A monopolist sells travel services to two groups of people with the following

Monopoly, pricing, uncertainty and signaling:Problem Set #91. A monopolist sells travel services to two groups of people with the followingdemand curves Q1 = 100 – 2P1 (and MR1 = 50 – Q1) and Q2 = 60 – P2 (and MR2 = 60 –2Q2) . The marginal cost of providing one unit of travel service to either of thegroups is the same for the monopolist, i.e., MC = $10 per unit.(a) Identify whether group 1 or group 2 has more elastic demand.(b) If the monopolist can price discriminate, then what prices would the monopolistcharge the two groups for travel services? What quantities will the monopolistsell to each group?(c) Suppose the monopolist is forced to charge a single price to all consumersregardless of which group they belong to. What is the profit maximizing priceand quantity? Who benefits from this policy? Who loses?(d) What would be equilibrium price and quantity if the market was competitive?2. Suppose a monopoly can produce at any level of output it wishes at a constantmarginal (and average) cost of $5 per unit. Assume the monopoly sells its goods intwo different markets separated by some distance. The demand curve in the firstmarket is given by: Q1 = 55 – P1. And the demand curve in the second market is givenby: Q2 = 70 – 2P2. If the monopolist can maintain the separation between the twomarkets, what level of output should be produced in each market, and what pricewill prevail in each market? What are total profits in this situation?3. Suppose Sarah’s individual demand curve for the number of hours she would like toplay tennis per week is given by: Q = 10 – (0.1)*P, where Q is measured in hours andP is the measured in $ per hour. Suppose further that for the local tennis club themarginal cost of providing a tennis court is a constant $50 per hour. What is theoptimal two-part tariff solution to this problem? What are the profits that the tennisclub can earn by charging Sarah this two part tariff? If the tennis club could onlycharge an hourly rate how much would it charge Sarah? How much profit would itnow earn?4. Jill wants to rent a DVD but she has to decide whether to shop at the “Big Store” orat the “Small Store.” Jill doesn’t like to shop at the “Big Store” but they always havethe DVD she wants. On the other hand, she doesn’t mind going to the “Small Store”but there is a 20% chance that they don’t have the DVD she wants. Jill gets 50 Utilsof happiness if she gets to watch the DVD she wants, and looses 15 Utils if she shopsat the “Big Store.” Note that Jill doesn’t have time to go to both shops. Where shouldJill go to get her DVD? How valuable is it to Jill (in terms of Utils) to find outwhether the “Small Store” has the DVD she wants?5. A farmer’s tomato crop is wilting and he must decide whether to water it. If hewaters the tomatoes or if it rains, the crop will yield $1000 in profits; but if thetomatoes get no water, they will yield only $500 in profits. The operation of thefarmer’s irrigation system costs $100. The farmer’s goal is to maximize expectedprofits from tomato sales.(a) If the farmer believes that there is a 50% chance it might rain, should he water histomatoes?(b) What is the maximum amount the farmer would be willing to pay a weatherforecaster that predicts rain with 100% accuracy?(c) How would your answer to part (b) change if the forecaster is only 90% accurate?6. Two consumers are buying software and their reservation prices for the Spreadsheetsoftware and the Word processing software are given as follows:SpreadsheetWord ProcessingAmir’s WTP(Willingness to Pay orReservation Price)150100Glen’s WTPWillingness to Pay orReservation Price)100150Suppose that the marginal costs are constant at $10 for each package. Should we seta different price for Spreadsheet software and Word Processing software? Or shouldwe bundle them? What exact prices should we set?