Lecture 5: Firms, Costs, and Profit Maximization

Firms and Profit Maximization

Today’s goal:

Understand how firms decide how much to produce.

We’ll move in stages:

1. Simple costs \(\implies\) clear decisions
   
2. Realistic costs \(\implies\) same decision rule

What Is a Firm Doing?

A firm chooses output to maximize:

\[ \text{Profit} = \text{Revenue} - \text{Cost} \]

Key idea: a firm is not trying to maximize profit in general – they ask, “Should we produce one more unit?”

Profit maximization is a marginal decision

A World with Constant Marginal Cost

Start with a deliberately simple technology:

• Each extra unit costs the same to produce
• No capacity constraints
• Production is easy to scale

Marginal cost (MC) is constant.

Example:

• Additional hours of work at a fixed wage rate (no overtime)

Average and Constant Marginal Cost

Profit with constant MC

\[\text{Revenue} = \text{Price} \times \text{Quantity} \] \[\text{Cost} = \text{MC} \times \text{Quantity} \] \[\text{Profit} = \text{Price} \times \text{Quantity} - \text{MC} \times \text{Quantity}\]

Height is profit, Y-axis is price, X-axis is quantity

Solve for profit

Constant Marginal Cost: Isoprofit Curves

How to Read This Picture

• Demand limits what the firm can sell
  
• Isoprofit curves rank outcomes by profit
  
• The firm wants the highest isoprofit curve it can reach

Key intuition:

Profit maximization is about trading off price vs quantity

Profit Maximization (Simple Case)

Why This Is Too Simple

Ask yourself:

• Is it realistic that producing one more unit always costs the same?
• Do firms really scale without frictions?

Short answer: no.

Two Types of Short-run Costs

• In the short run, some costs are fixed and some are variable.

Economies of Scale

In many industries:

• Producing more lowers average cost
• Fixed setup costs are spread over more units
• Specialization and learning reduce costs

This explains:

• Why large firms often outcompete small ones
• Why marginal cost may change with output

From Simple to Realistic Costs

So far:

• Constant MC helped us see how decisions are made

Next:

• Realistic short-run production
• Fixed and variable costs
• MC that falls, then rises

Same decision rule. Richer cost structure.

The Paper Airplane Factory

Recall the your small paper airplane firms:

• One class period (short run)
• Simple technology
• Identical output

Marginal Cost: One More Airplane

Think unit by unit:

Marginal cost first falls, then rises.

Average and Marginal Costs

From the same production process:

• AFC: fixed cost per unit
• AVC: variable cost per unit
• ATC: total cost per unit (AVC + fixed cost per unit)
• MC: marginal cost per unit – the cost of producing one more unit

How do average costs change with output?

Average cost formulas and example

• Average Fixed Cost (AFC) = FC / Q (undefined at Q=0)
• Average Variable Cost (AVC) = VC / Q (undefined at Q=0)
• Average Total Cost (ATC) = TC / Q (undefined at Q=0)

Cost Curves

Cost Curves: Average Fixed Cost

Cost Curves: Average Variable Cost

Cost Curves: Average Total Cost

Cost Curves: Marginal Cost

Cost Curves: The “Nike Swoosh”

Key Question for the Firm

“Should we produce one more airplane?”

That decision depends on how marginal cost compares to the marginal revenue (the extra revenue from selling one more unit).

When has the firm maximized profit?

Below is a firm’s table of total revenue, total cost, and profit. Fill in the missing values.

Step 1: Profit for each quantity

|————-:|——————-:|—————-:|—————–:|—————-:|—————-:| | 0 | 0 | 0 | 0 | | | | 1 | 80 | 50 | 30 | 80 | | | 2 | 150 | 80 | 70 | 70 | | | 3 | 210 | 140 | 70 | 60 | | | 4 | 270 | 220 | 50 | 60 | | | 5 | 320 | 310 | 10 | 50 | |

Step 2: Marginal Revenue (MR = \(\Delta\)TR)

Step 3: Marginal Cost (MC = \(\Delta\)TC)

When was profit maximized?

The Firm’s Decision Rule (Still!)

Even with realistic costs:

• If \(MR > MC\) \(\implies\) produce more
• If \(MR < MC\) \(\implies\) produce less

Profit-maximizing output satisfies: \(\boxed{MR = MC}\)

Big Takeaway

We started with simple costs to see decisions clearly.
Then we made costs realistic — and the decision rule survived.

That’s economics.

Geometry of Profit Maximization

1. Start with the MC curve
2. Add the MR curve
3. Find their intersection
4. That quantity maximizes profit

Adding in Demand and Marginal Revenue

From Quantity to Price

Once \(Q^*\) is chosen:

• Price comes from the demand curve
• Firms can be price takers (take price as given) or price setters (set price themselves)

Profit, Loss, and Surplus

At the chosen output:

• Profit = \((P - ATC) \times Q\)
• Can be positive, zero, or negative

But:

Producing can be optimal even with losses.

Why Market Power Matters (Preview)

A firm has market power if:

• It faces little competition
• Its demand curve is less elastic
• It can set its own price

Result:

• Price > MC
• Some gains from trade are lost

What You Should Take Away

1. Firms make marginal decisions
2. Profit maximization:
   \[ \boxed{MR = MC} \]
3. Shutdown depends on AVC
4. Break-even depends on ATC

Coming Next

• Perfect competition
• Supply curves
• Market equilibrium
• Why price-taking changes everything

Credit

Core-Econ, The Economy 2.0: Microeconomics, Unit 7
“Firms and Their Customers”
Adapted and reorganized for ECON Principles