Final answer:
To calculate total revenue, multiply the price per unit by the quantity sold. Marginal revenue is the change in total revenue divided by the change in quantity. Total cost is the sum of fixed costs and variable costs. Marginal cost is the change in total cost divided by the change in quantity. The profit maximizing quantity is the level of output where marginal revenue equals marginal cost.
Step-by-step explanation:
To calculate total revenue, multiply the price per unit by the quantity sold. In this case, the price per unit is $72 and the quantity sold ranges from one to five units. So, the total revenue for each output level is as follows:
One unit: $72
Two units: $144
Three units: $216
Four units: $288
Five units: $360
Marginal revenue is the change in total revenue divided by the change in quantity. For example, the marginal revenue of the second unit is $144 (total revenue of two units) minus $72 (total revenue of one unit), which equals $72. The marginal revenue for each output level is as follows:
One unit: $72
Two units: $72
Three units: $72
Four units: $72
Five units: $72
Total cost is the sum of fixed costs and variable costs. Fixed costs in this case are $100. Variable costs for each output level are:
One unit: $64
Two units: $84
Three units: $114
Four units: $184
Five units: $270
So, the total cost for each output level is as follows:
One unit: $164
Two units: $184
Three units: $214
Four units: $284
Five units: $370
Marginal cost is the change in total cost divided by the change in quantity. For example, the marginal cost of the second unit is $184 (total cost of two units) minus $164 (total cost of one unit), which equals $20. The marginal cost for each output level is as follows:
One unit: $20
Two units: $20
Three units: $30
Four units: $70
Five units: $86
The profit maximizing quantity is the level of output where marginal revenue equals marginal cost. In this case, that occurs at three units.
Below is a table summarizing the calculations:
Summary of CalculationsOutput LevelTotal RevenueMarginal RevenueTotal CostMarginal Cost1$72$72$164$202$144$72$184$203$216$72$214$304$288$72$284$705$360$72$370$86
On the first diagram, sketch the total revenue and total cost curves. The total revenue curve will be a straight line with a positive slope representing the increase in revenue as output increases. The total cost curve will be a curved line starting at the fixed cost level and increasing at a faster rate as output increases.
On the second diagram, sketch the marginal revenue and marginal cost curves. Both curves will start at the same point as the total revenue and total cost curves, but the marginal revenue curve will have a constant slope equal to the price per unit, while the marginal cost curve will have a steeper slope as output increases.
The profit-maximizing quantity is the level of output where the marginal revenue curve intersects the marginal cost curve. In this case, that occurs at three units.