Farms is an 80-acre hay farm in Colorado. The owners are considering changing the farm’s name to Blissful Acres and growing marijuana instead of hay. Use the table below to answer the following two questions.
If they continue to only grow hay, how many acres should Hayfever Farms devote to growing hay in order to maximize profits?
MR $ (hay) 730 730 730 730 730 730 730 730
MR $ (marijuana) 5600 5600 5600 5600 5600 5600 5600 5600
Number of MC S acres 10 20 30 40 50 60 70 80
Number acres 320 200 540 730 1200 3200 5600 6700
If the owners decide to only grow marijuana how many acres should Blissful Acres devote to growing marijuana in order to maximize profits?
Number acres
The Correct Answer and Explanation is:
Objective:
Maximize profits by allocating the optimal number of acres to growing hay or marijuana, based on marginal revenue (MR) and marginal cost (MC).
Profit-maximization rule:
A firm maximizes profit when MR = MC, as long as MR ≥ MC.
1. If they continue to only grow hay:
- MR (hay) = 730 (constant across all acres)
- Look for the point where MC ≤ MR (730) and the next MC > MR.
From the table:
| Acres | MC | MR (hay) |
|---|---|---|
| 10 | 320 | 730 |
| 20 | 200 | 730 |
| 30 | 540 | 730 |
| 40 | 730 | 730 ✅ |
| 50 | 1200 | 730 ❌ |
At 40 acres, MC = MR = 730, and beyond that, MC exceeds MR, meaning profits start to decline.
👉 Optimal hay acreage = 40 acres
2. If they only grow marijuana:
- MR (marijuana) = 5600 (constant)
- Look for the point where MC ≤ 5600, and the next MC > 5600.
From the table:
| Acres | MC | MR (marijuana) |
|---|---|---|
| 10 | 320 | 5600 |
| 20 | 200 | 5600 |
| 30 | 540 | 5600 |
| 40 | 730 | 5600 |
| 50 | 1200 | 5600 |
| 60 | 3200 | 5600 |
| 70 | 5600 | 5600 ✅ |
| 80 | 6700 | 5600 ❌ |
At 70 acres, MC = MR = 5600, and going further leads to higher costs than revenues.
👉 Optimal marijuana acreage = 70 acres
Summary:
- Hay: Grow on 40 acres
- Marijuana: Grow on 70 acres
Explanation) equals marginal cost (MC). If MR exceeds MC, a firm should produce more; if MC exceeds MR, it should produce less. For Hayfever Farms (or Blissful Acres), this rule guides how many acres to allocate to hay or marijuana.
In the case of hay, the MR per acre is consistently $730. The marginal cost rises with additional acreage. At 40 acres, the marginal cost is exactly $730—equal to the marginal revenue. Beyond 40 acres, the cost of producing hay exceeds the revenue it brings, reducing profit. Therefore, growing hay on more than 40 acres would result in diminishing returns. Thus, Hayfever Farms should devote 40 acres to hay for maximum profitability.
If the owners switch to marijuana, the situation is even more pronounced due to the much higher MR of $5600 per acre. Marginal cost also rises sharply, but only at 70 acres does the cost equal the marginal revenue. Up to that point, the farm earns more in revenue than it pays in cost. At 80 acres, the MC jumps to $6700, which is greater than the MR, indicating a loss on the final units. Hence, the farm should allocate 70 acres to marijuana to optimize profits.
This analysis enables the farm to make a rational economic decision using marginal analysis principles.
