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Unformatted text preview: . Every day at school Debby eats tater tots (good 1), pizza (good 2), and soda (good 3). Her preferences
are u(X1,X2,X3)=min{5X,2X2,X3}. Prices are R =1, P2 = 3, and P3 =2. Suppose that the required level of utility is J =10. (10 points) a. What is her EMP (expenditure minimization problem)? b. In this speciﬁc case, what are (X; ,XZ' ,X ) , the solutions to the EMP? Hint: Your answer
should be numbers. C. In this speciﬁc case, how much is she Spending at this optimal bundle? Hint: Your answer should
be a number. 10. A consumer likes good 1 and good 2. Prices are P] and P2 , and income is m. The utility function is
u(X1,X2) = X,2 + X22. Suppose that we also know that P1 > 1’2. (10 points) a. What is the UMP (utility maximization problem)? b. What is the MRS? c. What is the optimal bundle, (X 1' JG), the solutiOns to the UMP? 11. The following graph depicts an increase inP1 . Is good 1 ordinary or Giffen? 39M 35 5094 ; 12. The following graph depicts a decrease in P1 . Point “A” is the initial bundle. Indifference curves are
linear; their slope is the same as that of the initial budget line. Draw and label bundles “B” and “C.” 90ml 3.
im‘h‘gl '
h"‘" F” [gala
mm {Jim W“ 500%! l 13. The expected utility function is U(c ,9) = (1 — 7011075 + 71'  cg” . Calculate the coefﬁcient of absolute
risk aversion to determine whether preferences are risk averse, risk~loving, or risk—neutral. 14. Multiple choice. Consider a lottery or gamble that entails winning $10 with probability 0.5 and winning
$2 with probability 0.5. Which of the following is evidence that a consumer is risk loving? (Please circle one response.) 1 1
a. 51400) + 5;;(2) > 14(3) 1 1
b. E u(10) + 511(2) > u(8) 0. $1410) + %u(2) < u(8) d. %u(10) + %u(2) < u(3) 15. In the insurance example, suppose the consumer’s expected utility function is
U (cl ,c2) : (1 —— 7T)  cI + 7r  c2 , and the price of insurance is greater than the probability of state 2, i.e. y > 7r. As before, c] = w — ya and c2 = w —ya — D + a , where w is income; D is the loss; and a is
the number of units of insurance. (10 points) a. What is the UMP (utility maximization problem)? b. What is the ﬁrstorder condition (FOC) with respect to a , the number of units of insurance? c. What is the optimal a ? ...
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 Fall '08
 NINKOVIC
 Microeconomics

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