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Alex and Ben each have preferences over hours spent playing darts (good x 1 ) and hours spent playing pool (good x 2 ) at
Alex and Ben each have preferences over hours spent playing darts (good x 1 ) and hours spent playing pool (good x 2 ) at their local pub that can be described by the utility function U(x 1 ,x 2 )=(x 1 1)(x 2 1). One can show (by solving their utility-maximization problems) that both Alex and Ben have demand functions for the two activities of: x 1 = 2p 1 Mp 1 p 2 , if p 1 M p 2 and x 1 =0, if p 1 >M p 2 x 2 = 2p 2 M p 1 p 2 , if p 2 M p 1 and x 2 =0, if p 2 >M p 1 Suppose that p 2 =1 and that their incomes for spending on pub games are M=9 for Alex and M=5 for Ben. What is Ben's reservation price for darts (i.e., the value of p 1 at and above which Ben demands zero hours of darts)? p 1
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