The manager\'s utility function for profit is U(n) = 101n(), where is the dollar
ID: 1119384 • Letter: T
Question
The manager's utility function for profit is U(n) = 101n(), where is the dollar amount of profit. The manager is considering a risky decision with the four possible profit outcomes shown below The manager makes the following subjective assessments about the probability of each profit outcome: 3. Probability 0.05 0.10 0.35 0.50 Profit outcome Project A $1,000 $8,000 $12,000 $20,000 Profit outcome Project B $14,000 $14,000 $14,000 $14,000 a. What is the expected profit of Project A and Project B? b. What is the manager's expected utility of profit for Project A and Project B? c. If this manager is maximizing expected utility, which project will be chosen?Explanation / Answer
A) Expected profit of A = (0.05*1000) + 0.1(8000) + ... + 0.5(20,000) = $15,050
Expected profit of B = (0.05*14000) + 0.1(14000) + ... + 0.5(14000) = $14,000
B) Expected utility of profit of A = 0.05(10ln(1000)) + .... + 0.5(10ln(20,000)) = 3.45 + 8.98 + 32.87 + 49.52 = 94.82 utils
Expected utility of profit of B = 0.05(10ln(14000)) + .... 0.5(10ln(14000)) = 95.46 utils
C) Since EU of B is greater than A, the manager should chose B
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