Answer keys for PS 3

Transcription

1 Econ0 nswer kes for S 3. Solution: Income = $50 (CDs) = $5 (CTs) = $5 a. X intercept= I = 50/5 = 0 Y intercept = I = 50/5 = 6 b. Slope= = - 5/5 = - 3/5 Budget constraint in slope- intercept form: = (-3/5) + 6 Concerts 6 Slope= -0/5= -/5 Slope = -5/5= -3/5 0 5 CDs. Solution: I = $400 (dinner) = $0 (movie) unknown Optimal bundle: $00 on dinners and $00 on movies MRS at optimal bundle = 0.4 a. The optimal bundle consists of positive amounts of both dinners and movies, so t ===> MRS = ===> 0.4 = 0 ===> = $50 b. Optimal bundle: Dinners = 00/0 = 0 dinners Movies = 00/50 = 4 movies Budget constraint line: Intercept on horizontal ais = Intercept on vertical ais = Slope= I = 400/0 = 0 I = 400/50 = 8 = -0/50 = -0.4

2 Econ0 movies nswer kes for S dinners c. Slope = -0.4 Intercept on vertical ais = 8 Jeff s budget constraint in slope-intercept form: = d. the price of dinner is $0, and the price of movie is $50, then to bu one more movie, ou have to spend $50 more on movie, that means, ou would spend $50 less on dinner, and the price of dinner is $0, so ou sacrifice 50/0=.5 dinners for one more movie. e. fter dinner s price increases, Intercept on horizontal ais = I ' = 400/5 = 6 New slope = ' = -5/50 = -/ The new budget constraint line pivots clockwise. Jeff can no longer afford his initial bundle (0, 4), since under new price, it would cost = 450 dollars. 3. Solution: a. Slope of indifference curve through = - ===> MRS= Bundle : 0 cups of coffee and 0 donuts Bundle B: cups of coffee and 9 donuts t bundle, MRS=: Dave is willing to give up donut and get cups of coffee in return. Bundle B means Dave gives up donut and gets cup of coffee as a compensation, which obviousl falls short of his requirement. ===> Dave prefers bundle to bundle B

3 Econ0 coffee nswer kes for S 3 B donut b. Slope of indifference curve through = -/ ===> MRS=/ Bundle : 0 cups of coffee and 0 donuts Bundle B: cups of coffee and 9 donuts t bundle, MRS=/: Dave is willing to give up donut and get / cups of coffee in return. Bundle B means Dave gives up donut and gets cup of coffee as compensation. ===> Dave prefers bundle B to bundle coffee B / donut c. Donuts and coffee are perfect complements on one to one basis Bundle : 0 cups of coffee and 0 donuts Bundle C: cups of coffee and 0 donuts coffee = C 0 donut

4 Econ0 nswer kes for S 3 Dave will feel indifferent between bundle and C as he alwas consumes donut with cup of coffee. Bundle C, compared to, has the same number of donuts, while one more cup of coffee. So Dave will still consume 0 donuts and 0 cups of coffee with the etra cup of coffee being useless. 4. Solution: I = $0,000 (voting machine) = $,000 (education program) = $500 = (5,0) Slope of indifference curve at bundle = -3 a. No. Bundle is not the optimal bundle for the state of Florida. Since consists of positive amounts of both goods, the condition for utilit maimization would require that MRS = at the optimal bundle. t bundle, MRS = 3, = 000/500 =, and this condition does not hold. b. The fact that MRS = 3 at bundle implies that Florida is willing to give up 3 education programs for an additional voting machine, and maintains the same level of utilit. The slope of budget constraint tells us that given its budget and the current prices Florida would onl have to give up education programs for an additional voting machine. If giving up 3 programs and gaining machine keeps Florida on the same indifference curve, then giving up programs and still gaining machine should put them on a higher indifference curve. Thus, Florida should be better off buing less education programs and more voting machine. Education programs 0 Slope=- MRS at = Voting machines c. I` = $5,000 X intercept: I = 5,000/,000 = 5 Y intercept: I = 5,000/500 = 30

5 Econ0 Education programs nswer kes for S new budget line slope of new budget line = slope of old budget line = Voting machines With the $5,000 grant from the federal government, the budget constraint would shift out parallell. d. Restricted grant: spent on voting machines onl. Education programs 30 0 new budget line slope of new budget line (when >5) = slope of old budget line = Voting machines 5. The vertical demand curve means that the quantit demanded for good X will not change as price changes. So in a standard diagram, the initial quantit demanded for X is X (point 0). When the price of X falls, the quantit demanded of X remains X (point ). Draw a line parallel to the new budget line and tangent to the original indifference curve. Denote the tangent point as. The substitution effect is ( X ), and the income effect is ( X ). We could infer with the decrease of price of good X, X is relativel cheaper and consumer would bu more X, so substitution effect ( X ) is positive. Then income effect ( X ) is negative. It is with the increase of income (budget constraint line changes from DE to C, the quantit demanded of X would decrease. So this good X with vertical demand curve is inferior goods.

6 Econ0 ll other goods nswer kes for S 3 D 0 X X B E C Good X