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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