4 Using the data in GPA3.RAW, the following equation was estimated for the fall and second semester students: trmgpa = -2.12 + .900 ersgpa + .193...
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Question

Mary has the utility function U(X,Y) = X2/3Y1/3, where X is the quantity of apples consumed, and Y is the quantity of oranges consumed. Let income be I = 90.


(a) Suppose that the price of apples is PXa = 2 and the price of oranges is PY = 2. What are the quantities of apples and oranges demanded when Olive maximizes her utility subject to her budget constraint?


(b) Suppose that the price of apples decreases to PXb = 1 and the price of oranges stays constant at PY = 2. What are the quantities of apples and oranges demanded by Olive after this price change?


(c) What is the substitution effect from the price change above? [Hint: what is the expenditure minimizing way of achieving the utility level in part (a) at the prices in part (b)?]


(d) What is the income effect from the price change above? [Hint: what is the difference between the total effect in part (b) and the substitution effect in part (c)?].


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Questions 7 refer to a consumer whose utility function is U=U(x,y)=xxy+x+2xy+2 where x and y are the quantities she consumes of the only two products X (food) and Y (entertainment) available to her. This consumer is always maximizing her utility subject to her budget constraint. Question 7 if the best affordable bundle for the consumer is (15*, y...) = (6, 3), that is, six (6) units of food and three (3) units of entertainment, then the relative price of food in terms of entertainment is exactly A. $0.50 B. 0.50 C. 52.00 D. 2.00 E. Not enough information is supplied to provide an answer

4 Using the data in GPA3.RAW, the following equation was estimated for the fall and second semester students: trmgpa = -2.12 + .900 ersgpa + .193 cumgpa + .0014 tothrs (.55) (.175) (.064) (.0012) [.55] [.166] [.074] [.0012] + .0018 sat - .0039 hsperc + .351 female - .157 season (.0002) (.0018) (.085) (.098) [.0002] [.0019] [.079] [.080] n = 269, R2 = .465. Here, trmgpa is term GPA, crsgpa is a weighted average of overall GPA in courses taken, cumgpa is GPA prior to the current semester, tothes is total credit hours prior to the semester, sat is SAT score, hsperc is graduating percentile in high school class, female is a gender dummy, and season is a dummy variable equal to unity if the student's sport is in season during the fall. The usual and heteroskedasticity-robust standard errors are reported in parentheses and brackets, respectively.

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