# Profit

The profit for a monopolist is the revenue minus the costs of production.

## Example

Zoe is the only lemonade seller on her street. People who drive home stop by to purchase liters of her lemonade.

The demand for lemonade is: $$P = 10 - 2Q$$

When Zoe produces a quantity Q of lemonade, her revenue is $$R \left( Q \right) = PQ = \left( 10 - 2Q \right) Q$$

Her cost follows the equation $$C \left( Q \right) = 2 Q$$

Overall, her profit is $$\Pi \left( Q \right) = R \left( Q \right) - C \left( Q \right) = \left( 10 - 2Q \right) Q - 2 Q = 8Q - 2 Q^2$$

If Zoe makes 2 liters of lemonade (Q = 2), her profit is $$\Pi \left( 2 \right) = 8 \times 2 - 2 \times 2^2 = 8$$

She would make a profit of \$8.

### Question

This question is available to anyone who signs up.