Question

5. Problems and Applications Q5 Four roommates are planning to spend the weekend in their dorm room watching old movies, and they are debating how many to watch. Here is their willingness to pay for each film: Willingness to Pay (Dollars) Kevin Rajiv Yakov Charles First film 10 9 6 3 Second film 9 7 4 2 Third film 8 5 2 1 Fourth film 7 3 0 0 Fifth film 6 1 0 0 Within the dorm room, the showing of a movie ( IS OR IS NOT ) a public good. If it costs $8 to rent a movie, the roommates should rent__________movies in order to maximize the total surplus. Suppose the roommates choose to rent the optimal number of movies you just indicated and then split the cost of renting equally. This means that each roommate will pay $__________. Complete the following table with each roommate's total willingness to pay for this many movies and the surplus each person obtains from watching the movies. Roommate Total Willingness to Pay Consumer Surplus (Dollars) (Dollars) Kevin ________ ________ Rajiv ________ ________ Yakov ________ ________ Charles ________ ________ In order to split the cost in a way that ensures that everyone benefits, the cost could be divided up based on the benefits each roommate receives. The practical problem with this solution is that each roommates has an incentive to ( UNDERSTATE OR OVERSTATE ) the value of the movies to him. Suppose they agree in advance to choose the efficient number and to split the cost of the movies equally. True or False: When Kevin is asked his willingness to pay, he will have an incentive to tell the truth. True False This examples teaches you that the optimal provision of a public good will occur if individuals ( DO NOT HAVE OR DO HAVE ) an incentive to hide their valuation of the good.

Answer 1

There are four roommates who are planning to spend their weekend watching movies in their dorm and they debate on the number of movies to watch. As dorm is a non-excludable and non-rival good within the dorm, the showing of movie is a public good Below table shows the marginal value for each film Willingness to Pay Dollars 2 Kevin YakovCharles Marginal Value RajIv 10 4 First Film 5 Second Film 6 Third Film 7 Fourth Film 8 Fifth Film 4 16 10 0 0 0 Below table shows the formula used for the calculation Willingness to Pay Dollars Kevin Rajiv Yakov Charles Marginal Value 4 First Film 10 5 Second Film 9 6 Third Film 8 7 Fourth Film 7 8 Fifth Film 6 B4+C4+D4+E4 B5+C5+D5+E5 B6+C6+D6+E6 B7+C7+D7+ B8+C8+D8+E8 If it costs S8 to rent a movie, the roommates will keep renting up to the point where their marginal value is greater than the price. Therefore they rent FOUR movies to maximized total surplus

As there are four roommates and four movies each roommate pays $8 in order to equal the cost of renting. Below table shows the total willingness to pay and consumer surplus: Total Willingness to Consumer Pay Surplus 2 Roommate (Dollars) (Dollars) 3 Kevn(10+9+8+7) 34 (34-8) 26 4 Rajiv 5 Yakov 6 Charles(3+2+1+0)6 (6-8)-2 (9+7+5+3) 24 (6+4+2+0) 12 (24-8) 16 (12-8)4 As Kevin has the greatest consumer surplus he would pay the greatest share this gives each roommate to understate the value of the movies to him. The given statement is TRUE. The optimal provision of a public good will occur if individuals DO NOT HAVE an incentive