he only 9. Serena is a single-price, profit-maximizing monopolist in the sale of her own patented perfume, whose demand and marginal cost curves are as shown. (LO4, LO5, LO6) in por- d runs f eight shown o fixed is $12 60 МС AN 50 45 8.1 Th tab 40 no 30 20 15 Annual 10 Fixed c Variable MR Total co 0 4 6 8 12 16 24 harge Ounces/day Averag how What per 9 day 8.2 W a. Relative to the consumer surplus that would resul at the socially optimal quantity and price, how much consumer surplus is lost from her selling a the monopolist's profit-maximizing quantity and We its? and of tom- m es to duce 1 he price? re b. How much total surplus would result if Serena th could act as a perfectly u price-discriminating monopolist? $ per ounce E

he only 9. Serena is a single-price, profit-maximizing monopolist in the sale of her own patented perfume, whose demand and marginal cost curves are as shown. (LO4, LO5, LO6) in por- d runs f eight shown o fixed is $12 60 МС AN 50 45 8.1 Th tab 40 no 30 20 15 Annual 10 Fixed c Variable MR Total co 0 4 6 8 12 16 24 harge Ounces/day Averag how What per 9 day 8.2 W a. Relative to the consumer surplus that would resul at the socially optimal quantity and price, how much consumer surplus is lost from her selling a the monopolist's profit-maximizing quantity and We its? and of tom- m es to duce 1 he price? re b. How much total surplus would result if Serena th could act as a perfectly u price-discriminating monopolist? $ per ounce E

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter15: Imperfect Competition

Section: Chapter Questions

Problem 15.10P: Inverse elasticity rule Use the first-order condition (Equation 15.2 ) for a Cournot firm to show...

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Use the accompanying graph to answer the questions that follow. (LO1, LO2) a. Suppose this monopolist is unregulated. (1) What price will the firm charge to maximize its profits? (2) What is the level of consumer surplus at this price? b. Suppose the firm’s price is regulated at $80. (1) What is the firm’s marginal revenue if it produces 7 units? (2) If the firm is able to cover its variable costs at the regulated price, how much output will the firm produce in the short run to maximize its profits? (3) In the long run, how much output will this firm produce if the price remains regulated at $80?
As the manager of a monopoly, you face potential government regulation. Your inversedemand is P = 40 − 2Q, and your costs are C(Q) = 8Q. (LO1, LO2, LO6)a. Determine the monopoly price and output.
6. The accompanying diagram shows the demand, marginal revenue, and marginal cost of a monopolist. (LO1, LO3, LO5) a. Determine the profit-maximizing output and price. b. What price and output would prevail if this firm’s product were sold by price-taking firms in a perfectly competitive market? c. Calculate the deadweight loss of this monopoly. 8. The elasticity of demand for a firm’s product is –2.5 and its advertising elasticity of demand is 0.2. (LO8) a. Determine the firm’s optimal advertising-to-sales ratio. b. If the firm’s revenues are $40,000, what is its profit-maximizing level of advertising?
A monopolist’s inverse demand function is P = 150 − 3Q. The company produces out- put at two facilities; the marginal cost of producing at facility 1 is MC1(Q1) = 6Q1, and the marginal cost of producing at facility 2 is MC2(Q2) = 2Q2. (LO1, LO8) a. Provide the equation for the monopolist’s marginal revenue function. (Hint: Recall thatQ1 +Q2 =Q.) b. Determine the profit-maximizing level of output for each facility. c. Determine the profit-maximizing price.
V5. You are the manager of Taurus Technologies, and your sole competitor is Spider Technologies. The two firms' products are viewed as identical by most consumers. The relevant cost functions are C(Qi) = 2Qi, and the inverse market demand curve for this unique product is given by P =290 - 3Q. Currently, you and your rival simultaneously (but independently) make production decisions, and the price you fetch for the product depends on the total amount produced by each firm. However, by making an unrecoverable fixed investment of $500, Taurus Technologies can bring its product to market before Spyder finalizes production plans. (Assume Taurus Technologies is the leader in this scenario.) What are your profits if you do not make investment? What are your profits if you do make investment? Instructions: Do not include the investment of $500 as part of your profit calculation. Should you invest the $500? no or yes
4. You are the manager of a monopoly, and your demand and cost functions are given by P = 300 − 3Q and C(Q) = 1,500 + 2Q2, respectively. (LO3, LO4) 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? 6. The accompanying diagram shows the demand, marginal revenue, and marginal cost of a monopolist. (LO1, LO3, LO5) a. Determine the profit-maximizing output and price. b. What price and output would prevail if this firm’s product were sold by price-taking firms in a perfectly competitive market? c. Calculate the deadweight loss of this monopoly. 8. The elasticity of demand for a firm’s product is –2.5 and its advertising elasticity of demand is 0.2.…
You are a pricing analyst for QuantCrunch Corporation, a company that sells a statistical software package. To date, you only have one client. A recent internal study reveals that this client’s inverse demand for your software is P=1500-5Q and that it would cost you $1,000 per unit to install and maintain software at this client’s site. What is the profit that results from two-part pricing? (Hint: set the per-unit price for each unit of the software installed and maintained equal to marginal cost; and charge a fixed “licensing fee” that extracts all consumer surplus from the client)
Suppose you are the economic adviser ofa company producing three brands of mobile pnones;Nokia 10, Samsung X and iPhone 7. Suppose further that, your company currently sells 120units of iPhone Z at e800 per unit, 150 units of Samsung X at e800 per unit and 200 units ofNokia 10 at e100 per unit, but in a bid to maximize profit, the company's managing directorproposes an increase in price of Samsung X from e800 to e1000 per unit for which quantitydemanded is anticipated to fall from 150 to 100 units; iPhone Z from e800 to e 1200 per unitfor which quantity demanded is anticipated to fall from 120 to 100 units; and Nokia 10 from100 to 200 per unit for which quantity demanded is expected to fall from 200 to 100 unitsUsing the mid-polint formula. compute the price elasticity of demand for each brand.From your answer in i, what is the type and economic interpretatiom of each brand'sii.value of elasticity.
Assume that annual inverse demand for a particular product is P=150-Q. The product is offered by a pair of Bertrand competitors, each with marginal costs of $75. The discount factor is 0.9. What is the current equilibrium price and total surplus? Now, assume though that if R&D is conducted at rate x, it incurs one-off costs of r(x)=10x^2 and reduces the marginal costs to (75-x). Suppose that one firm decides to conduct R&D at rate x=10. This research will be protected by a patent of T years. a) What profit(ignoring the one-off costs of R&D) does the innovating firm make each year during the period of patent protection? b) What is the new equilibrium price and total surplus once patent protection expires? c) Use your answer above to write the total surplus from the innovation
Two firms with the same (constant) marginal costs are engaging in Bertrand competition. One of the companies exits the industry. As a aconsequence, the price for the other firm increases by 50%. What is the elasticity of demand in this market?O. 3O. 2O. 2.5O. 4
While there is a degree of differentiation between major grocery chains like Albertsons and Kroger, theregular offering of sale prices by both firms for many of their products provides evidence that these firmsengage in price competition. For markets where Albertsons and Kroger are the dominant grocers, thissuggests that these two stores simultaneously announce one of two prices for a given product: a regularprice or a sale price. Suppose that when one firm announces the sale price and the other announces theregular price for a particular product, the firm announcing the sale price attracts 1000 extra customers toearn a profit of $5000, compared to the $3000 earned by the firm announcing the regular price. Whenboth firms announced the sale price, the two firms split the market equally (each getting an extra 500customers) to earn profits of $2000 each. When both firms announced the regular price, each companyattracts only its 1500 loyal customers and the firms each earned $4500 in…
4. You are the manager of a firm that produces products X and Y at zero cost. Youknow that different types of consumers value your two products differently, but you are unable toidentify these consumers individually at the time of the sale. In particular, you know there arethree types of consumers (100 of each type) with the following valuations for the two products: Consumer Type Product X Product Y1 $90 $ 602 $70 $1403 $40 $160 a. What are your profits if you charge $40 for product X and $60 for product Y?b. What are your profits if you charge $90 for product X and $160 for product Y?c. What are your profits if you charge $150 for a bundle containing one unit of product X andone unit of product Y?d. What are your profits if you charge $210 for a bundle containing one unit of X and one unit ofY, but also sell the…