Download Econ Problem Set 4: Income Curve, Budget Constraints, & Consumer Surplus and more Assignments Microeconomics in PDF only on Docsity! Tea Other Income consumption curve Price of tea falls Level of tea consumption increases 0 100 200 300 400 0 5 10 15 20 25 Leisure L ab or Kink in budget line Slope = -20 Slope = -10 Economics 323H Professor Gronberg Fall 2007 Problem Set 4 - Answer Key 1. 5.20) a) If the income consumption curve is vertical the utility function has no income effect. This will occur, for example, with a quasi-linear utility function. This utility function will have the same marginal rate of substitution for any particular value of tea regardless of the level of total utility. If the price of tea falls, flattening the budget line, the consumer will reach a new optimum where the marginal rate of substitution is equal to the slope of the new budget line. Since the budget line has flattened, this cannot occur at the previous optimum amount of tea. The substitution effect implies that this new optimum level of tea will be greater than the previous level. Thus, when the price of tea falls, the quantity of tea demanded increases, implying a downward sloping demand curve. This can be seen in the following figure. b) Yes, the values will be exactly $30. When the income consumption curve is vertical, the consumer's utility function has no income effect. As stated in the text, when there is no income effect, compensating and equivalent variation will be identical and these will also equal the change in consumer surplus measured as the change in the area under the demand curve. 5.21) a) 0 100 200 300 400 0 5 10 15 20 25 Leisure L ab or 12 160 Because the wage rate changes for any hours worked over eight (leisure less than sixteen) the budget line has a kink at sixteen hours of leisure. b) With this set of indifference curves, the consumer reaches an optimum at 12 hours of leisure and 12 hours of labor, or $160 of income. 5.22) If Terry's wage rate is w, then the income he earns from working is (24 - L)w. Since PY = 1, the number of units of other goods he purchases is Y = (24 - L)w. Now at an optimal bundle, Terry's MRSL,Y must equal the price ratio w/PY = w. Therefore, the tangency condition tells us that . The two conditions Y L w 1+ = imply w(1 + L) = (24 + L)w. This means that the optimal amount of leisure is L = 11.5. You can see that this does not depend on the wage rate. 2.
