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Unformatted text preview: Problem Set 1  SOLUTIONS Question 1 Let s denote sacks of potatoes and y denote crocks herring. In this case prices are p s = 9 and p c = 5, while quantities demanded are s = 5 and c = 10. Since Lars spends his entire income on potatoes and herring, we can write down his budget constraint and solve for his income m : m = p s s + p c c = 9 5 + 5 10 = 45 + 50 = 95. The newly introduced subsidy of 5 crowns per sack of potatoes esentially reduced the price of one sack of potatoes to p s = 9 5 = 4, while the price of one crock of herring remains unchanged at 5 crowns. The new income tax reduces Lars income by 20 crowns each months, so him new income will be m = 95 20 = 75. Therefore, Lars new budget constraint is 4 s + 5 c = 75. Correct answer (4). Question 2 To graph Marys indifference curves, start with a diagram with avocados (A) on the horizontal axis and grapefruit (G) on the vertical axis. Along the 45 line, the quantities of A and G consumed are equal. Above the diagonal (where she consumes more G than A), her indifference curves are straight lines with a slope of 2 and the equation of the line is 2 A + G = k , where k > 0 is a constant representing an arbitrarily chosen utility level. Below the diagonal (where she consumes more A than G), her indifference curves are straight lines with a slope of 1 / 2, and the equation of the line is A + 2 G = k . The two segments of the indifference curve meet along the 45 line. In order for Mary to be indifferent between the bundles (14 , 20) and (26 , G ), both bundles have to be situated on the same indifference curve, since only along one indif ference curve is utility constant. The bundle with 14 avocados and 20 grapefruits is located on the segment above the 45 line. We need to determine is the bundle (26 , G ) is located above of below the diagonal. If (26 , G ) is located above the diagonal, then it must satisfy the equation 2 14 + 20 = 2 26 + G , from where G = 48 52 = 4 < 0 which is not possible, since Mary cannot consume negative quantities of grapefruit. Therefore, the bundle (26 , G ) must be situated on the segment below the 45 line, in which case the two bundles must satisfy the equation 2 14 + 20 = 26 + 2 G , from where G = (48 26) / 2 = 22 / 2 = 11. Correct answer (1)....
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 Summer '10
 IOANADAN
 Microeconomics

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