7chapter. Making Decisions. 1. a. Hiro s accounting profit is:

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1 Making Decisions 1. a. Hiro s accounting profit is: $1, (total revenue) $55, (travel, other expenses, and supplies) $2, (depreciation) $43, (accounting profit) b. Hiro s economic profit is: $1, (total revenue) $55, (travel, other expenses, and supplies) $2, (depreciation) $1 (interest forgone) $5, (salary as economics professor) $7,1 (economic profit) c. Since Hiro s economic profit is negative, he would be better off if he didn t operate the consulting business and taught economics instead. 7chapter 2. a. Jackie s accounting profit is: Total revenue $5,. (The only cost that her accountant would add into the accounting profit calculation is depreciation.) For this to be just equal to zero, her total revenue would have to be $5,. b. Jackie s economic profit is: Total revenue $5, $2, $6, = Total Revenue $67,. (Depreciation, the opportunity cost of not renting out the room, and the opportunity cost of Jackie s time are all costs that figure in the calculation of economic profit.) For this to be just equal to zero, Jackie s total revenue would have to be $67,. 3. a. Your yearly accounting profit is: $2, (total revenue) $1, (cost of bikes) $2, (electricity, taxes, and so on) $8, (accounting profit) But not renting the store to the retail chain is an opportunity cost, and not being able to make $4, as an accountant is also an opportunity cost, so your yearly economic profit is: $2, (total revenue) $1, (cost of bikes) $2, (electricity, taxes, and so on) $4, (opportunity cost of your time) $5, (opportunity cost of not renting the store) $1, (economic profit) So although you make an accounting profit each year, you would be better off renting the store to the large chain and becoming an accountant yourself, since your opportunity cost of continuing to run your own store is too high. 4. a. Your parents are wrong. They are making the mistake of considering sunk costs. Since the $1, that you have already paid for the meal plan is nonrefundable, it should not enter into your decision making now. Your decision of where to eat should depend only on those costs and benefits that are affected by your decision. Since both the cafeteria meals and the restaurant meals are free, you should choose to eat where the benefit to you (convenience, quality of food, and so on) is greater. 7-1

2 7-2 CHAPTER 7 b. Your roommate is wrong. Since the $1, that you have already paid for the meal plan is nonrefundable, it should not enter into your decision making now. In deciding where to eat, you should weigh the benefit and cost of eating in the restaurant (where each meal costs $2) against the benefit and cost of eating in the cafeteria (where meals are free). You may decide to eat in the restaurant, but only if that gives you a benefit that is at least $2 greater than the benefit you get from eating in the cafeteria. 5. Yes, you are making the correct decision If you had known about the baseball game before buying the ticket to the soccer game, your decision would have been as follows: Go to the soccer game Go to the baseball game $2 (benefit) $35 (benefit) $1 (cost of ticket) $2 (cost of ticket) $1 $15 Since the baseball game would have given you the greater total net gain, you should have gone to the baseball game. But after you have already bought the ticket to the soccer game, your decision is different: the ticket to the soccer game (since it cannot be resold) is now a sunk cost, and you should no longer take it into account. Your decision now looks as follows: Go to the soccer game Go to the baseball game $2 (benefit) $35 (benefit) $2 (cost of ticket) $2 $15 So, since you had already bought the ticket to the soccer game before you heard about the baseball game, it is optimal for you to go to the soccer game. 6. a. The table shows Amy s, Bill s, and Carla s marginal costs. Amy s Bill s Carla s Quantity marginal marginal marginal of lawns Amy s cost of Bill s cost of Carla s cost of mowed total cost lawn mowed total cost lawn mowed total cost lawn mowed $ $ $ $2 $1 $

3 MAKING DECISIONS 7-3 The diagram shows Amy s, Bill s, and Carla s marginal cost curves. Marginal cost of lawn mowed $3 Amy s Carla s 2 Bill s Quantity of lawns mowed b. From the information in the table or from the diagram, you can see that Amy has decreasing marginal cost, Bill has constant marginal cost, and Carla has increasing marginal cost. (Also note that all of them have increasing total cost.) 7. a. The marginal benefit of each customer is $15.25: each additional customer you admit increases the total benefit to the gym by $ You should therefore admit three customers per hour. Here is how you could think about that decision. Suppose currently you admit no customers. Admitting the first customer gives the gym a marginal benefit of $15.25 and a marginal cost of $14.. Since the marginal benefit of that first customer exceeds the marginal cost, you want to admit the first customer. For the second customer, the marginal benefit ($15.25) also exceeds the marginal cost ($14.5), so you do want to admit the second customer, too. The same is true for the third customer: the marginal benefit ($15.25) exceeds the marginal cost ($15.), so you also want to admit the third customer. For the fourth customer, however, the marginal cost ($15.5) exceeds the marginal benefit ($15.25), so you do not want to admit a fourth customer. b. By reasoning similar to that in part a, you now want to admit five customers: for the fifth customer, the marginal benefit ($16.25) exceeds the marginal cost ($16.). For the sixth customer, however, the marginal cost ($16.5) exceeds the marginal benefit, so you do not want to admit a sixth customer. 8. The marginal cost of one more class is always $2: each additional class that Lauren or Georgia takes will cost an additional $2. a. The optimal number of classes per week for Lauren is one. The marginal benefit to Lauren of the first class is $23, and the marginal cost is $2. Since the marginal benefit exceeds the marginal cost, Lauren wants to take that first class. For the second class, Lauren s marginal benefit ($19) is less than the marginal cost ($2), so she does not want to take a second class. b. Georgia would be better off adding a second class per week. For the second class, the marginal benefit to Georgia ($22) exceeds the marginal cost ($2), so she wants to take the second class. For the third class, the marginal cost ($2) would exceed the marginal benefit ($15), so Georgia does not want to take the third class. For Georgia, the optimal number of classes per week therefore is two.

4 7-4 CHAPTER 7 9. a. The accompanying table gives the marginal benefit and the marginal cost of smallpox vaccination. The marginal benefit is the additional number of lives saved if we vaccinate an additional 1 percent of the population. For instance, if instead of vaccinating zero percent of the population (resulting in 2 deaths from smallpox), we vaccinate 1 percent of the population (resulting in 18 deaths from smallpox), we have saved 2 lives. That is, the marginal benefit of vaccinating 1 percent (instead of zero percent) of the population is 2 lives. Repeating this for the step from 1 percent to 2 percent vaccination, and so on, gives us the marginal benefit numbers in the table. The marginal cost is the additional number of lives lost if we vaccinate an additional 1 percent of the population. For instance, if instead of vaccinating zero percent of the population (resulting in deaths due to side effects), we vaccinate 1 percent of the population (resulting in 4 deaths due to side effects), we have lost 4 lives. That is, the marginal cost of vaccinating 1 percent (instead of zero percent) of the population is 4 lives. Repeating this for the step from 1 percent to 2 percent vaccination, and so on, gives us the marginal cost numbers in the table. Net gain of 1% Percent of population Marginal benefit Marginal cost increment in vaccinated in lives saved in lives lost population vaccinated b. The optimal percentage of the population that should be vaccinated is 5 percent. Suppose we were vaccinating 4 percent of the population. Then vaccinating an additional 1 percent (to bring the total up to 5 percent) would give us a marginal benefit of 2 lives saved. And vaccinating that additional 1 percent would give us a marginal cost of 17 lives lost. Since the marginal benefit exceeds the marginal cost, we do indeed want to vaccinate that additional 1 percent of the population. But do we want to go beyond 5 percent vaccination? Vaccinating an additional 1 percent (to bring the total up to 6 percent) would result in a marginal benefit of 2 lives saved and a marginal cost of 24 lives lost due to side effects. Since the marginal cost exceeds the marginal benefit, we do not want to increase the vaccination rate from 5 to 6 percent. 1. a. We first need to work out Patty s marginal benefit and marginal cost of each additional hour worked, which are shown in the accompanying table. For instance, as Patty increases the number of hours worked from two to three, her benefit increases from $55 to $75; that is, her marginal benefit is $2. Similarly, as she increases the number of hours worked from two to three, her cost increases from $21 to $34; that is, her marginal cost is $13. Repeating this for increases in the number of hours from zero to one, from one to two, and so on, gives the data in the accompanying table.

5 MAKING DECISIONS 7-5 Quantity Marginal benefit Marginal cost Net gain of hours worked of hour worked of hour worked of hour worked $3 $1 $ Query to team: Should this last column be: Total net gain of hour worked? Patty should therefore work for three hours. This is because her marginal benefit of going from two hours to three hours ($2) exceeds the marginal cost of going from two hours to three hours ($13). But going from three hours to four hours, Patty s marginal cost ($16) would exceed her marginal benefit ($15), so working that additional fourth hour is not optimal. b. The accompanying table shows Patty s total net gain in the fourth column. The total net gain is the difference between total benefit and total cost. Quantity of hours worked Total benefit Total cost Total net gain $ $ $ Therefore, Patty s loss from working for only one hour instead of the optimal three hours is $41 $2 = $21.

6 7-6 CHAPTER a. The accompanying table shows the marginal benefit and marginal cost of each diamond. The accompanying diagram graphs marginal benefit and marginal cost. From the diagram, you can conclude that the optimal number of diamonds to produce is five. Quantity of diamonds Total benefit Marginal benefit Total cost Marginal cost $ $ $1, $5 1 1, , , , , ,5 1,5 4 1, 7 4,9 2,5 3 1,3 8 5,2 3,8 Marginal benefit, marginal cost of diamond $1,4 1,2 1, Optimal point MB Optimal quantity Quantity of diamonds b. The accompanying table calculates the total gain to DeBeers from producing each quantity of diamonds. The quantity that gives DeBeers the greatest total net gain is five diamonds. This is, of course, just what you found in part a. Quantity of diamonds Total benefit Total cost Total net gain $ $ $ 1 1, ,9 1 1,8 3 2,7 2 2,5 4 3,4 4 3, 5 4, 8 3,2 6 4,5 1,5 3, 7 4,9 2,5 2,4 8 5,2 3,8 1,4

7 MAKING DECISIONS If you choose to get $1.2 million paid out over four years, the present value of those payments is $3, $3, $3, $3, $3, = $3, $3, $3, + = $3, + $25, + $28,333 + $173,611 = $931, Since this is less than $1 million, you would prefer to get $1 million now instead of $1.2 million over four years. 13. a. The net present value is $4 million $4 million $4 million $ 1 million = $ 392, Since the net present value is negative, Pfizer should not invest in the development of this drug: it would be better off putting the $1 million into a bank account that pays 12 percent interest. b. The net present value is $4 million $4 million $4 million $ 1 million = $38, Since the net present value is positive, Pfizer should invest in the development of this drug: the return on its initial investment of $1 million would be better than what it could get if it put the $1 million into a bank account paying 8 percent interest instead.