11. A decision maker wishes to maximize the total benefit associated with three activities, X, Y, and Z. The price per unit of activities X, Y, and Z is $1, $2, and $3, respectively. The following table gives the ratio of the marginal benefit to the price of the activities for various levels of each activity:
Level of activity MBXPX MBYPY MBZPZ 1 10 22 14 2 9 18 12 3 8 12 10 4 7 10 9 5 6 6 8 6 5 4 6 7 4 2 4 8 3 1 2
a. If the decision maker chooses to use one unit of X, one unit of Y, and one unit of Z, the total benefit that results is $______
b. For the fourth unit of activity Y, each dollar spent increases total benefit by $______. The fourth unit of activity Y increases total benefit by $______.
c. Suppose the decision maker can spend a total of only $18 on the three activities. What is the optimal level of X, Y, and Z? Why is this combination optimal? Why is the combination 2X, 2Y, and 4Z not optimal?
d. Now suppose the decision maker has $33 to spend on the three activities. What is the optimal level of X, Y, and Z? If the decision maker has $35 to spend, what is the optimal combination? Explain.
11. A decision maker wishes to maximize the total benefit associated with three activities, X, Y, and Z. The price per unit of activities X, Y, and Z is $1, $2, and $3, respectively. The following table gives the ratio of the marginal benefit to the price of the activities for various levels of each activity:
| Level of activity | MBXPX | MBYPY | MBZPZ |
| 1 | 10 | 22 | 14 |
| 2 | 9 | 18 | 12 |
| 3 | 8 | 12 | 10 |
| 4 | 7 | 10 | 9 |
| 5 | 6 | 6 | 8 |
| 6 | 5 | 4 | 6 |
| 7 | 4 | 2 | 4 |
| 8 | 3 | 1 | 2 |
a. If the decision maker chooses to use one unit of X, one unit of Y, and one unit of Z, the total benefit that results is $______
b. For the fourth unit of activity Y, each dollar spent increases total benefit by $______. The fourth unit of activity Y increases total benefit by $______.
c. Suppose the decision maker can spend a total of only $18 on the three activities. What is the optimal level of X, Y, and Z? Why is this combination optimal? Why is the combination 2X, 2Y, and 4Z not optimal?
d. Now suppose the decision maker has $33 to spend on the three activities. What is the optimal level of X, Y, and Z? If the decision maker has $35 to spend, what is the optimal combination? Explain.
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Emmanuel enjoys growing zucchini in his garden and then selling his produce at the local farmers' market. The table below shows his marginal benefit and marginal cost for each hour he spends in his garden per week. The figure below plots the marginal benefit and marginal cost points.
| Emmanuel's Marginal Benefit and Marginal Cost of Gardening | ||
|
Hours Spent Gardening |
Marginal Benefit (dollars) |
Marginal Cost (dollars) |
| 1 | $21 | $3 |
| 2 | 18 | 6 |
| 3 | 15 | 9 |
| 4 | 12 | 12 |
| 5 | 9 | 15 |
| 6 | 6 | 18 |
| 7 | 3 | 21 |
a. Given the information above, what is Emmanuel's optimal amount of time spent gardening each week?
- 1 hour
- 4 hours
- 0 hours
- 7 hours
b. If Emmanuel were to spend 2 hours each week gardening:
- marginal cost would exceed marginal benefit by $12.
- marginal benefit would exceed marginal cost by $12.
- marginal benefit would equal marginal cost.
- marginal benefit would exceed marginal cost by $18.
c. If Emmanuel were to spend 6 hours each week gardening:
- marginal cost would exceed marginal benefit by $12.
- marginal benefit would exceed marginal cost by $18.
- marginal benefit would exceed marginal cost by $12.
- marginal benefit would equal marginal cost.
