Ch 6 Insert C - Eugene Giaquinto - Homemrgsbiz.weebly.com/uploads/5/3/8/8/53888763/smchap007.doc · Web viewLAST WORD In what way is criminal behavior similar to consumer behavior?

Chapter 07 - Utility Maximization


McConnell Brue Flynn 20e

DISCUSSION QUESTIONS

1. Complete the following table and answer the questions below: LO1

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 1 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.

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2. Mrs. Simpson buys loaves of bread and quarts of milk each week at prices of $1 and 80 cents, respectively. At present she is buying these 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 utility-maximizing combination of bread and milk? If not, how should she reallocate her expenditures between the two goods? LO2

Answer: Mrs. Wilson 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. Wilson should buy more milk and less bread.

3. How can time be incorporated into the theory of consumer behavior? Explain the following comment: “Want to make millions of dollars? Devise a product that saves Americans lots of time.” LO2

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 or 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 behavior (with time taken into account) would therefore have this consumer going to the theater.

4. Explain: LO2a. 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 7 Eleven, Kwik Shop, and Circle K), although their prices are generally much higher than prices in large supermarkets. What explains the success of the convenience stores? LO2

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. This is in contrast to the former procedure of having a central meter for the entire complex and dividing up the collective water expense as part of the rent. Where individual meters have been installed, water usage has declined 10 to 40 percent. Explain that drop, referring to price and marginal utility. LO3




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-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. LO4

Answer: 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).

8. ADVANCED ANAYLSIS A “mathematically fair bet” is one in which the amount won will on average equal the amount bet, for example when a gambler bets, say, $100 for a 10 percent chance to win $1,000 ($100 = .10 x $1,000). Assuming diminishing marginal utility of dollars, explain why this is not a fair bet in terms of utility. Why is it even a less fair bet when the “house” takes a cut of each dollar bet? So is gambling irrational? LO4

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 ($1,000 - $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. LAST WORD In what way is criminal behavior similar to consumer behavior? Why do most people obtain goods via legal behavior as opposed to illegal behavior? What are society's main options for reducing illegal behavior?




Answer: Both the lawful consumer and the criminal try to maximize their total utility. (Answers may vary.)Most people choose legal behavior because they see the price of illegal behavior to be greater than the marginal benefit. The costs include guilt, direct costs (supplies and tools), loss of freedom, and the forgone income earned through legal behavior.Society's main option to reduce illegal behavior is to increase the cost of engaging in it. They can do this many ways. Guilt costs can be increased through family, educational, and religious efforts. They can get better locks and alarms forcing the criminal to spend more money on better tools. They can provide higher incomes for legal behavior, increasing the opportunity cost. They can increase policing to make it more likely the criminal will be caught.

REVIEW QUESTIONS

1. True or false. The law of diminishing marginal utility predicts the consumption behavior of addicts quite well. LO1

Answer: false.The law of diminishing marginal utility does not predict the consumption behavior of addicts well at all. That is because the law predicts that, other things equal, successive units will be less and less valuable to a person. Thus, people should not keep on consuming additional units relentlessly. But an alcoholic, for instance, will often purse a 15th drink on a given day with as much intensity as he pursued his first drink that day. And a gambling addict will often bet his final dollar with as much alacrity as he bet his first. Those suffering from addiction appear to behave as if the marginal utility of the drug or behavior to which they are addicted remains high no matter how much of the drug or behavior they engage in.

2. Frank spends $75 on 10 magazines and 25 newspapers. The magazines cost $5 each and the newspapers cost $2.50 each. Suppose that his MU from the final magazine is 10 utils while his MU from the final newspaper is also 10 utils. According to the utility-maximizing rule, Frank should: LO2a. Reallocate spending from magazines to newspapers.b. Reallocate spending from newspapers to magazines.c. Be satisfied because he is already maximizing his total utility.d. None of the above.




Answer: a, reallocate spending from magazines to newspapers

Frank is not currently maximizing the utility that he could get from his $75 budget and should reallocate spending from magazines to newspaper in order to increase the total utility that he receives from his budget.This can be seen by examining the MU per dollar that he is currently getting from the last magazine and the last newspaper. The MU per dollar from the last magazine is 10/$5 = 2 utils per dollar. The MU per dollar from the last newspaper is 10/$2.50 = 4 utils per dollar. Thus, Frank could gain more total utils if he spent less on newspapers and more on dollars. As an example, imagine that Frank cut his purchases of magazines by one, reducing them from 10 purchased to only 9 purchased. That would free up $5 that he could spend on newspapers. Since newspapers cost $2.50 each, he could purchase two newspapers. Now, look at what happens to his total utility as he makes that change in consumption. He will lose 10 utils by consuming one fewer magazine (because the MU of magazines is 10). But he will gain more than 10 utils by consuming two additional newspapers (because the MU of an additional newspaper is 10 utils and he will be consuming two additional newspapers). Thus, by reallocating his spending from the product with the lower MU per dollar to the product with the higher MU per dollar, Frank will be able to increase the total utility that he receives from his budget.

3. Demand curves slope downward because, other things held equal, LO3a. An increase in a product’s price lowers MU.b. A decrease in a product’s price lowers MU. c. A decrease in a product’s price raises MU per dollar and makes consumers wish to purchase more units.d. An increase in a product’s price raises MU per dollar and makes consumers wish to purchase more units.

Answer: c, A decrease in a product’s price raises MU per dollar and makes consumers wish to purchase more units.Rational consumers decide how to spend their limited budgets by comparing the marginal utilities per dollar that they can get from various products. If the prices of all other products stay the same while the price of product X falls, then the MU per dollar of money spent on product X will increase. That will mean that any money spent purchasing units of product X will get the consumer more MU than previously. Thus, consumers interested in getting as much utility as possible when spending their limited budges will want to spend more of their limited budgets on product X. This behavior explains the downward slope of demand curves because a decrease in the price of product X leads to an increase in the quantity demanded of product X.




4. Jermaine spends his money on cucumbers and lettuce. If the price of cucumbers falls, the MU per dollar of cucumbers will ______________ and Jermaine will _______________ cucumbers for lettuce. LO4a. Fall; substituteb. Rise; substitutec. Fall; supplyd. Rise; demand

Answer: b, rise; substituteWhen the price of cucumbers falls, the MU per dollar of cucumbers will rise. As a result, each dollar spent on cucumbers will now bring more marginal utility than it did previously. Cucumbers thus become relatively more attractive than they were previously and so Jermaine will switch, or substitute, some of his spending away from lettuce and towards cucumbers in order to maximize his utility given the new, lower price of cucumbers.

5. Tammy spends her money on lemonade and iced tea. If the price of lemonade falls, it is as though her income __________________. LO4a. increasesb. decreasesc. stays the same

Answer: a, increases.A person’s income is not same thing as their budget. Rather, their income is the amount of goods and services that they can purchase with their budget. Thus, when the price of something that they purchase falls, their income rises because they can now purchase more goods and services than they did before.Consider the following example. Suppose that Tammy originally has a $6 budget and maximizes utility by purchasing 2 glasses of lemonade for $2 each and 2 glasses of iced tea for $1 each. So her income of goods and services is 2 glasses of lemonade and 2 glasses of iced tea. Then suppose that the price of iced tea falls in half, to only $1 per glass. Her budget of $6 remains unchanged, but she will now be able to purchase more total items and thereby enjoy a higher income due to the lower price of lemonade. This can be seen most directly by noting that her old income of 2 glasses of lemonade and 2 glasses of iced tea will now only cost $4—which means that she has $2 left over to increase her consumption of either iced tea or lemonade. The price reduction allows her to consume more overall, which is the same as saying that her income of goods and services has increased.




PROBLEMS

1. Mylie’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 Mylie’s total utility begins to decrease, does each additional singing of the song hurt more than the previous one or less than the previous one? LO1

Answers: 50, 40, -20, -50, -70, -150; More than the previous one.

Feedback: Consider the following values: Mylie’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.Mylie's marginal utility can be found by calculating the change in total utility as she sings the song one more time. The utility from singing the song the first time is 50, which is the total utility of singing the song the first time, 50, minus the total utility of not singing the song at all, 0. The utility from singing the song the second time is 40, which is the total utility from singing the song the second time, 90, minus the total utility from singing the song the first time, 50. Apply the same procedure to following repetitions of the song. The marginal utility of the third time is -20 (= 70 - 90). The fourth time, -50 (= 20 - 70), the fifth time, -70 (= -50 - 20). The sixth time, -150 (= -200 - (-50) = -200 + 50).Once Mylie's total utility begins to decrease, each additional song hurts more than the previous one because she is becoming worse in terms of utility (which is a measure of individual welfare). As we can see above, after the second repetition, Mylie is actually worse off. Also, the decline in utility increases after the second repetition.

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 diminishing marginal utility for Coke or does he show increasing 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? LO1

Answers: Increasing; Yes; Yes.




Feedback: Consider the following values: 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. Also, assume John has $3 in his pocket and Cokes cost $1 each.John's marginal utility equals the change in total utility as he consumes an additional unit. Thus, his marginal utility from the first Coke is 10 (= 10 - 0), his second Coke is 15 (= 25 - 10), and his third Coke is 25 (= 50 -25). Since his marginal utility is increasing at an increasing rate he shows increasing marginal utility for Coke. If John consumes the first can of Coke, we know that his marginal utility per dollar was sufficient to induce the purchase. Since his marginal utility increases as he consumes more Coke, his marginal utility per dollar will also increase (price does not change). This implies that he will purchase the second Coke because it provides even more marginal utility per dollar than the first Coke did. The same is true for the third can of Coke. He will spend his entire income on Coke, thus it is fair to say he is addicted to Coke.

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 for the second he eats, 8 for the third he eats, 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? LO2

Answer: $10.

Feedback: Consider the following example: 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 for the second he eats, 8 for the third he eats, 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 and/or coffee.To answer this question, we first need to calculate the marginal utility per dollar for doughnuts. Recall that the marginal utility per dollar for a good is the marginal utility divided by the price of the good (=MU/P). For the first doughnut we have 10 (=10/$1), the second doughnut 9 (=9/$1), third 8, fourth 7, fifth 6, sixth 5, seventh 4, eighth 3, ninth 2, and tenth 1.The marginal utility per dollar for every cup of coffee is 1.5 (=1.5/$1). To determine how big the budget would have to be before John would spend a dollar buying his first cup of coffee, we compare the marginal utility per dollar values. John will purchase the first doughnut before he buys a cup of coffee because the marginal utility per dollar for the doughnut is greater than the marginal utility per dollar for the cup of coffee (10>1.5). The same is true for the second through the ninth doughnut. This implies John will buy 9 doughnuts at the price of $1 before he buys his first cup of coffee. Therefore his budget will need to $10 before he buys his first cup of coffee, $9 on the doughnuts and $1 for the cup of coffee.




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, respectively, $18, $6, $4, and $24 and that Ricardo has an income of $106. LO2

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 (verify that all of the income has been exhausted between the various goods and savings).

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)

Feedback: Consider the following information and use the table above: the prices of A, B, C, and D are, respectively, $18, $6, $4, and $24 and Ricardo has an income of $106.

The first step is to convert the marginal utility values into marginal utility per dollar values. Recall this is MU/P.

Marginal Utility

per dollar unit 1

Marginal Utility

per dollar unit 2

Marginal Utility

per dollar unit 3

Marginal Utility

per dollar unit 4

Marginal Utility

per dollar unit 5

Marginal Utility

per dollar unit 6

Marginal Utility

per dollar unit 7

Marginal Utility

per dollar unit 8

units

Column 1 Good A

4.00 3.00 2.50 2.00 1.50 1.00 0.83 0.67 4

Column 2 Good B

4.00 2.50 2.00 1.50 1.17 0.83 0.33 0.17 3

Column 3 Good C

3.75 3.00 2.00 1.75 1.25 1.00 0.88 0.75 3

Column 4 Good D

1.50 1.25 1.00 0.75 0.54 0.29 0.17 0.08 0

Column 5 Saving

5.00 4.00 3.00 2.00 1.00 0.50 0.25 0.13 4




The table above reads across rows (for example, the first row labeled 'Column 1-Good A' is marginal utility per dollar for good A). The columns represent the marginal utility per dollar for the different goods for each unit consumed and saving (for example, column 1 'Marginal Utility per dollar unit 1' tells us the marginal utility per dollar for the first unit of every good and savings). This will makes the comparison a little easier.

To determine the optimal amount of goods that Ricardo will purchase, we choose the goods with the highest marginal utility per dollar as we move from left to right. We continue to do this until income is exhausted. We see that the first unit of savings ($1) provides $5.00 worth of utility per dollar, so Ricardo makes this choice. Next he purchases one unit of good A and good B with a marginal utility per dollar of 4 He will also save the second dollar (an additional $1) because the marginal utility per dollar is 4. The next decision leads Ricardo to purchase the first unit of good C with a marginal utility per dollar of 3. Then he moves on to purchase the second unit of good A, the second unit of good B, and he saves an additional dollar because the marginal utility per dollar is 3for these goods. After these purchases, he has an income left of $53. Since he has income left, he continues to buy more goods using the approach above.

In conclusion, Ricardo will consume 4 units of good A, 3 units of good B, 3 units of good C, zero units of good D, and saves $4. This will exhaust his income $106 (= $18 x 4 + $6 x 3 +$4 x 3 + $24 x 0 + $4).

5. You are choosing between two goods, X and Y, and your marginal utility from each is as shown in the table 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 (prices and quantities demanded table) for X. LO3

Answer: X = 2 units, Y = 5 units; total utility = 48; X = 4, Y = 5; Demand schedule =

Price Demanded Quantity Demanded2 21 4




Feedback: Consider the following table and information as an example:

Your income is $9 and the prices of X and Y are $2 and $1, respectively.

The first step is to convert the marginal utility values into marginal utility per dollar values. Recall this is MU/P. See the table below.

Marginal Utility

per dollar unit 1

Marginal Utility

per dollar unit 2

Marginal Utility

per dollar unit 3

Marginal Utility

per dollar unit 4

Marginal Utility

per dollar unit 5

Marginal Utility

per dollar unit 6

Units

Good Y (first price)

8.00 7.00 6.00 5.00 4.00 3.00 5

Good X (first price)

5.00 4.00 3.00 2.00 1.50 1.00 2

Good Y (second price)

8.00 7.00 6.00 5.00 4.00 3.00 5

Good X (second price)

10.00 8.00 6.00 4.00 3.00 2.00 4

The first two rows define the marginal utility per dollar for goods X and Y when the price of good X is $2 and the price of Good Y is $1. Each column is the marginal utility for the unit consumed (Marginal utility per dollar for unit 1 is for the first unit consumed, Marginal utility per dollar for unit 2 is for the second unit consumed, etc...). To determine the optimal number of goods to purchase we choose the goods with the highest marginal utility per dollar as we move from left to right. We continue to do this until income is exhausted.




First, we only consider the first two rows for Goods X and Y for the first price of good X (price of X is $2). We purchase the first unit of good Y with a marginal utility per dollar of 8. Next we purchase the second unit of good Y with a marginal utility per dollar of 7. Followed by the third unit of good Y with a marginal utility per dollar of 6. Continuing on, we purchase the fourth and fifth unit of Good Y and the first and second unit of good X 5and4marginal utility per dollar). Thus, we purchase 5 units of good Y and 2 units of good X. The total cost is $9 (= $5 x 5 + $2 x 2), which exhausts income.The total utility is then found by adding up the marginal utility values for the goods consumed using the values in the original table. The total utility from good Y is 30 (=8 + 7 + 6 + 5 + 4) and the total utility from good X is 18 (=10 + 8). The sum of these two values is the total utility, which equals 48 (=30 + 18).Now we consider the case where the price of good X falls to $1.Here, we only consider the last two rows for Goods X and Y for the second price of good X. Here our first purchase is the first unit of good X with a marginal utility per dollar of 10. Next we purchase the second unit of good X and the first unit of good Y with a marginal utility per dollar of 8.00. We continue this process until income is exhausted. The optimal consumption level for good X is 4 and for good Y is 5.This gives us the ordered pairs for good X: (P = 2, Q = 2) and (P = 1, Q = 4). We can use these ordered pairs to graph the demand schedule (not required).

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? LO3

Answer: $7 on good B; $3 on good A; MUA = 7, MUB = 7.

Feedback: To solve this system of equations we set the MUA=MUB. This is required if we are maximizing utility. This leaves with only x and y to solve for using the individual's budget constraint.Consider the following equations: 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. Also, assume that the consumer has $10 to spend on A and B—that is, x + y = 10.We know from our optimization rule that MUA=MUB, which implies 10 - x = 21 - 2y. Or, after some rearranging, 2y - x = 11. Combining this equation with our budget constraint, x + y =10, we have two equations and two unknowns (x and y).

Use the budget constraint to solve x, or x = 10 - y. Substitute x from this equation into our optimality rule (2y - x = 11), which gives us 2y - (10 -y) = 11. Again after some rearranging, we have 2y - 10 + y = 11, or 3y = 21. Thus, we spend $7 on good B. Using our budget constraint 9x + y =10), this implies we spend $3 on good A.To check our answer, substitute these values into the marginal utility equations: MUA= 10 - x, or MUA = 10 -3 = 7 and MUB = 21 - 2y = 21 -2x7 = 7. Thus, MUA=MUB., and the marginal dollar will yield 7 utils.




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? LO4

Answers: 30 pieces of sushi and 20 bagels; $80 (= (30 x $2) + (20 x $1)); $20.

Feedback: Consider the following values as an example. 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.This implies that Deborah bought 30 pieces of Sushi (=$60/$2) and she bought 20 bagels (=$40/2) before the price change.If Deborah purchased the same quantities of Sushi and bagels with the new prices it would only cost her $80. She still spends $60 on Sushi because the price hasn't changed (still $2) and she was consuming 30 pieces. However, the cost of the 20 bagels has fallen to $20 because the price of the bagel is only $1 now. This implies Deborah has an additional $20 to spend as a result of the price decrease on bagels (= $100 (original cost) - $80 (new cost)).



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Ch 6 Insert C - Eugene Giaquinto - Homemrgsbiz.weebly.com/uploads/5/3/8/8/53888763/smchap007.doc · Web viewLAST WORD In what way is criminal behavior similar to consumer behavior?