Lecture 6: Profits, Prices, and Supply

Where we left off (Lecture 5)

• We built cost curves: MC, AFC, AVC, ATC
• Today we use them to answer three real questions:

1. How much should a firm produce?
2. Can profit be positive, zero, or negative?
3. Why does supply slope up?

A firm is a decision-maker

A firm repeatedly asks:

• One more? (produce one more unit / work one more hour)
• Operate at all today? (shutdown decision)
• What happens if price changes? (demand & revenue)

Uber driver as a firm

Decision first

Rule of thumb: Keep going if the next hour adds profit.

Question: When should the driver stop?

Decision first

Rule of thumb: Keep going if the next hour adds profit.

Question: When should the driver stop?

Answer: Stop after hour 4.

The stopping rule

• MR = marginal revenue (extra revenue from one more unit)
• MC = marginal cost (extra cost from one more unit)

Profit-max output:

\[ \textbf{Produce until } MR = MC \]

Interpretation: The last unit produced just breaks even.

Common mistake

“If MR = MC, then profit is zero.”

Fix: MR = MC implies marginal profit is zero on the last unit.

Total profit depends on profits from all units (and fixed costs).

Profit can be positive, zero, or negative

At the chosen quantity (where MR = MC):

• Profit positive if \(P > ATC\)
• Profit zero if \(P = ATC\)
• Profit negative if \(AVC < P < ATC\) (operate at a loss in the short run)

Shutdown vs break-even

Two separate questions:

1. How much to produce? → choose \(q\) where \(MR = MC\)
2. Whether to produce at all today? → compare price to \(AVC\)

Shutdown rule (short run): - If \(P < AVC\), shut down (produce 0) - If \(P \ge AVC\), operate (even if profit is negative)

Visual: Cost curves

Where demand enters: revenue intuition

How did prices work before price tags?

• Price tags ended bargaining (less price discrimination)
• Posted prices force firms to think: how do customers respond to price?

Intuition: If price rises…

• Elastic demand → quantity falls a lot → revenue may fall
• Inelastic demand → quantity falls little → revenue rises

A quick revenue check

If price goes up by 10%:

• If rides fall by more than 10% → revenue falls (elastic)
• If rides fall by less than 10% → revenue rises (inelastic)

A simple revenue simulation

From MR to supply (competitive case)

On Uber, drivers largely take price as given. They are “price takers.”

Price takers effectively face a perfectly elastic demand curve.¹

MR = P

So the stopping rule becomes:

P = MC

That means: for each fare level, the Uber driver chooses whether to supply a trip.

That relationship generates a supply curve (above \(AVC\)).

Visual: MC becomes supply

MC becomes the firm’s supply curve above the shutdown point.

Supply Elasticity

Like demand, labor supply has an elasticity¹:

\[ \varepsilon^s = \frac{\% \text{change in quantity supplied}}{\% \text{change in price}} = \frac{\Delta q^s/q^s}{\Delta p/p} \]

And the midpoint formula is the default:

\[ \varepsilon^s = \frac{q_1^s - q_0^s}{(q_1^s + q_0^s)/2} / \frac{p_1 - p_0}{(p_1 + p_0)/2} \]

Determinants of labor supply elasticity

Reality check: where the model can fail (one slide)

Even if the model is a useful benchmark, real decisions can deviate:

• Target earnings / reference points (stop after “hitting a goal”)
• Inattention / not optimizing moment-by-moment
• Constraints (fatigue, rules, risk, imperfect info)

Evidence from taxi/ride-hailing:

• Some drivers appear to stop earlier after reaching income targets (debated; nuanced evidence) Times (2016)
• Though evidence that drivers start optimizing with experience (Sheldon 2016)
• Institutional compensation schemes change incentives and behavior (leases vs proportional fees) (Angrist, Caldwell, and Hall 2021)

Uber real time tracker

Uber shifts incentives to get people to drive more.

Uber supply elasticity

Uber supply elasticity (from (Sheldon 2016))

Big-picture takeaways

1. Marginal thinking: keep producing while \(MR > MC\)
2. MR = MC is a stopping rule, not a profit statement
3. Profit can be positive, zero, or negative depending on price vs costs
4. Shutdown depends on \(P\) vs \(AVC\); break-even on \(P\) vs \(ATC\)
5. Supply comes from MC (above the shutdown point)
6. Next step: use demand + supply together to predict market outcomes

References