4. Suppose that an amusement park is a local monopoly. It has daily fixed costs of $30,000 and marginal cost ofzero. There are 1000 identical people who wish to visit the park each day. The preferences of a typical parkvisitor are defined over the number of rides x he "consumes" and the number of dollars m left in his pocket atthe end of the day. These preferences are represented by the utility function U(x,m) = 10 x -x14 + m. Supposethat each visitor comes to the park with l=200 dollars in his pocket.a. If p is the price of rides, what is a typical park visitor's budget constraint over bundles (x,m)?b. What is a typical park visitor's demand function for rides, x*(p)? Sketch this function in a graph, being sureto label the vertical and horizontal intercepts. What is the market demand for rides?c. Suppose the amusement park operates as a "simple" monopolist (i.e., charges a linear price for rides).What price, p*, will it set? (Depict p* in your graph.) How much profit, n*, will it earn? How muchconsumer surplus, CS*, will each consumer enjoy? How much per capita dead-weight loss is generated,DWL*?d. Suppose the monopolist practices second-degree price discrimination by charging each visitor an entry fee,4, and a price per ride of p. What price for rides, p**, will the park set? What entry fee, **, will it set?How much profit, a*, will it earn? How much consumer surplus, CS**, will each consumer enjoy? Howmuch per capita dead-weight loss will be generated, DWL**?

Utility function :U (x , m ) = 10x - x2/4 + m Income of visitors = 200 Price of ride (x) = p Price…

4. Suppose that an amusement park is a local monopoly. It has daily fixed costs of $30,000 and marginal cost of zero. There are 1000 identical people who wish to visit the park each day. The preferences of a typical park visitor are defined over the number of rides x he "consumes" and the number of dollars m left in his pocket at the end of the day. These preferences are represented by the utility function U(x,m) = 10 x-x14 + m. Suppose that each visitor comes to the park with I=200 dollars in his pocket. If p is the price of rides, what is a typical park visitor's budget constraint over bundles (x,m)? b. What is a typical park visitor's demand function for rides, r*(p)? Sketch this function in a graph, being sur to label the vertical and horizontal intercepts. What is the market demand for rides? c. Suppose the amusement park operates as a "simple" monopolist (i.e., charges a linear price for rides). What price, p*, will it set? (Depict p* in your graph.) How much profit, n*, will it earn? How much consumer surplus, CS*, will each consumer enjoy? How much per capita dead-weight loss is generated, DWL*? d. Suppose the monopolist practices second-degree price discrimination by charging each visitor an entry fee ill it

4. Suppose that an amusement park is a local monopoly. It has daily fixed costs of $30,000 and marginal cost of zero. There are 1000 identical people who wish to visit the park each day. The preferences of a typical park visitor are defined over the number of rides x he "consumes" and the number of dollars m left in his pocket at the end of the day. These preferences are represented by the utility function U(x,m) = 10 x-x14 + m. Suppose that each visitor comes to the park with I=200 dollars in his pocket. If p is the price of rides, what is a typical park visitor's budget constraint over bundles (x,m)? b. What is a typical park visitor's demand function for rides, r(p)? Sketch this function in a graph, being sur to label the vertical and horizontal intercepts. What is the market demand for rides? c. Suppose the amusement park operates as a "simple" monopolist (i.e., charges a linear price for rides). What price, p, will it set? (Depict p* in your graph.) How much profit, n, will it earn? How much consumer surplus, CS, will each consumer enjoy? How much per capita dead-weight loss is generated, DWL*? d. Suppose the monopolist practices second-degree price discrimination by charging each visitor an entry fee ill it

Principles of Economics, 7th Edition (MindTap Course List)

7th Edition

ISBN:9781285165875

Author:N. Gregory Mankiw

Publisher:N. Gregory Mankiw

Chapter15: Monopoly

Section: Chapter Questions

Problem 7PA

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