10 An entrepreneur is considering building a new restaurant

10) An entrepreneur is considering building a new restaurant. She knows that if the restaurant is built and the economy improves there will be a profit next year of $70,000; if the restaurant is built and there is a recession, there will be a loss next year of $10,000. If she buys a particular established restaurant and the economy improves, there will be a profit of $40,000 next year; if she buys the established restaurant and there is a recession, there will be a profit of $8,000 next year. A) Construct a payoff table for the situation described above. B) For the situation above, find the expected profit of perfect information if the probability of a recession is 1/4. C) For the situation above, find the expected profit of perfect information if the probability of a recession is 1/3.

Solution

PAYOFF TABLE

X1 = RESTAURANT BUILT AND ECONOMY IMPROVES = +70,000

X2 = RESTAURANT BUILT AND RECESSION = -10,000

X3 = BUY RESTAURANT AND ECONOMY GROW = +40,000

X4 = BUY RESTAURANT AND RECESSION = -8,000

B) E(X) = X*P(X)+.....XN*P(XN)

HERE P (RECESSION ) = 1/4

GROWTH = 3/4

EXPECTED WHEN BUILD = 70000*(3/4) - 10000(1/4) = 50000

EXPECTED WHEN BOUGHT = 40000*(3/4) - 10000(1/4) = 27500

C) E(X) = X*P(X)+.....XN*P(XN)

HERE P (RECESSION ) = 1/3

GROWTH = 2/3

EXPECTED WHEN BUILT = 70,000*2/3 + 1/3*10,000 = 46666.66 - 3333.33 = 43333.33

EXPECTED WHEN BOUGHT = 40000*2/3 - 1/3*8000 = 26666.66 - 2666.66 = 24000