Final answer:
To determine the profit-maximizing quantity of output, calculate the total revenue, marginal revenue, total cost, and marginal cost for each output level. The profit-maximizing quantity occurs where marginal revenue equals marginal cost, in this case, at three units of output. Sketch the total revenue and total cost curves, as well as the marginal revenue and marginal cost curves to visualize the relationship between quantity and revenue/cost.
Step-by-step explanation:
The profit-maximizing quantity of output can be determined by analyzing the relationship between total revenue and total cost. To calculate total revenue, we multiply the price per unit by the quantity sold. In this case, the price per unit is $20 and the quantity levels range from one to five units. The total cost is the sum of the fixed costs and variable costs at each quantity level.
Using this information, we can construct a table to calculate total revenue, marginal revenue, total cost, and marginal cost for each output level. Based on the table, we can see that total revenue increases as quantity increases, whereas total cost increases at a decreasing rate due to economies of scale. The profit-maximizing quantity occurs where marginal revenue equals marginal cost. In this case, it occurs at three units of output, where marginal revenue is $20 and marginal cost is $35.
To sketch the total revenue and total cost curves, we can plot total revenue on the y-axis and quantity on the x-axis. The total revenue curve will start at $0 when quantity is 0 and increase linearly as quantity increases. The total cost curve will start at the fixed cost level and increase at a decreasing rate.
Similarly, we can sketch the marginal revenue and marginal cost curves by plotting marginal revenue and marginal cost on the y-axis and quantity on the x-axis. The marginal revenue curve will start at the price per unit and decrease as quantity increases. The marginal cost curve will start at the variable cost level and increase at an increasing rate.