Problem Set 5 (Answers) PDF

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notes for ECN 110...

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ANSWERS TO QUESTIONS AND PROBLEMS FROM CHAPTER 6

Questions 1. Complete the following table and answer the questions below:

a. At which rate is total utility increasing: a constant rate, a decreasing rate, or an increasing rate? How do you know? b. ―A rational consumer will purchase only one unit of the product represented by these data , since that amount maximizes marginal utility.‖ Do you agree? Explain why or why not. c. ―It is possible that a rational consumer will not purchase any units of the product represented by these data.‖ Do you agree? Explain why or why not. Answer: Missing total utility data, top – bottom: 18; 33. The missing total utility for the second unity can be found by adding the marginal utility (change in utility) to the total utility for the first unit. By consuming the second unit, 8 more units of utils are added; thus total utility is 18 (= 10 + 8). Missing marginal utility data, top – bottom: 7; 5; 1. The missing marginal utility values are found by subtracting the total utility for the previous unit consumed from the total utility of the unit with the missing value (the change in utility). The marginal utility for the third unit is 7, which equals 25 (total utility for the third unit) minus 18 (total utility for the second unit). (a) A decreasing rate; because marginal utility is declining. (b) Disagree. The marginal utility of a unit beyond the first may be sufficiently great (relative to product price) to make it a worthwhile purchase. Consumers are interested in maximizing total utility, not marginal utility. (c) Agree. This product’s price could be so high relative to the first unit’s marginal utility that the consumer would buy none of it. 2. Mrs. Simpson buys loaves of bread and litres of milk each week at prices of $1 and 0.80 cents, respectively. At present she is buying these two products in amounts such that the marginal utilities from the last units purchased of the two products are 80 and 70 utils, respectively. Is she buying the utilitymaximizing combination of bread and milk? If not, how should she reallocate her expenditures between the two goods? Answer: Mrs.Simpson is not buying the utility-maximizing combination of bread and milk because the marginal utility per cent spent on each good is not equal. The marginal utility per cent of bread is 0.8 (= 80 utils/100 cents); the utility per cent of milk is 0.875 (= 70 utils/80 cents). Mrs. Simpson should buy more milk and less bread.

3. How can time be incorporated into the theory of consumer behaviour? Explain the following comment: ―Want to make millions of dollars? Devise a product that saves Canadians lots of time.‖ LO 6.2 Answer: Time is money. This expression is a time-saving way of making the point that for a person who can make so much per hour, every hour spent not working is so much money not made. A person can be said to ―consume‖ a ball game or an evening at the theater. If the ball game costs $10 and the theater $20, at first sight one could say the ball game is a better deal. But if the person makes $20 an hour and is forgoing this in taking the time off, then we must take into account the time spent at the ball game and at the theater. If the ball game goes into extra innings and takes 4 hours, then its total cost is $90 (= $10 + $80). If the theater takes 3 hours, its total cost is $80 (= $20 + $60). Assuming the marginal utility of the ball game and attending the theater are the same, the theory of consumer behaviour (with time taken into account) would therefore have this consumer going to the theater. 4. Explain what is meant by the following statements: a. Before economic growth, there were too few goods; after growth, there is too little time. b. It is irrational for an individual to take the time to be completely rational in economic decision making. c. Telling your spouse where you would like to go out to eat for your birthday makes sense in terms of utility maximization. Answer: (a) Before economic growth, most people lived at the subsistence level. By practically anyone’s definition, this implies ―too few goods.‖ After economic growth, goods are in relative abundance. To make (or consume) more takes time, but the relative abundance of goods means that there are already many goods to enjoy. So, now there is a clash between the use of time to make more goods and the use of time to relax and enjoy the goods one already has. There just isn’t enough time. (b) To be completely rational in economic decision making, provided one does not take time into consideration, one has to take account of every factor. This would take a great deal of time. One could not, for example, make any purchase without first searching the classifieds to see whether a better deal could be had, rather than simply heading for the nearest store. However, this would be most irrational, for time does have value. While making an extensive search before making any deal, one would be forgoing the income to make this or any deal. For every penny saved to make the perfect deal, one would be losing dollars in income because of the time spent in making the perfect deal. (c) There is little time sacrificed in making a request to your spouse for the restaurant where you eat on your birthday. If you eat there, the benefit will likely exceed the cost. It also reduces the probability of eating at a restaurant where the market value (purchase price) exceeds the utility to the recipient. 5. In the last decade or so there has been a dramatic expansion of small retail convenience stores (such as Mac’s,7 Eleven, Becker’s , etc), although their prices are generally much higher than prices in large supermarkets. What explains the success of the convenience stores? Answer: These stores are selling convenience as well as the goods that are purchased there. Because of their small size and convenient locations, they save busy consumers time. In an era when most consumers are working at least 40 hours per week, their time is valuable, and when only a few items are needed, the time saved must be worth the additional cost one pays for shopping at these convenience stores. (You seldom, if ever, see anyone buying a week’s worth of groceries at such shops.) 6. Many apartment-complex owners are installing water meters for each apartment and billing the occupants according to the amount of water they use, in contrast to the former procedure of having a central meter for the entire complex and dividing up the water expense as part of the rent. Where individual meters have been installed, water usage has declined 10 - 40 percent. Explain that drop, referring to price and marginal utility.

Answer: 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 10 apartments in the complex; each apartment would be billed for one-tenth of the cost of the water. A single gallon of water would carry a price equal to one-tenth the amount charged by the water district. The very low price per gallon would encourage the use of water until the marginal utility of an additional gallon 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. 7. Using the utility-maximizing 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. Answer: The utility-maximizing 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 perfect 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). 8. ADVANCED ANAYLSIS A mathematically ―fair bet‖ is one in which a gambler bets, say, $100 for a 10 percent chance to win $1000 ($100 = 0.10 x $1000). Assuming diminishing marginal utility of dollars, explain why this is not a fair bet in terms of utility. Why is it an even a less fair bet when the house takes a cut of each dollar bet? So is gambling irrational? Answer: Because the marginal utility of money diminishes the more you have, the utility of the $100 used to make the bet is greater than the $900 that you might gain ($1000 - $100) if you win the bet. It is even less of a ―fair bet’’ when the house takes its cut, because the $100 bet has the possibility of yielding less than $900 in winnings. Is gambling irrational? Maybe. The activity of gambling may provide enough extra utility to offset the poor utility odds of winning. 9. Suppose that Ike is loss averse. In the morning, Ike’s stockbroker calls to tell him that he has gained $1000 on his stock portfolio. In the evening, his accountant calls to tell him that he owes an extra $1000 in taxes. At the end of the day, does Ike feel emotionally neutral since the dollar value of the gain in his stock portfolio exactly offsets the amount of extra taxes he has to pay? Explain. Answer: If Ike is loss averse he will feel losses more intensely than gains. This implies that the increase in taxes of $1000 will cause a greater level of disutility than the gain in utility Ike derives from the $1000 increase in his stock portfolio. In effect, because Ike is loss averse, he worse off in terms of utility. If we use the intensity figure from the textbook, the $1000 loss is felt 2.5 more intensely than the $1000 gain. 10. You just accepted a job helping to raise money for your school’s athletic program. You are told to draft a fundraising letter. The bottom of the letter asks recipients to write down a donation amount. If you want to raise as much money as possible, would it be better to mentioned that your school is Number 3 in the nation in sports, or that you are better than 99 percent of other schools at sports? Explain. Answer: The framing effect suggests that we might raise more revenue by stating that the school is better in sports than 99 percent of other schools. This is because the value 99 serves as an "anchor" number and

may increase the size of the donation. That is, if an individual has been exposed to a larger number prior to making the donation they will likely use this number as a reference point. If, on the other hand, we stated the school was Number 3 in sports, the donations might be lower because people will use 3 as their reference number or "anchor."

Problems 1. Myley’s total utility from singing the same song over and over is 50 utils after one repetition, 90 utils after two repetitions, 70 utils after three repetitions, 20 utils after four repetitions, -50 utils after five repetitions, and -200 utils after six repetitions. Write down her marginal utility for each repetition. Once Myley’s total utility begins to decrease, does each additional repetition of the song hurt more than the previous one or less than the previous one? Answers: 50, 40, -20, -50, -70, -150; More than the previous one. 2. John likes Coca-Cola. After consuming one Coke, John has a total utility of 10 utils. After two Cokes, he has a total utility of 25 utils. After three Cokes, he has a total utility of 50 utils. Does John show increasing or decreasing marginal utility for Coke? Suppose that John has $3 in his pocket. If Cokes cost $1 each and John is willing to spend one of his dollars on purchasing a first can of Coke, would he spend his second dollar on a Coke, too? What about the third dollar? If John’s marginal utility for Coke keeps on increasing no matter how many Cokes he drinks, would it be fair to say that he is addicted to Coke? Answers: Increasing; Yes; Yes. 3. Suppose that Omar’s marginal utility for cups of coffee is constant at 1.5 utils per cup no matter how many cups he drinks. On the other hand, his marginal utility per doughnut is 10 for the first doughnut he eats, 9 utils for the second, 8 for the third, and so on (that is, declining by 1 util per additional doughnut). In addition, suppose that coffee costs $1 per cup, doughnuts cost $1 each, and Omar has a budget that he can spend only on doughnuts, coffee, or both. How big would that budget have to be before he would spend a dollar buying a first cup of coffee? Answer: $10. 4. Columns 1 through 4 in the table below show the marginal utility, measured in utils, that Ricardo would get by purchasing various amounts of products A, B, C, and D. Column 5 shows the marginal utility Ricardo gets from saving. Assume that the prices of A, B, C, and D are, $18, $6, $4, and $24 respectively, and that Ricardo has an income of $106.

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. Answer: (a) 4 units of good A, 3 units of good B, 3 units of good C, zero units of good D; (b) $4; (c) $106 (= $18x4 + $6x3 +$4x3 + $24x0 + $4) 5. 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 $2 and $1, 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 $1. What quantities of X and Y will you now purchase? Using the two prices and quantities for X, derive a demand schedule ( a table showing prices and quantities demanded) for X.

Answer: X = 2 units, Y = 5 units; total utility = 48; X = 4, Y = 5; Demand schedule = Price Demanded Quantity Demanded 2 2 1 4 6. ADVANCED ANAYLSIS Let MUA = z = 10 - x and MUB = z = 21 - 2y, where z is marginal utility per dollar measured in utils, x is the amount spent on product A, and y is the amount spent on product B.

Assume that the consumer has $10 to spend on A and B—that is, x + y = 10. How is the $10 best allocated between A and B? How much utility will the marginal dollar yield? Answer: $7 on good B; $3 on good A; MUA = 7, MUB = 7. 7. Suppose that with a budget of $100, Deborah spends $60 on sushi and $40 on bagels when sushi costs $2 per piece and bagels cost $2 per bagel. But then, after the price of bagels falls to $1 per bagel, she spends $50 on sushi and $50 on bagels. How many pieces of sushi and how many bagels did Deborah consume before the price change? At the new prices, how much money would it have cost Deborah to buy those same quantities (the ones that she consumed before the price change)? Given that it used to take Deborah’s entire $100 to buy those quantities, how big is the income effect caused by the reduction in the price of bagels? Answers: 30 pieces of sushi and 20 bagels; $80 (= 30*$2 + 20*$1); $20....