using marginal cost & marginal benefit (so that your marginal cost is not greater than your marginal…
using marginal cost & marginal benefit (so that your marginal cost is not greater than your marginal benefit)---\nup to how many hours should jerry keep his store open each day?\nthe marginal cost is what jerry has to pay to keep the store open for each additional hour.\nhours open | total revenue (total benefit) $ | marginal benefit (δ total benefit) $ | marginal cost $\n0 | $0 | 0 | 0\n1 | 25 | 25 | 10\n2 | 45 | 20 | 10\n3 | 60 | 15 | 10\n4 | 70 | 10 | 10\n5 | 75 | 5 | 10\n6 | 79 | 4 | 10\n7 | 81 | 3 | 10\noptions: 8, 5, 3, 4
Answer
Explanation:
Step1: Understand the Rule
We need to find the number of hours where marginal benefit (MB) is at least equal to marginal cost (MC), and stop when MB < MC. MC is $10 per hour (constant here).
Step2: Check Each Hour
- Hour 1: MB = 25, MC = 10 (25 ≥ 10)
- Hour 2: MB = 20, MC = 10 (20 ≥ 10)
- Hour 3: MB = 15, MC = 10 (15 ≥ 10)
- Hour 4: MB = 10, MC = 10 (10 ≥ 10)
- Hour 5: MB = 5, MC = 10 (5 < 10) → Stop here? Wait, no, check hour 4: at hour 4, MB = MC = 10. For hour 5, MB (5) < MC (10), so we should stop at the last hour where MB ≥ MC.
Wait, let's list MB and MC:
| Hour | MB | MC |
|---|---|---|
| 1 | 25 | 10 |
| 2 | 20 | 10 |
| 3 | 15 | 10 |
| 4 | 10 | 10 |
| 5 | 5 | 10 |
| 6 | 4 | 10 |
| 7 | 3 | 10 |
We need to find the maximum hours where MB ≥ MC. At hour 4, MB = MC = 10. At hour 5, MB (5) < MC (10), so we don't go to hour 5. Wait, but let's check the total revenue. Wait, the rule is marginal cost not greater than marginal benefit. So we keep opening as long as MB ≥ MC.
So for each hour, check if MB ≥ MC:
- Hour 1: 25 ≥ 10 → yes
- Hour 2: 20 ≥ 10 → yes
- Hour 3: 15 ≥ 10 → yes
- Hour 4: 10 ≥ 10 → yes
- Hour 5: 5 ≥ 10 → no
Wait, but the options include 4, 5, 3, 8. Wait, the table goes up to 7 hours. Wait, the options: 8,5,3,4. Wait, the selected option is 4, but let's recheck.
Wait, at hour 4, MB = 10, MC = 10 (equal). At hour 5, MB = 5 < 10. So we should stop at hour 4, because for hour 5, the marginal benefit is less than marginal cost. So the maximum hours where MB ≥ MC is 4.
Wait, but let's confirm: the decision rule is to produce (or in this case, stay open) as long as MB ≥ MC. So we compare MB and MC for each additional hour.
Hour 1: MB=25, MC=10 → 25≥10 → open Hour 2: MB=20, MC=10 → 20≥10 → open Hour 3: MB=15, MC=10 → 15≥10 → open Hour 4: MB=10, MC=10 → 10≥10 → open Hour 5: MB=5, MC=10 → 5<10 → don't open
So the maximum hours is 4.
Answer:
4 (the option with "4" as the answer, likely the selected one in the screenshot, but following the calculation, it's 4)