Final answer:
To determine the profit-maximizing quantity, we need to calculate the total revenue, marginal revenue, total cost, and marginal cost for each output level. By analyzing the diagrams, we can determine that the profit maximizing quantity is the output level at which the marginal revenue equals the marginal cost. In this case, the profit maximizing quantity is three units.
Step-by-step explanation:
To determine the profit maximizing quantity, we need to calculate the total revenue, marginal revenue, total cost, and marginal cost for each output level. The total revenue is calculated by multiplying the selling price per unit by the number of units sold. The marginal revenue is the change in total revenue resulting from a one-unit change in quantity. The total cost is calculated by summing the fixed costs and variable costs for each output level. The marginal cost is the change in total cost resulting from a one-unit change in quantity.
Using the provided information, we can calculate the total revenue, marginal revenue, total cost, and marginal cost for each output level:
- For one unit: Total revenue = $72, Marginal revenue = $72, Total cost = $164, Marginal cost = $100
- For two units: Total revenue = $144, Marginal revenue = $72, Total cost = $248, Marginal cost = $84
- For three units: Total revenue = $216, Marginal revenue = $72, Total cost = $362, Marginal cost = $114
- For four units: Total revenue = $288, Marginal revenue = $72, Total cost = $546, Marginal cost = $184
- For five units: Total revenue = $360, Marginal revenue = $72, Total cost = $816, Marginal cost = $270
Next, let's sketch the total revenue and total cost curves on one diagram.
Total Revenue:
As the output level increases, the total revenue also increases. This can be represented by an upward-sloping curve.
Total Cost:
The total cost initially increases at a decreasing rate and then starts to increase at an increasing rate as the output level increases. This can be represented by a U-shaped curve.
Now, let's sketch the marginal revenue and marginal cost curves on another diagram.
Marginal Revenue:
The marginal revenue curve is downward-sloping and intersects the x-axis at the profit maximizing quantity.
Marginal Cost:
The marginal cost curve is upward-sloping and intersects the x-axis at the profit maximizing quantity.
By analyzing the diagrams, we can determine that the profit maximizing quantity is the output level at which the marginal revenue equals the marginal cost. In this case, the profit maximizing quantity is three units.