## The Firm and Profit Maximization

### What is a firm?

• A firm is any entity that sells goods in order to make a profit
• Assumption: every firm’s objective is to maximize profit
• Can sell any type of product
• Can take any form
• Firms are considered a black box in IO
• Firms purchase input goods that are used to produce a final product
• We don’t care about the in-between steps
• We only care about what inputs are used, how much of the final good is created, and how much it costs to produce

### Profit Maximization

Profit maximization is the act of buying and transforming inputs and selling outputs in a way that leads to the highest possible profit. Firms choose quantity, q, that maximizes the following equation:

$\Pi(q)=TR(q)-TC(q)$

• $$\Pi(q)$$ denotes the profit of producing q units
• $$TR(q)$$ denotes the total revenue of producing q units
• $$TC(q)$$ denotes the total cost of producing q units

### Common Assumptions

• Downward sloping demand
• Non-decreasing marginal cost as $$q → \infty$$
• Production function and demand function are continuous and differentiable

Note: in this class, we will take these assumptions as given