Because some acres are better suited for wheat production than others, the first acre can produce 1,000 bushels of wheat, the second acre 900, the third 800, and so on.
a. Use the table below to help answer the following questions. How many bushels will each of the farmer's five acres produce? How much revenue will each acre generate? What are the TR and MR for each acre?
| Acre | That Acre's Yield (bushels) | That Acre's Revenue | TR | MR |
|---|---|---|---|---|
| 0 | - | - | $0 | - |
| 1 | | | | |
| 2 | | | | |
| 3 | | | | |
| 4 | | | | |
| 5 | | | | |
b. If the marginal cost of planting and harvesting an acre is $14,000 per acre for each of the five acres, how many acres should the farmer plant and harvest?
Answer (2)
Calculate the revenue for each acre: Multiply the yield of each acre by the price per bushel ($20). Revenue for Acre i = Yield of Acre i * $20.
Calculate the Total Revenue (TR) for each acre: TR for Acre i is the sum of the revenues from Acre 1 to Acre i .
Calculate the Marginal Revenue (MR) for each acre: MR for Acre i is the difference between the TR of Acre i and the TR of Acre i − 1 .
Calculate the profit for each acre: Profit for Acre i = TR for Acre i - (Marginal Cost * i ). The farmer should plant 3 acres. 3
Explanation
Problem Analysis and Setup Let's analyze the farmer's wheat production and determine the optimal number of acres to plant. We'll start by calculating the yield, revenue, total revenue (TR), and marginal revenue (MR) for each of the five acres. We'll assume a price of $20 per bushel since the price isn't provided.
Calculating Yield for Each Acre The yield for each acre is as follows:
Acre 1: 1000 bushels
Acre 2: 900 bushels
Acre 3: 800 bushels
Acre 4: 700 bushels
Acre 5: 600 bushels
Calculating Revenue for Each Acre Now, let's calculate the revenue for each acre, assuming a price of $20 per bushel:
Acre 1: 1000 × 20 = $20 , 000
Acre 2: 900 × 20 = $18 , 000
Acre 3: 800 × 20 = $16 , 000
Acre 4: 700 × 20 = $14 , 000
Acre 5: $600 \times 20 = $12,000
Calculating Total Revenue (TR) for Each Acre Next, we calculate the Total Revenue (TR) for each acre:
Acre 1: $20,000
Acre 2: $20,000 + 18,000 = $38,000
Acre 3: $38,000 + 16,000 = $54,000
Acre 4: $54,000 + 14,000 = $68,000
Acre 5: $68,000 + 12,000 = $80,000
Calculating Marginal Revenue (MR) for Each Acre Now, let's calculate the Marginal Revenue (MR) for each acre:
Acre 1: $20,000
Acre 2: $38,000 - 20,000 = $18,000
Acre 3: $54,000 - 38,000 = $16,000
Acre 4: $68,000 - 54,000 = $14,000
Acre 5: $80,000 - 68,000 = $12,000
Calculating Profit for Each Acre Now, let's calculate the profit for each acre, given a marginal cost of $14,000 per acre:
Acre 1: $20,000 - 14,000 = $6,000
Acre 2: $38,000 - (14,000 \times 2) = $10,000
Acre 3: $54,000 - (14,000 \times 3) = $12,000
Acre 4: $68,000 - (14,000 \times 4) = $12,000
Acre 5: $80,000 - (14,000 \times 5) = $10,000
Determining the Optimal Number of Acres Based on the profit calculations, the farmer should plant and harvest 3 acres or 4 acres to maximize profit, since both yield a profit of $12,000. However, since the question asks for a whole number, we can choose 3 acres.
Completed Table Here's the completed table:
Acre
That Acre's Yield (bushels)
That Acre's Revenue
TR
MR
0
-
-
$0
-
1
1000
$20,000
$20,000
$20,000
2
900
$18,000
$38,000
$18,000
3
800
$16,000
$54,000
$16,000
4
700
$14,000
$68,000
$14,000
5
600
$12,000
$80,000
$12,000
Final Answer The farmer should plant and harvest 3 acres to maximize profit.
Examples
Understanding marginal revenue and marginal cost is crucial in many business decisions. For example, a company deciding whether to launch a new product needs to consider the marginal cost of production and the marginal revenue they expect to generate. If the marginal revenue exceeds the marginal cost, launching the product is likely a good decision. Similarly, a farmer deciding how many acres to plant needs to consider the cost of planting and harvesting each additional acre versus the revenue generated by that acre. This kind of analysis helps businesses and individuals make informed decisions to maximize their profits or returns.
To maximize profit, the farmer should plant 3 acres of wheat, generating the highest profit of $12,000. Revenue decreases with each acre planted due to fewer bushels produced. The detailed revenue and profit calculations also indicate that planting 4 acres yields the same profit, but planting 3 acres is preferred as a whole number.
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