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Price, and Revenue
Chapter 9: Limited Decision-Making in Perfect Competition
The market-determined price for your good is $80. Therefore, your total revenue equals
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Your total cost function is
Therefore, your total profit equation is
In order to determine the profit maximizing quantity, you take the following steps:
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1. Take the derivative of total profit with respect to quantity.
2. Set the derivative equal to zero and solve for q.
3. Divide both sides of the equation by 0.1.
Thus, 700 units of the good is the profit-maximizing quantity.
4. To determine total profit, simply substitute 700 for q in the total profit equation.
Total profit equals $12,000.
Maximizing profit as a marginal decision
To maximize profit by using marginal revenue and marginal cost, you focus on the contribution one additional unit of output makes to your revenue relative to its contribution to your cost.
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Marginal revenue is the change in total revenue that occurs when one additional unit of output is produced. Thus,
This equation indicates that marginal revenue is the slope of the total revenue function.
As I note in Chapter 8, marginal cost is the change in total cost that occurs when one additional unit of output is produced.
So, marginal cost is the slope of the total cost equation.
In order to maximize profit, you want to maximize the difference between total revenue and total cost. Thus, if your marginal revenue is greater than your marginal cost (MR>MC), an additional unit of output adds more to your firm’s revenue than it adds to your firm’s cost, and the additional unit earns you more profit.
On the other hand, if your marginal revenue is less than your marginal cost (MR<MC), then the additional unit adds less to your revenue than it adds to your cost, and your profit decreases.
In order to maximize profit, you want to produce the quantity of output that corresponds to marginal revenue equals marginal cost (MR=MC).
Figure 9-2 indicates the profit-maximizing quantity of output by using marginal revenue equals marginal cost.
Figure 9-2:
Profit maximization with marginal revenue and marginal cost.
