Brief Principles of Macroeconomics...
Brief Principles of Macroeconomics...
Jamal has a utility function U = W1/2, where W is his wealth in millions of dollars and U is the utility he obtains from that wealth. In the final stage of a game show, the host offers Jamal a choice between (A) $4 million for sure, or (B) a gamble that pays $1 million with probability 0.6 and $9 million with probability 0.4.
a. Graph Jamal’s utility function. Is he risk averse? Explain.
b. Does A or B offer Jamal a higher expected prize? Explain your reasoning with appropriate calculations. (Hint: The expected value of a random variable is the weighted average of the possible outcomes, where the probabilities are the weights.)
c. Does A or B offer Jamal a higher expected utility? Again, show your calculations.
d. Should Jamal pick A or B? Why?
Sub part (a):
Diminishing marginal utility.
The utility function is
Figure 1 illustrates the diminishing marginal utility
Sub Part (b):
Expected value.
Sub part (c):
Expected utility.
Sub part (d):
greaterExpected utility.
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