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Problem Set3

# Problem Set3 - BPUB250 Problem Set3 Due February 22-23 2012...

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BPUB250 Problem Set3 Due: February 22-23, 2012 in Class Question 1 Suppose Tom has \$20 and decides to go to the movies. A movie ticket costs him \$8. He can spend the rest of his money at the concession stand on popcorn ( c ) or Twizzlers ( t ). For this problem treat c and t as continuously divisible. Popcorn costs \$1/bag, and Twizzlers cost \$p/box. Tom’s utility function over popcorn and Twizzlers is: U(c, t) =6c 0.5 t 0.5 (a) Calculate Tom’s marginal rate of substitution. Calculate the demand functions for popcorn and Twizzlers as a function of p . For the rest of the question, assume that the original price of Twizzlers is \$3/box. Suppose Tom has a subsidy from the Movie Theater that gives him \$1 dollar off the price of each box of Twizzlers if he buys the movie ticket. He can buy as many boxes of Twizzlers with the subsidy as he can afford. (b) After the subsidy, how much money would Tom need to attain the same utility as he had when p=\$3? (c) Calculate the Compensating Variation. (d) Calculate also the Equivalent Variation. (e) How much would this subsidy cost the Movie Theater, assuming Tom is the only beneficiary? (f) Devise a program for the Movie Theater which spends the same amount of money, but makes Tom happier. Make sure you show calculations that demonstrate Tom is indeed happier under the new program.

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