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Part III: Market Structures and the Decision-Making Environment Using the demand equation to derive total revenue as a function of q requires the following steps:
1. Add 200P to both sides of the demand equation.
2. Subtract q from both sides of the equation.
3. Divide both sides of the equation by 200.
4. To determine total revenue, multiply both sides of the demand equation by q.
This equation tells you how much total revenue equals given any value for quantity, q. Thus, total revenue is a function of q. If your total cost equation is
total profit, π, is determined by subtracting total cost from total revenue, or
After you have the total profit equation, the following steps enable you to determine the profit-maximizing quantity and price:
1. Take the derivative of the total profit equation with respect to quantity.
2. Set the derivative equal to zero and solve for q.
This is your profit-maximizing quantity of output.
