"The one place producer theory is harder than consumer theory is you're not given a budget constraint. You get to choose how much you have. You get to choose how much to produce."

"Oligopoly is really the way markets almost all look, which is a number of firms competing, but not too many. Think of the auto industry. There's more than one car company, but there aren't 1,000 car companies."

Price-Takers: In a perfectly competitive market, all firms are price-takers. No action by any individual firm can affect the market price.

Figure 7-1: In perfect competition, each firm faces perfectly elastic demand. Note: x-axis is little q (firm), not big Q (market).

"This does not say the market demand is perfectly elastic. The demand for any given firm is very elastic. I'm not saying the demand for Eiffel Tower statuettes in general is perfectly elastic. I'm saying that across sellers, the firm-specific demand is perfectly elastic."

eBay (Almost Perfect):

• Products are (somewhat) identical
• Prices are listed
• Easy to shop

But violations exist:

• Shipping costs hidden (shrouded attribute)
• Products not truly identical
• Time to search = transaction cost

The Eiffel Tower Keychain Example:

"Think of the Eiffel Tower. There are literally hundreds of guys who have spread out blankets selling the same damn little Eiffel Tower keychain. I can easily see what people are charging. They're right next to each other. There's little transaction costs. I can see it's the same damn keychain."

Result: A student verified that all sellers right near the Eiffel Tower charged identical prices! But once you got further away, prices differed (different location = not identical anymore).

max π(q) = R(q) - C(q)

where R(q) = revenue, C(q) = cost

Take derivative and set to zero:

dπ/dq = dR/dq - dC/dq = 0

MR = MC

General Rule: Marginal Revenue = Marginal Cost

"In a competitive market, we know what the marginal revenue is. What do you get from selling the next unit? Well, you get the market price, p. It's given to you. The marginal revenue is always p."

P = MC

The profit maximization rule in perfect competition

• Cost function: C(q) = 10 + 5q²
• Market price: p = 30
• Marginal cost: MC = dC/dq = 10q

Set P = MC:

30 = 10q

q* = 3

Figure 7-2: Left: Revenue (R) and Cost (C) curves. Right: Profit curve showing maximum at q = 3.

"Think of yourself as climbing a mountain that's in the clouds. And you're trying to get to the top of the mountain, but you can't see more than one step in front of you. If you take a step forward and you go up, you know you're heading up the mountain. Take a step forward and you go down, you're heading down the mountain."

Marginal Decision-Making:

• At q = 1, 2, 3: MR > MC → each unit adds to profit → keep going up!
• At q = 4, 5, 6: MR < MC → each unit reduces profit → going down!
• At q = 3: MR = MC → at the top of the hill

Figure 7-3: Profit = (P - ATC) × q = blue rectangle.

Step 1: Find Average Cost at q = 3

AC = C(q)/q = (10 + 5q²)/q = 10/q + 5q

AC(3) = 10/3 + 5(3) = 3.33 + 15 = 18.33

Step 2: Calculate Profit per Unit

Profit per unit = P - AC = 30 - 18.33 = 11.67

Step 3: Calculate Total Profit

π = (P - AC) × q = 11.67 × 3 ≈ 35

Profit = (Price - Average Cost) × Quantity

This is the area of the blue rectangle in Figure 7-3

Question: What happens if the firm must pay $10 per unit sold?

New cost function:

C(q) = 10 + 5q² + 10q

Note: NOT 20 + 5q². The tax is per unit, not a flat amount!

New MC: d(10 + 5q² + 10q)/dq = 10q + 10

Set P = MC:

30 = 10q + 10

q* = 2 (down from 3)

Figure 7-4: With tax, MC shifts up. Profit rectangle shrinks in both width (fewer units) and height (lower profit per unit).

"In the short run, losing money is not necessarily a reason to shut down. You can lose money and want to stay in business."

With C(q) = 10 + 5q² and p = 10:

• MC = 10q, so at p = MC: q* = 1
• Revenue = 10 × 1 = 10
• Cost = 10 + 5(1)² = 15
• Profit = 10 - 15 = -5 (losing money!)

If you produce q = 1: Profit = -5

If you produce q = 0: Profit = -10 (still pay fixed costs!)

Better to produce and lose 5 than shut down and lose 10!

Shut down when: P < AVC

Keep producing as long as price covers variable costs

"Fixed costs are, in the short run, sunk. They're irrelevant. You already paid them. You just want to ask for the next unit: Will I make money?"

For C(q) = 10 + 5q²:

• VC = 5q²
• AVC = 5q
• At optimum (MC = P): 10q = P → q = P/10
• So AVC = 5(P/10) = 0.5P

Since AVC = 0.5P < P always, the firm never shuts down with this cost function.

Figure 7-5: At each price, the firm produces where P = MC.

• At P = 10: produce q = 1
• At P = 20: produce q = 2
• At P = 30: produce q = 3
• At P = 40: produce q = 4

The Supply Curve IS the Marginal Cost Curve

"The demand curve was the marginal willingness to pay for a good. The supply curve is the marginal cost of producing the next good."

Figure 7-6: Short-run firm supply curve S = MC = 10q.

Technical Definition:

Short-run supply curve = MC curve above the shutdown point

(above minimum AVC)

"In the long run, if you've done all your optimizing and you're still losing money, you're just shit out of luck. You should get out of the business because there's no more optimization you can do."

Figure 7-7: Adding identical firms makes market supply more elastic. S₁ = 1 firm, S₂ = 2 firms, S₃ = 3 firms.

With n identical firms:

• Each firm: q = P/10
• Market: Q = n × (P/10)

Example with n = 1:

• At P = 10: Q = 1
• At P = 30: Q = 3

Example with n = 2:

• At P = 10: Q = 2
• At P = 30: Q = 6

More identical firms → Flatter (more elastic) market supply curve

"If I said competitive markets have an infinite number of firms and the more firms there are, the more elastic the supply curve, think about what that implies to the supply curve..."

(We'll explore this next lecture!)

"This is the beauty of being at MIT. You'll never find an introductory economics course that does this. Before Paul Samuelson taught this class, people would teach the graph and be done with it. You guys want the math? I'm giving you the math."

1. Start with production function: q = √(L × K)

2. Given: w = 5, r = 10, K̄ = 1

3. Derive cost function: C(q) = 10 + 5q²

4. Get MC: MC = 10q

5. Firm supply (P = MC): q = P/10

Assume n = 6 firms

Q = 6 × (P/10) = 3P/5

Market supply: Q = (3/5)P

From consumer theory: Q = 48 - P

Set supply = demand:

(3/5)P = 48 - P

(3/5)P + P = 48

(8/5)P = 48

P* = 30

Q* = 18

• Market quantity Q* = 18
• With 6 identical firms: each produces q* = 18/6 = 3
• Check: At P = 30, firm sets MC = P → 10q = 30 → q = 3 ✓

The magic of the market: Everyone is satisfied!

Coming up: Competition II - What happens when there are infinitely many firms? Long-run equilibrium and the role of entry/exit.