DOC PREVIEW
UW-Madison ECON 101 - Problem Set

This preview shows page 1 out of 4 pages.

Save
View full document
View full document
Premium Document
Do you want full access? Go Premium and unlock all 4 pages.
Access to all documents
Download any document
Ad free experience
Premium Document
Do you want full access? Go Premium and unlock all 4 pages.
Access to all documents
Download any document
Ad free experience

Unformatted text preview:

Professor Scholz Posted: 11/03/2009 Economics 101, Problem Set #8 Due: 11/10/2009 Monopolies, Oligopolies, and Monopolistic Competition Please complete work on sheet and SHOW your work! Problem 1: Profit Maximization for a Monopolist In Madison, Charter Communications can be considered a monopolist in providing cable television services to local consumers. The market demand for cable television in Madison, WI is given by P=1,000-4QD. Charter’s cost curves are as follows: MC= 2q ATC=q. For the following subsections, assume that Charter is a rational profit maximizing monopolist. a.) Find the optimal quantity and price pair for profit maximization. By doing the following steps 1.) Find Charter’s associated Marginal Revenue Curve. (Hint: MR has the same equation as demand, except the slope is doubled) 2.) Find the quantity where Marginal Revenue equals Marginal Cost. 3.) Calculate how much consumers are willing to pay for this quantity. This is what Charter will charge. b.) Find the associated profit at the profit-maximizing (PM, QM) pair. c.) What is the consumer surplus at (PM, QM)? What is the producer surplus at (PM, QM)? d.) Now, assume Charter is no longer a monopoly in the local cable industry and instead acts like a perfectly competitive firm. What would price quantity pair (PPC, QPC) be in equilibrium? e.) What is Charter’s associated profit when it acts as in perfect competitor of each firm at (PPC, qPC)? f.) What is the consumer surplus at (PPC, QPC)? What is the producer surplus at (PPC, QPC)?g.) Is there a deadweight loss when we go from perfect competition to monopoly? If so, calculate this. Explain what happens to price and quantity when a monopoly, like Charter takes control of a local cable service. Question 2: Natural Monopoly Madison Gas and Electric (MGE) can be considered a natural monopoly in Madison, WI for electricity. MGE’s cost functions are as follows: ATC=105/q+24 and marginal costs are constant regardless of the quantity produced, MC=24. Market Demand for gas and electricity in Madison is given by P=80-4 QD. Q is measured in Kilowatt-hours (kWh) of electricity. a.) Graph the cost functions, demand curve, and marginal revenue curve all on one graph. b.) Now solve for the profit-maximizing quantity chosen by the monopolist. (Hint: Find the equation for Marginal Revenue and set this equal to Marginal Cost to find Q). What price will MGE charge per kWh of electricity? c.) Does MGE earn economic profit or incur a loss? Show this amount graphically. Now, let’s assume that MGE discovers some of its meters are faulty and they need to reinstall proper devices in over 100 Madison homes. This increases total costs for the company, and thus, MGE’s average total cost will also increase. The new ATC=350/q+40 but marginal costs remain constant (MC=24) as does aggregate demand. d.) Now graph the new average total cost curve with the original marginal cost, demand, and marginal revenue curves. e.) Calculate the new profit-maximizing quantity chosen by the monopolist, along with the price MGE will charge per kWh of electricity. Indicate these amounts on the graph. f.) Now, does MGE earn an economic profit or incur a loss? Show this graphically. g.) Explain how natural monopolies differ from regular monopolies. What is in the main difference in terms of costs?Problem 3: Marginal Revenue Curves for the Monopolist a.) Fill in the table Quantity Price Total Revenue Marginal Revenue 0 11 0 -- 1 10 3 8 4 7 6 5 7 4 9 2 10 1 b.) How much would this firm produce if their goal was to maximize total revenue? c.) Graph the Marginal Revenue and Total Revenue Curves on two separate graphs. Do this in a way that the Marginal Revenue graph is directly above the Total Revenue graph. Find the equation for the Marginal Revenue and then the equation for the Demand Curve. Add the Demand Curve to the graph with the Marginal Revenue curve. What do you observe about the relationship between Marginal Revenue when the Total Revenue curve is at its maximum? d.) Go back to the original table. Now assume there is a constant marginal cost equal to $4. How many units will this monopolist produce? What price will it charge? How much profit will it make? Question 4: You have a monopoly over the supply of your autograph (i.e. signature), which has suddenly become valuable to other people due to your newfound celebrity status as an economics 101 wizard. Assume that it costs you nothing to provide an autograph (i.e. no fixed or marginal costs) and that you would like to maximize your profit from giving your autograph out to people. Both men and women want your autograph, but each group has a different demand function for your autograph. Specifically, the demand function for men is given by MQ =8-P and the demand function for women is given by WQ =4-P.a.) What is the maximum profit you can obtain for your autograph? b.) Now assume that you cannot charge different prices for men and women (i.e. you must aggregate women’s and men’s demand and find the associated marginal revenue curve.) Now how much profit would you make? Compare this to the profit in part a. Question 5: Monopolistic Competition Assume that the market for luxury hotels in Las Vegas is monopolistically competitive. There are numerous firms in the market, but each has a slightly differentiated product. In particular, this means that each hotel has provides similar, but slightly different services. For instance, while both hotels provide the same general accommodations, the Bellagio features free gym access and wireless internet and the Palms offers complementary beverages and particularly attractive bellhops. If each hotel faces a demand curve of QD = 100-(1/2)P and a new hotel, The Bank wants to enter the market. Its Total Cost function is given by: TC=320+4Q+5Q2 and its Marginal Cost is given by MC=4+10Q. a.) Write down the equation for Marginal Revenue and the Average Total Cost for the new hotel. b.) Graph the demand curve, marginal revenue curve, and marginal cost curve. c.) What is the optimal quantity for The Bank to produce in the short run? d.) What is the associated price in the short run? e.) With the price and quantity you found in c) and d) how much profit is The Bank making? f.) What do you think is going to happen in the long run in this industry? Draw this on a new


View Full Document

UW-Madison ECON 101 - Problem Set

Documents in this Course
Exam 1

Exam 1

8 pages

Exam 1

Exam 1

8 pages

Load more
Download Problem Set
Our administrator received your request to download this document. We will send you the file to your email shortly.
Loading Unlocking...
Login

Join to view Problem Set and access 3M+ class-specific study document.

or
We will never post anything without your permission.
Don't have an account?
Sign Up

Join to view Problem Set 2 2 and access 3M+ class-specific study document.

or

By creating an account you agree to our Privacy Policy and Terms Of Use

Already a member?