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# Problem Set 1 Answers - Exercise 2A.2 Demonstrate how my...

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Exercise 2A.2 Demonstrate how my budget constraint would change if, on the way into the store, I had lost \$300 of the \$400 my wife had given to me. Does my opportunity cost of pants (in terms of shirts) or shirts (in terms of pants) change? What if prices of pants and shirts had doubled while I was driving to the store? Exercise 2A.3 How would my budget constraint change if, instead of a 50% off coupon for pants, my wife had given me a 50% off coupon for shirts? What would the opportunity cost of pants (in terms of shirts) be? Exercise 2A.4 Suppose that the two coupons analyzed above were for shirts instead of pants. What would the budget constraints look like? 2.1 Suppose my brother and I both go on a week-long vacation in Cayman and, when we arrive at the airport on the island, we have to choose between either renting a car or taking a taxi to our hotel. Renting a car involves a fixed fee of \$300 for the week, with each mile driven afterwards just costing 20 cents — the price of gasoline per mile. Taking a taxi involves no fixed fees, but each mile driven on the island during the week now costs \$1 per mile. A: Suppose both my brother and I have brought \$2,000 on our trip to spend on “miles driven on the island” and “other goods”. On a graph with miles driven on the horizontal and other consumption on the vertical axis, illustrate my budget constraint assuming I chose to rent a car and my brother’s budget constraint assuming he chose to take taxis. (a) What is the opportunity cost for each mile driven that I faced? (b) What is the opportunity cost for each mile driven that my brother faced? B: Derive the mathematical equations for my budget constraint and my brother’s budget constraint, and relate elements of these equations to your graphs in part A. (a) Where in your budget equation for me can you locate the opportunity cost of a mile driven? (b) Where in your budget equation for my brother can you locate the opportunity cost of a mile driven? 2.3 Suppose the only two goods in the world are peanut butter and jelly. A: You have no exogenous income but you do own 5 jars of peanut butter and 2 jars of jelly. The price of peanut butter is \$4 per jar, and the price of jelly is \$6 per jar. (a) On a graph with jars of peanut butter on the horizontal and jars of jelly on the vertical axis, illustrate

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