Cost-Benefit Analysis

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AP Microeconomics › Cost-Benefit Analysis

Questions 1 - 7
1

A delivery company is deciding how many additional delivery routes to add on Saturdays (each unit is one route). According to the marginal benefit and marginal cost data in the table, at which quantity should the company stop adding routes?

Routes (Q)MB, $MC, $
1900500
2800600
3700700
4600800
5500900

Stop after 2 routes

Stop after 5 routes

Stop after 4 routes

Stop after 1 route

Stop after 3 routes

Explanation

Marginal cost-benefit analysis is a key skill in microeconomics for making optimal decisions about resource allocation. Marginal benefit (MB) is the additional benefit from one more unit, while marginal cost (MC) is the additional cost; the decision rule is to proceed with additional units as long as MB ≥ MC and stop at the first unit where MB < MC. In this data, the inequality flips at the fourth route, where MB of $600 is less than MC of $800. Therefore, the company should stop after three routes, as that is the last where MB ≥ MC, optimizing profits. A common mistake is using average costs or benefits instead of marginals, which can mislead on incremental value. To apply this transferable strategy, always compare MB and MC unit-by-unit starting from the first. Additionally, ignore sunk costs and focus only on future benefits and costs; on graphs, look for where the MB and MC curves intersect to find the optimal quantity.

2

A university is deciding how many additional tutoring sessions to fund for an introductory economics course (each unit is one session). According to the marginal benefit and marginal cost data in the table, what is the optimal number of sessions to fund?

Tutoring sessions (Q)MB, $MC, $
11,200400
21,000600
3800750
4650900
55001,050

Fund 3 sessions

Fund 2 sessions

Fund 5 sessions

Fund 1 session

Fund 4 sessions

Explanation

Marginal cost-benefit analysis is a key skill in microeconomics for making optimal decisions about resource allocation. Marginal benefit (MB) is the additional benefit from one more unit, while marginal cost (MC) is the additional cost; the decision rule is to proceed with additional units as long as MB ≥ MC and stop at the first unit where MB < MC. In this data, the inequality flips at the fourth session, where MB of $650 falls below MC of $900. This justifies funding three sessions, as each of the first three has MB exceeding MC, providing the greatest net value to students. A common mistake is focusing on total benefits without subtracting total costs, but marginal analysis ensures efficient stopping points. To apply this transferable strategy, always compare MB and MC unit-by-unit starting from the first. Additionally, ignore sunk costs and focus only on future benefits and costs; on graphs, look for where the MB and MC curves intersect to find the optimal quantity.

3

A homeowner is deciding how many additional insulation upgrades to install (each unit is one upgrade step). According to the marginal benefit and marginal cost data in the table, should the homeowner undertake the 3rd upgrade step?

Upgrade step (Q)MB (annual energy savings), $MC (installation cost), $
1600250
2450350
3320330
4250380
5200420

No, because the homeowner should stop at the step with the highest marginal benefit (the 1st step)

Yes, because the average marginal benefit through 3 steps exceeds the marginal cost of the 3rd step

Yes, because total benefits must be compared to total costs rather than marginal values

Yes, because the homeowner should continue as long as marginal benefit is positive

No, because the marginal cost of the 3rd upgrade step exceeds its marginal benefit

Explanation

Marginal cost-benefit analysis is a key skill in microeconomics for making optimal decisions about resource allocation. Marginal benefit (MB) is the additional benefit from one more unit, while marginal cost (MC) is the additional cost; the decision rule is to proceed with additional units as long as MB ≥ MC and stop at the first unit where MB < MC. In this data, for the third upgrade, MB of $320 is less than MC of $330, indicating the flip. Therefore, the homeowner should not undertake the third, as it would result in a net loss despite positive MB. A common mistake is averaging benefits over all units instead of evaluating each marginally. To apply this transferable strategy, always compare MB and MC unit-by-unit starting from the first. Additionally, ignore sunk costs and focus only on future benefits and costs; on graphs, look for where the MB and MC curves intersect to find the optimal quantity.

4

A firm is deciding how many additional quality inspections to perform per day (each unit is one inspection). According to the marginal benefit and marginal cost data in the table, what is the optimal number of inspections?

Inspections (Q)MB, $MC, $
1500150
2420220
3340300
4260360
5200420

Perform 5 inspections

Perform 3 inspections

Perform 1 inspection

Perform 2 inspections

Perform 4 inspections

Explanation

Marginal cost-benefit analysis is a key skill in microeconomics for making optimal decisions about resource allocation. Marginal benefit (MB) is the additional benefit from one more unit, while marginal cost (MC) is the additional cost; the decision rule is to proceed with additional units as long as MB ≥ MC and stop at the first unit where MB < MC. In this data, the inequality flips at the fourth inspection, where MB of $260 is less than MC of $360. Thus, the optimal is three inspections, as each of the first three has MB exceeding or equaling MC, maximizing net benefits. A common mistake is calculating total benefits versus total costs instead of using marginal comparisons for incremental choices. To apply this transferable strategy, always compare MB and MC unit-by-unit starting from the first. Additionally, ignore sunk costs and focus only on future benefits and costs; on graphs, look for where the MB and MC curves intersect to find the optimal quantity.

5

A city parks department is deciding how many additional weekend lifeguard shifts to staff at a public beach this month. The department has already spent $2,000 on training equipment (a sunk cost). According to the marginal benefit and marginal cost data in the table, what is the optimal number of lifeguard shifts to staff?

Additional shifts (Q)Marginal Benefit (MB), $Marginal Cost (MC), $
1900400
2700500
3550600
4450700
5350800

Staff 3 additional shifts

Staff 1 additional shift

Staff 2 additional shifts

Staff 4 additional shifts

Staff 5 additional shifts

Explanation

Marginal cost-benefit analysis is a key skill in microeconomics for making optimal decisions about resource allocation. Marginal benefit (MB) is the additional benefit from one more unit, while marginal cost (MC) is the additional cost; the decision rule is to proceed with additional units as long as MB ≥ MC and stop at the first unit where MB < MC. In this data, the inequality flips at the third shift, where MB of $550 falls below MC of $600. Thus, the optimal number is 2 shifts, as both the first and second have MB exceeding MC, adding net value, but the third does not. A common mistake is including sunk costs like the $2,000 training in the decision, but these should be ignored since they are already spent. To apply this transferable strategy, always compare MB and MC unit-by-unit starting from the first. Additionally, ignore sunk costs and focus only on future benefits and costs; on graphs, look for where the MB and MC curves intersect to find the optimal quantity.

6

A coffee shop is considering extending its hours by adding one more hour each night (each “unit” is one added hour per night for the month). According to the marginal benefit and marginal cost data in the table, should the shop add the 4th hour?

Added hour (Q)MB from added hour, $MC of added hour, $
1220120
2180140
3150150
4120170
590190

No, because the marginal cost of the 4th hour exceeds its marginal benefit

Yes, because total marginal benefits are still positive

Yes, because the marginal benefit is greater than the average marginal cost through 4 hours

Yes, because the 3rd hour had $\text{MB}=\text{MC}$ so the shop should continue past it

No, because the shop should stop when $\text{MB}=\text{MC}$ occurs (at the 3rd hour)

Explanation

Marginal cost-benefit analysis is a key skill in microeconomics for making optimal decisions about resource allocation. Marginal benefit (MB) is the additional benefit from one more unit, while marginal cost (MC) is the additional cost; the decision rule is to proceed with additional units as long as MB ≥ MC and stop at the first unit where MB < MC. In this data, for the fourth hour, MB of $120 is less than MC of $170, indicating the inequality has flipped. Therefore, the shop should not add the fourth hour, as it would reduce net benefits compared to stopping at three. A common mistake is focusing on total benefits being positive instead of comparing marginal values for each incremental decision. To apply this transferable strategy, always compare MB and MC unit-by-unit starting from the first. Additionally, ignore sunk costs and focus only on future benefits and costs; on graphs, look for where the MB and MC curves intersect to find the optimal quantity.

7

A student is deciding how many practice exams to complete before an AP Microeconomics test (each unit is one practice exam). According to the marginal benefit and marginal cost data in the table, what is the optimal number of practice exams to complete?

Practice exams (Q)MB (points of expected score gain)MC (hours of study time)
1123
294
375
456
547

Complete 2 practice exams

Complete 1 practice exam

Complete 5 practice exams

Complete 4 practice exams

Complete 3 practice exams

Explanation

Marginal cost-benefit analysis is a key skill in microeconomics for making optimal decisions about resource allocation. Marginal benefit (MB) is the additional benefit from one more unit, while marginal cost (MC) is the additional cost; the decision rule is to proceed with additional units as long as MB ≥ MC and stop at the first unit where MB < MC. In this data, the inequality flips at the fourth exam, where MB of 5 points is less than MC of 6 hours. Therefore, the optimal is three exams, as the first three satisfy MB ≥ MC, balancing score gains against time costs. A common mistake is comparing totals rather than marginals, which can lead to over- or under-estimating the best quantity. To apply this transferable strategy, always compare MB and MC unit-by-unit starting from the first. Additionally, ignore sunk costs and focus only on future benefits and costs; on graphs, look for where the MB and MC curves intersect to find the optimal quantity.