# ECON 402 ECON402 Midterm 1 with Answers (Penn State University)

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ECON 402 ECON402 Midterm 1 Answer (Penn State University)

2. Suppose that P1,P2 together own a business whose proceeds are shared equally between P1 and P2. The firm’s profit is 2xy C 6x, where x is the effort exerted by P1 and y the effort exerted by P2. The cost to P1 of exerting an effort level x is x2 and the cost to P2 of exerting an effort level y is y2.

3. Suppose that a beach is divided into five regions, labeled A through E, with respectively 20, 20, 10, 30, and 20 people in it, where the regions are as indicated in the picture below.

Suppose that P1 and P2 simultaneously and independently have to choose a region to set up their lemonade stand. Suppose further that all people will purchase one cup of lemonade at a profit of \$1, purchasing from the stand in the region closest to them (with the lemonade stands equally splitting customers who are equally far away).

. Please consider the graph below with the best response curves for P1, P2, as indicated. Please indicate all rationalizable strategy profiles. Hint: it’s a rectangle but (if you prefer) you can alternatively indicate the strategies for each player that make up the rationalizable strategy profiles. [3]

5. Bonus question: Firm 1 produces nuts and firm 2 produces bolts. Each nut costs 1 cent to produce and so does each bolt. Consumers need one of each and their demand for one nut and oneboltis8.p1 Cp2/,wherep1 isthepricesetbyfirm1andp2 thepricesetbyfirm2

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