ECON 310 – Fall 2006. Chapter 5 – “The Theory of Demand.” “Review Questions” (pages 179-180): 1, 2, 3, 5, 7, and 8. “Problems” (pages 180-182): 5.1, 5.2, 5.5, 5.6, 5.8, 5.9, 5.10, 5.12, 5.15, 5.16, 5.17, and 5.19. Additional Questions: 1) Consider a consumer with demand for commodity one given by 1*12pIx = . Sketch the demand curve for this commodity supposing 000,1=I . Sketch the demand curve for this commodity supposing instead that 800=I . Based upon the curves you have drawn, does this good appear to be a normal or inferior good? Explain. 2) A consumer with }2,min{)(21xxXu= maximizes utility by consuming 21122ppIx+= and 2122 ppIx+=. Sketch the price consumption curve for a change in the price of commodity one. Based upon the shape of this curve, does commodity one appear to be an ordinary good or a Giffen good? Based upon the shape of this curve, does commodity two appear to be a substitute for or a complement to commodity one? Clearly explain. 3) Suppose demand is given by the linear function ppD 5100)( −= (for 200 ≤≤ p). a. Determine Consumer Surplus at a price of 15=p. b. Determine Consumer Surplus at a price of 10=p. c. In general, should Consumer Surplus increase or decrease as price increases? Are your answers to parts (a) and (b) consistent with this general insight? Explain. d. Determine Consumer Surplus as a function of p, for any arbitrary price 200 ≤≤ p. 4) Must a Giffen Good be an Inferior Good? Clearly explain why or why not. Must an Inferior Good be a Giffen Good? Clearly explain why or why not.5) A consumer with 221)( xxXu = maximizes utility by consuming 113pIx = and 2232pIx = . Suppose that 600=I and 12=p . a. Graphically illustrate demand for commodity one. Determine the quantity demanded of commodity one at 8ˆ1=p and 11=p . b. For the remainder of this question, consider a decrease in the price of commodity one from 8ˆ1=p to 11=p . b.i. Graphically illustrate the change in Consumer’s Surplus resulting from this price change. b.ii. Determine the value of the Equivalent Variation in income for this decrease in the price of commodity one. b.iii. Determine the value of the Compensating Variation in income for this decrease in the price of commodity one. b.iv. It can be shown that the increase in Consumer’s Surplus resulting from this price change is equal to 89.415)8ln(200≈=ΔCS . Do the values that you obtained for EV and CV seem consistent with this value for CSΔ? Explain why or why not. 6) Liam’s Income Consumption Curve is illustrated below. Based upon the shape of this curve, does either good ever appear to be “Inferior”? Explain. Alcohol 0 0 Cigarettes ICC7) Napoleon’s Engel Curve for Tater Tots is illustrated below. Based upon the shape of this curve, answer the questions below. a. If Napoleon’s income were to increase from $250 to $300, would his consumption of Tater Tots increase or decrease? Explain. b. Suppose Napoleon’s income were to increase from $750 to $800. Would this result in an increase or decrease in his demand for Tater Tots? Explain. c. Napoleon’s “income elasticity of demand for Tater Tots” is currently equal to 14.,−=TTIε. Could his income possibly be equal to $400? Explain why or why not. d. With income of $800, Napoleon would purchase 30 units of =1x (Tater Tots) and 680 units of =2x(all other goods). Is his Income Consumption Curve through the point ==),(21xxX (30, 680) positively sloped or negatively sloped? Explain. Income 0 0 Tater Tots TTE 500 36
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