# Chapter 5 End of Chapter Review Question KEY

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2 Column Column Column Column Column Units Units Units Units No. of of A MU of B MU of C MU of D MU \$ saved MU 9. 0 / / / a. What quantities of A, B, C, and D will Ricardo purchase in maximizing his utility? b. How many dollars will Ricardo choose to save? c. Check your answers by substituting them into the algebraic statement of the utility-maximizing rule. (a) units of A; units of B; units of C, and 0 units of D. (b) Save \$. (c) /\$ = /\$ = /\$ = /\$. The marginal utility per dollar of the last unit of each product purchased is. - (Key Question) You are choosing between two goods, X and Y, and your marginal utility from each is as shown below. If your income is \$9 and the prices of X and Y are \$ and \$ respectively, what quantities of each will you purchase to maximize utility? What total utility will you realize? Assume that, other things remaining unchanged, the price of X falls to \$. What quantities of X and Y will you now purchase? Using the two prices and quantities for X, derive a demand schedule (price-quantity-demanded table) for X. Units of X MU x Units of Y MU y 0 Buy units of X and units of Y. Marginal utility of last dollar spent will be equal at (= /\$ for X and /\$ for Y) and the \$9 income will be spent. Total utility = (= 0 + for X plus for Y). When the price of X falls to \$, the quantity of X demanded increases from to (income effect). Total utility is now (= for X plus for Y). Demand schedule for X: P = \$; Q =. P = \$; Q =. - How can time be incorporated into the theory of consumer behaviour? Explain the following comment: Want to make a million dollars? Devise a product that saves Americans lots of time.

4 part of the rent. Where individual meters have been installed, water usage has declined 0 to 0 percent. Explain this drop, referring to price and marginal utility. The way we pay for a good or service can significantly alter the amount purchased. An individual living in an apartment complex who paid a share of the water expense measured by a central meter would have little incentive to conserve. Individual restraint would not have much impact on the total amount of water used. Suppose there were 0 apartments in the complex, each apartment would be billed for one-tenth of the cost of the water. A single litre of water would carry a price equal to one-tenth the amount charged by the water district. The very low price per litre would encourage the use of water until the marginal utility of an additional litre was correspondingly low. If the tenants paid separately for their own water, the full market price of water would be considered when making their consumption choices. -9 Using the utility-maximization rule as your point of reference, explain the income and substitution effects of an increase in the price of product B, with no change in the price of product A. The utility-maximization rule compares the marginal utilities per dollar of goods under consideration (in this case A and B). An increase in the price of product B would reduce the marginal utility per dollar of B. This would discourage consumption of B, and with a pure income effect, would not alter consumption of A. If the increased price of B caused the marginal utility per dollar of the last unit of B to fall below the MU/\$ of the next unit of A, we would expect the consumer to substitute A for B in consumption (substitution effect). -0 A vice president of a company argues that the president of the company should raise workers wages if the president wants less absenteeism. The president says that wages probably should be cut so that the workers could not afford to miss so much work. Evaluate the two views using the income and substitution effects in your analysis. The analysis must be based on the idea that most workers prefer leisure to working for the president of the company. Therefore, the higher their income, the more leisure they can afford (income effect). On the other hand, the higher their wage, the more costly it will be to give up an hour of work, and the less leisure time-off they will substitute for work (substitution effect). The income and substitution effects tend to work in opposite directions. If the income effect outweighs the substitution effect, then the vice president is wrong. Paying the workers more will enable them to work shorter hours and earn enough to afford their added leisure despite the partly offsetting effect of the substitution effect that has made leisure more expensive per hour. If the substitution effect outweighs the income effect, then the vice president is right and the president is wrong. Paying the workers less will cause them to work fewer hours because they don t lose as much for each hour not worked. The effect of the lower income will partially offset the lower price of leisure, but not enough to cut the rate of absenteeism. In fact, absenteeism may increase.

5 Either could be correct. The solution depends on the strength of the income and substitution effects for the workers, and that, in turn, depends on many factors such as their present income status, the opportunities for using one s leisure time, and so on. - Use marginal-utility analysis to explain why the growing popularity of ipods over portable digital CD player. The improved technology of the ipod in terms of storage and portability created a higher marginal-utility-to-price ratio (=MU/P) than the ratios for alternative products. This shifted spending away from those products toward ipods in order to increase total utility. Because the marginal utility to price is quite low, consumers only purchased one ipod. - (Advanced analysis) A mathematically fair bet is one in which a gambler bets, say \$00, for a 0 percent chance to win \$000 dollars (\$00 =.0 x 000). Assuming diminishing marginal utility of dollars, explain why this is not a fair bet in terms of utility. Why is it even less fair a bet when the house takes a cut of each dollar bet? So is gambling irrational? Because the marginal utility of money diminishes the more you have, the utility of the \$00 used to make the bet is greater than the \$00 that you might gain (\$000 - \$900) if you win the bet. It is even less of a fair bet when the house takes its cut, because the \$00 bet has the possibility of yielding less than \$00 in winnings. Maybe. The activity of gambling may provide enough extra utility to offset the poor utility odds of winning. - (Advanced analysis) Let MU a = z = 0 - x and MU b = z = -y, where z is marginal utility measured in utils, x is the amount spent on product A, and y is the amount spent on B. Assume the consumer has \$0 to spend on A and B; that is, x + y = 0. How is this \$0 best allocated between A and B? How much utility will the marginal dollar yield? The consumer should spend \$ on A and \$ on B. The marginal dollar will yield utils. Proof: Substitutingin z 0 x, z 0 Substituting in z y, z (Answer to the Last Word) People at buffets put more on their plates and eat more the greater the variety of items they have to select from. How does this relate to the idea that diminishing marginal utility must be understood in context? Many people by to much on their credit cards, even though they know they will be sorry when they get their credit card bill. Relate this fact to the idea of time inconsistency. The greater the variety may reduce the rate at which diminishing marginal utility sets in because the goods are consumed together and there is more choice. This does not imply that diminishing marginal utility does not apply. The consumption of the good occurs immediately after the purchase of the good with a credit card (or quicker than), but the payment is in the future. This may result in time inconsistency if the individual does not fully internalize the future cost.

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