Economics Homework 3 Fall 2006 Stacy Dickert-Conlin

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1 Economics 0 - Homework Fall 00 Stacy Dickert-Conlin nswer Key. ndy collects baseball and football cards. The following graph shows a few of his indifference curves. The price of a pack of baseball cards is $, the price of a pack of football cards is $. ndy s allowance is $ a day. The price of baseball cards suddenly increases to $. ssume that ndy can buy less than whole packs of cards. a. On the graph below, draw ndy s original budget line and label it BC 0. lso put the label on his chosen consumption bundle. Label his initial indifference curve I 0. Before the price change: ndy consumes baseball cards and football cards. Equivalent loss in income Football Cards C B BC BCH income effect substitution effect total effect Baseball Cards BC0 I0 I b. On the graph, draw ndy s actual budget line after the price change and label it BC. Label his actual consumption bundle after the price change C and the new indifference curve I. fter the price change: ndy consumes 0. baseball cards and 9 football cards. c. On the graph, draw (as carefully as possible) ndy s budget line that reflects the substitution effect and label it BC H. (Hint: Use the new price ratio to reach the initial indifference curve). Label this intermediate consumption point B. With the substitution effect ONLY: ndy consumes. baseball cards and football cards. d. Does the substitution effect of the increase in the price of baseball cards make him buy more or less baseball cards? How many more or less? He consumes. fewer baseball cards (from to.) as a result of the substitution effect. Draw dashed horizontal lines (- - -) on your graph, one from to the horizontal axis, one from B to the horizontal axis and one from C to the horizontal axis. long the horizontal axis, label the income effect, the substitution effect and the total effect on the demand for baseball cards.

2 e. Fill in the blanks: The income effect of the increase in the price of baseball cards on ndy s demand for baseball cards is the same as the effect of a decrease in his income of $ per day. How do you know? The parallel shift that moves ndy from point B on IC 0 to point C on IC is equivalent to taking $ away from him. Look at the y-axis. On BC H the y-intercept is 9 (which is equivalent to $9 of income because the price of y is $.) On BC, the y-intercept is at (which is equivalent to $ of income because the price of y is $). f. Does the income effect make him consume more baseball cards or less? How many more or less? He consumes fewer (from. to 0.) as a result of the income effect. g. Can you tell whether football cards are a normal or inferior good? Can you tell whether baseball cards are a normal or inferior good? Why or why not? Both goods are normal goods because from B to C (the income effect) the consumption of both fell. h. On the following graph, using the information given above, plot two points on ndy s Marshallian demand curve for baseball cards and connect them. Label this D marshallian : When the price was $/pack, ndy bought, when the price increased to $/pack, he only bought 0. (see points and D above). Price of Baseball Cards $ C B D marshallian D hicksian Packs of Baseball Cards i. On the above graph, using the information given above, plot two points and connect them on ndy s Hicksian demand curve for baseball cards. Label this D Hicksian, Briefly explain the difference. The Hicksian demand curve ignores the substitution effect. It only reflects the fact that baseball cards got relatively more expensive. So, consumption would fall from to..

3 . Critically evaluate the following statements and explain in what way are they true, false, or uncertain. a. Suppose Kelly consumes only two goods, books-ontape and coffee mugs and she has typical U-shaped, convex indifference curves. If the price of books-ontape is $ and the price of coffee mugs is $ and Kelly s marginal rate of substitution for books-ontape in terms of coffee mugs is, she could increase her satisfaction by consuming fewer books-on-tape and more coffee mugs. ( graph is strongly advised.) In this case, Kelly s MRS = > the price ratio = /=. In other words, the benefit of an additional book on tape is more than the cost of an additional book on tape. The slope of the indifference curve is greater than the slope of the budget constraint. This would occur at a point like. Kelly should consume more books on tape in order to make herself better off. b. If the price of a good decreases and the quantity demanded increases, this implies that the good is normal. Coffee mugs T Books on tape False. This is just the law of demand. If the price decreases, the quantity demand increases for all goods. We can only tell if a good is inferior by knowing what happens when income increases or decreases. Or, by decomposing the total effect from a price change into the income and substitution effect. >> C Total effect, P decrease Q of S increases >> B Substitution effect B >> C Income effect - S is inferior C B I I 0 S

4 c. For a budget spent entirely on two goods, an increase in the price of one will necessarily decrease consumption of both, unless at least one of the goods is inferior. Your answer is not complete without a diagram. False. In the diagram below, an increase in the price of X leads to a reduction in the amount of X consumed, but an increase in the quantity of Y. In addition, you can see from B to C, which shows the income effect, that both goods are normal goods. That is, when the consumer feels the impact of the decline in income she consumes fewer X and Y. See question for another example. B Y C Y 0 I 0 BC 0 BC I X X 0

5 . Martha likes consume goods in an extremely well-balanced manner. In fact, for new home decor item she buys, she insists on creating exactly simple meals to go with it. Suppose she has an income of $0. The price of each home decor item is $0 per unit and the price of each meal is $0 per unit. a. On the graph, draw Martha s budget line, labeling it BC 0, and plot at least indifference curves Perfect Complements! b. How many new home decor items will Martha demand in this situation? How many new meals? Show your answer graphically ND algebraically (Hint: You have two equations and two unknowns. One equation tells the relationship between her consumption of home decor items and meals; the second equation is the budget constraint.) () Preferences: Y = X () BC: Y = -X Sub () into () Y = -(Y) and solve: Y = Y =, therefore X =. Labeled Point Q of Home Decor Items (Y) BC0 IC IC BCH BC =B C IC IC Q of Meals (X) Income effect= total effect c. Suppose the price of home decor items increases to $0 per unit. Graphically illustrate Martha s new optimal consumption point (including budget constraint and indifference curve). () Preferences: Y = X 0 0 () BC: Y = X = X 0 0 Sub () into () and solve: Y = ( Y) Y = Y = X = Labeled point C! d. What is the substitution effect from this price change? There is no substitution effect. Because these are perfect substitutes, the only point that touches the original indifference curve (IC in my diagram), that reflects the new prices is the original point! e. re meals and home decor items inferior or normal? Explain. They are both normal. The total effect is the income effect because the substitution effect is 0. When she moves from B to C, her purchasing power has fallen and you consume less of both.

6 f. Sketch Martha s Marshallian and Hicksian demand curves from the information above. P $0 D hicksian $0 D marshallian 0 Q of Home Décor Items

7 . Since losing his housekeeping job, Tony lives alone. He often has leftovers after cooking and he wraps them in aluminum foil. s far as he is concerned, square feet of generic aluminum foil is equivalent to square foot of Reynolds Wrap. That is, any job that can be done with square foot of Reynolds Wrap requires square feet of the generic brand to be done as well. Tony has $ to spend on aluminum foil. roll of Reynolds Wrap costs $ and a roll of generic aluminum foil is $. a. Graphically illustrate Tony s budget constraint and label it BC 0. b. Show at least of Tony s indifference curves. Perfect substitutes, therefore, straight line indifference curves with a MRS of ½ (slope of /) c. How much of each kind of aluminum foil will Tony use? Fully explain. Label this point on the graph. Because the indifference curves are linear with a slope different than the slope of the budget constraint, Tony will never reach a tangency. He will choose a corner solution on the highest indifference curve still touching the budget constraint. In this case, he will consume rolls of Reynolds Wrap and no generic luminum foil. This is at Point on the diagram. BC 0 and IC 0. Q of Reynold Wrap luminum Foil (Y) BC0 IC 0 IC IC Q of Generic luminum Foil (X) d. Suppose the price of Reynolds Wrap increases to $/roll and the price of generic aluminum foil remains at $/roll. Will he buy more generic aluminum? Carefully explain. If not, at what point will he buy more generic aluminum? In this case, the MRS and the opportunity cost of another roll of generic aluminum foil are both ½. This means that Tony can afford any point along BC and he is indifferent between any point along BC, because his indifference curve(ic ) lies along the same line. The price of Reynolds Wrap must be at least times the price of generic aluminum foil before Tony buys any of it. 0 Q of Reynold Wrap luminum Foil (Y) BC IC Q of Generic luminum Foil (X) 7

8 e. Return to the initial prices (Reynolds Wrap is $/roll and generic aluminum foil is $/roll). Suppose Tony receives a coupon from his grocery store for $ that can be used only on rolls of generic aluminum foil. Explain graphically ND verbally how, if at all, this coupon will alter Tony s decision, relative to part c. The new budget constraint is kinked (similar to the food stamp example) because the coupon can t be used on Reynolds Wrap but it is just like cash for generic aluminum foil. In this case, the best Tony can do is at point S where he uses the entire $ gift certificate for rolls of generic aluminum foil and uses his remaining $ for rolls of Reynolds Wrap. Q of Reynold Wrap luminum Foil (Y) S BC0 IC coupon BC coupon Q of Generic luminum Foil (X) f. Describe Tony s demand function for generic aluminum foil as a function of general prices and income. Let the prices of generic aluminum foil and Reynolds Wrap aluminum foil be p G and p RW, and let income be M. Using this notation, fill in the blanks. If p RW > p G, then the number of Reynolds Wrap foil he will demand is 0. If p RW < p G, then the number of Reynolds Wrap foil he will demand is M p answer should have letters in it). RW. (Hint: this If p RW = p G, he will be indifferent between any affordable combinations. (Hint: a number fills this blank.)

9 . Consider the following proposal to encourage energy conservation in East Lansing. Suppose that the city authorities placed a tax on each unit of electricity used by city residents. However, in order not to make people worse off the city gives each family a rebate check so that they can purchase the same combination of electricity and all other goods as before the tax was imposed. a) Using an indifference curve diagram illustrate the effect of the entire proposal on the consumption of electricity (x) and all other goods (y). Y Z BC tax IC tax+rebate IC 0 BC tax and rebate BC 0 E tax and rebate E 0 Electricity b. Will electricity consumption necessarily go down? Why or why not. The quantity of electricity demanded must decrease. t the original point, the MRS on IC 0 doesn t change after the policy is implemented, but the opportunity cost of electricity (slope of the budget constraint) is higher after the policy. This implies that the benefit of one more unit of electricity at Point is the same, but the cost is higher after the policy. Point can t be a tangency any longer and the consumer should consume less electricity in order to increase his/her satisfaction (move to point Z on IC tax+rebate ). c) Would the tax alone assure a reduction in electricity? Why or why not? Yes. The amount of the decrease depends on whether electricity is a normal or inferior good. If it is a normal good, the reduction in electricity consumption will be greater than if it is an inferior good because the income and substitution effects will work together. Graphically this would be shown by drawing the indifference curve tangent to BC tax. d) Will consumers be better or worse off after the tax and rebate proposal? Explain. Consumers are definitely better off because they are on a higher indifference curve. Their new budget constraint, BC tax and rebate intersects their old consumption point ND their old indifference curve. The consumers can definitely reach a higher indifference curve. e) Is there a way the government can get people to consume less electricity, make them no worse off than they were previously, and spend less money on rebates? Explain. Yes, just give them enough of a rebate (income effect) to get back to IC 0. This BC would be parallel to BC tax and rebate, but at a slightly lower level. Can you imagine how difficult this would be to do in principle? 9

10 . Suppose that you were considering offering a transfer of $00 a month to low income individuals. However, you are concerned about how they might use it in particular, you want to reduce the opportunity for them to use the transfer for social bads - like alcohol, tobacco, and illicit drugs. To reduce the opportunity to use it on these bads you can either give them the transfer as a Food Stamp (which must be used to purchase food) or a Rent Stamp (which must be used to pay a rent or mortgage). ssume the average recipient spends a small portion of their monthly budget on food ($00) and a large portion of their monthly budget on rent ($00) in the absence of the transfer. a. If you want to minimize how much they spend on social bads discuss whether it matters if the transfer is in the form of a Food Stamp rather than a Rent Stamp. Explain and support your answer using the figures provided. Y = Other Goods Y = Other Goods BC cash BC vouchers Y cash Y voucher Y no coucher I cash I voucher Y voucher or cash I no voucher Y no voucher I voucher or cash BC 0 BC vouchers I no voucher or cash BC 0 H no voucher H voucher Housing F no voucher F voucher Food F cash Housing Voucher: For an individual who was already spending a large share of income on housing the vouchers have the same effect as cash. ssuming they are both normal goods, the family will consume more of both goods. Food Voucher: Individuals who spends a small share of their income on food will also buy more food and Y with the voucher. BUT, if they had cash, they would buy even more Y and less food than with the voucher. The the budget constraint with cash gives the individual more satisfaction (higher indifference curve), than the BC with a voucher. Note that in both cases, the voucher does not prevent an increase in the consumption of "other goods". In the food voucher case, vouchers do minimize the amount spent on other goods, relative to cash. b. Is a black market in vouchers like to emerge in both markets? How would this affect your answer? black market is likely to arise in the food voucher market because consumers are happier with the cash than with the voucher. 0