The table below shows Ali's monthly costs of producing wheat. Suppose the current market price of wheat is $74.50 per bushel.
Ali's Wheat Production Costs
| Quantity (bushels) | AVC (dollars) | ATC (dollars) | MC (dollars) |
| :------------------ | :------------ | :------------ | :----------- |
| 0 | - | - | - |
| 500 | $19.50 | $49.50 | $4.50 |
| 1,600 | 16.50 | 32.00 | 14.56 |
| 1,500 | 14.50 | 29.50 | 22.50 |
| 2,000 | 19.50 | 30.75 | 34.50 |
| 2,500 | 24.50 | 33.50 | 44.50 |
| 3,000 | 29.50 | 37.00 | 54.50 |
| 3,500 | 34.50 | 40.93 | 64.50 |
| 4,000 | 39.50 | 45.13 | 74.50 |
| 4,500 | 44.50 | 49.50 | 84.50 |
| 5,000 | 49.50 | 54.00 | 94.50 |
Instructions: Round your answers to two decimal places. If you are entering a negative number include a minus sign.
a. If the market price is $74.50 per bushel of wheat, and Ali chooses to produce wheat, how much will he produce per month to maximize his profits in the short run?
4,000 bushels per month
b. Calculate All's monthly profits (express a loss as a negative number) if he chooses to produce the profit-maximizing quantity of wheat at a price of $74.50.
$
c. Assume that the market price of wheat falls to $22.50 per bushel. How much wheat will All choose to produce per month in order to maximize his profits in the short run?
1,500 bushels per month
d. Calculate All's monthly profits (express a loss as a negative number) if he chooses to produce the profit-maximizing quantity of wheat at a price of $22.50.
$
e. If the market price of wheat instead falls to $14.50 per bushel, how much wheat will Ali choose to produce per month in order to maximize his profits in the short run?
1,000 bushels per month
Answer (2)
Ali maximizes his profits by producing 4,000 bushels when the market price is $74.50, resulting in a profit of $117,480. With the price at $22.50, he should produce 1,500 bushels, leading to a loss of -$10,500. At $14.50, it is advisable that Ali reevaluates production, likely producing minimally if he continues to operate.
;
At a market price of $74.50, Ali's profit is calculated as: P ro f i t = ( 74.50 × 4000 ) − ( 45.13 × 4000 ) = $117480.00 .
At a market price of $22.50, Ali's profit is calculated as: P ro f i t = ( 22.50 × 1500 ) − ( 29.50 × 1500 ) = $ − 10500.00 .
At a market price of $14.50, Ali's profit is calculated as: P ro f i t = ( 14.50 × 1600 ) − ( 32.00 × 1600 ) = $ − 28000.00 .
Explanation
Understanding the Problem We are given Ali's wheat production costs and need to calculate his monthly profits under different market prices. We will calculate Total Revenue (TR) and Total Cost (TC) to find the profit (or loss) in each scenario. Profit is calculated as Total Revenue minus Total Cost, i.e., P ro f i t = TR − TC .
Calculating Profit at $74.50 When the market price is $74.50 per bushel and Ali produces 4,000 bushels: Total Revenue (TR) = Price × Quantity = $74.50 × 4,000 = $298,000 Total Cost (TC) = ATC × Quantity = $45.13 × 4,000 = $180,520 Profit = TR - TC = $298,000 - $180,520 = $117,480
Calculating Profit at $22.50 When the market price falls to $22.50 per bushel and Ali produces 1,500 bushels: Total Revenue (TR) = Price × Quantity = $22.50 × 1,500 = $33,750 Total Cost (TC) = ATC × Quantity = $29.50 × 1,500 = $44,250 Profit = TR - TC = $33,750 - $44,250 = -$10,500
Calculating Profit at $14.50 When the market price falls to $14.50 per bushel, we need to determine how much wheat Ali will produce to maximize his profits in the short run. From the table, we can see that at a quantity of 500, AVC is $19.50, ATC is $49.50 and MC is $4.50. At a quantity of 1,600, AVC is $16.50, ATC is $32.00 and MC is $14.56. Since the price is $14.50, Ali will produce 1,600 bushels per month to maximize his profits in the short run. Total Revenue (TR) = Price × Quantity = $14.50 × 1,600 = $23,200 Total Cost (TC) = ATC × Quantity = $32.00 × 1,600 = $51,200 Profit = TR - TC = $23,200 - $51,200 = -$28,000
Examples
Understanding production costs and market prices is crucial for businesses to make informed decisions about production levels. For instance, a bakery needs to determine how many loaves of bread to bake each day based on the cost of ingredients, the price they can sell the bread for, and the quantity that maximizes their profit. Similarly, a clothing manufacturer must analyze their production costs and market prices to decide on the optimal number of garments to produce. By carefully evaluating these factors, businesses can ensure they are operating efficiently and maximizing their profitability.
