S. Klepper, Economics 73-100, Fall 2011
Solution to Mini-test 2
Following the hint, the 1990 budget line and an arbitrary point to represent the combination of food and clothing chosen in 1990 are denoted in the figure below.† Since Social Security recipientsí income increased sufficiently between 1990 and 2000 that they could just purchase in 2000 the same combination of food and clothing chosen in 1990, the 2000 budget line must pass through the 1990 consumption point.† With the prices of food and clothing not rising by the same percentage, one of the two intercepts of the budget line must have increased and the other decreased.† Since the price of clothing went up by a smaller percentage than the price of food, this implies that the clothing intercept must have increased, reflecting a rise in the maximum amount of clothing that could be purchased, and the food intercept must have decreased, reflecting a decline in the maximum amount of food that could be purchased.†
With the two budget lines crossing, Social Security recipients did not sustain an unequivocal change in their real income between 1990 and 2000.† However, since Social Security recipients could consume the 1990 consumption bundle in 2000, they must have been at least as well off in 2000 as in 1990.† The bundle chosen in 1990 must represent a point of tangency between an indifference curve passing through the 1990 bundle and the 1990 budget line.† The same indifference curve must pass through the 1990 bundle in the year 2000, but it cannot be tangent to the 2000 budget line, which has a different slope than the 1990 budget line.† Therefore, Social Security recipients would not purchase the 1990 bundle in the year 2000.† With the price of food going up by a greater percentage than the price of clothing, they could actually get to a higher level of utility in 2000 than 1990 by increasing their clothing consumption and decreasing their food consumption to take advantage of the fact that clothing is cheaper relative to food in 2000 than 1990.
Based on this description, the answers to the individual questions are: