quantity combination maximizes revenue? e. Calculate the maximum revenues. f. Is demand elastic, inelastic, or unit elastic at the revenue-maximizing price-quantity combination?Question 4 A firm that can price discriminate wants to charge a high price to customers with O elastic, inelastic foreign, domestic O decreasing increasing O inelastic, elastic demand and a low price to customers with demand
