Mark M. Upp has just been fired as the university book store manager for setting prices too low (only 20 percent above suggested retail). He is considering opening a competing bookstore near the campus, and he has begun an analysis of the situation

Question

There are two possible sites under consideration. One is relatively small, while the other is large. If he opens at Site 1 and demand is good, he will generate a profit of $50,000. If demand is low, he will lose $10,000. If he opens at Site 2 and demand is high he will generate a profit of $80,000, but he will lose $30,000 if demand is low. He also has decided that he will open at one of these sites. He believes that there is a 50 percent chance that demand will be high. He assigns the following utilities to the different profits:

U(50,000 ) = ? U(-10,000 ) = 0.22
U(80,000 ) = 1 U(-30,000 ) = 0

For what value of utility for $50,000, U(50000), will Mark be indifferent between the two alternatives?

Answer 1

Expected utility (Site 1 ) = 0.5X + 0.5(0.22 )
Expected utility (Site 2 ) = 0.5(1 ) + 0.5(0 ) = 0.50
Therefore: 0.5X + 0.5(0.22 ) = 0.50
or: 0.5X = 0.50 - 0.11 = 0.39
and: X = 0.39/0.5 = 0.78
Therefore, if Mark has U(50,000 ) = 0.78 he will be indifferent between the two alternatives.