SUPPLY

ECON 2101 GEORGETOWN UNIVERSITY

C. ALAN BESTER FALL 2024
OUTLINE

• Varian, Chapters 23-24.

• In a perfectly competitive industry, a firm’s marginal cost curve is its supply curve.
• …or more precisely, the increasing portion of the MC curve.

• Firm profits are determined by market price and the AC curve.

• Profits and producer surplus are almost the same thing.
• The only difference is fixed cost, which cannot be recovered.
• In the short run, firms may choose to produce at a loss as long as 𝑝 >AVC, recouping a portion of FC.

• One way to understand firm vs industry supply is thinking “short vs long run”.
• In a competitive industry with no barriers to entry, if firms are making profits, more firms enter
• This continues until, in long run industry equilibrium, all firms make zero profit.
• This happens when price equals the minimum of long run average cost.
REVIEW: PROFIT MAXIMIZATION

• On the homework, I ask you to derive factor demands by maximizing a firm’s profit.
• Let’s look at the first couple of steps to get you started.
1 1
• Same production function as last lecture: 𝑓 𝐾, 𝐿 = 𝐾 𝐿 4 4

• Firm produces using capital (𝐾), which costs $𝑟 per unit, and labor (𝐿), which costs $𝑤/unit.
• Output good sells for price of $𝑝 per unit.
1 1
• Profits can therefore be written: 𝜋 𝐾, 𝐿 = 𝑝𝐾 𝐿 − 𝑟𝐾 − 𝑤𝐿
4 4

• Factor demands 𝐾 ∗ (𝑟, 𝑤, 𝑝) and 𝐿∗ (𝑟, 𝑤, 𝑝) are the levels of 𝐾 and 𝐿 that max profits.
• Take partial derivatives of 𝜋 𝐾, 𝐿 , set to zero, and solve:
𝜕𝜋 𝑝 −3 1 𝜕𝜋 𝑝 1 −3
= 𝐾 4 𝐿4 − 𝑟 = 0 = 𝐾 4𝐿 4 − 𝑤 = 0
𝜕𝐾 4 𝜕𝐿 4
REVIEW: COST CURVES

• Firm’s average cost function 𝐴𝐶(𝑦) is generally U-shaped

• Fixed costs don’t depend on 𝑦 so AFC is decreasing. $
• Diminishing RTS for large enough 𝑦 AVC is increasing. 𝑀𝐶(𝑦)

• MC crosses the AC and AVC curves at their minima.

𝐴𝐶(𝑦)
• Marginal cost curves across different plants/firms aggregate
horizontally (similar to demand curves). 𝐴𝑉𝐶(𝑦)

• In short run, when some input(s) fixed, can think of multiple

𝑆𝑅𝐴𝐶 curves depending on the level of fixed input(s)
𝑦
• 𝐿𝑅𝐴𝐶 is the lower envelope of all 𝑆𝑅𝐴𝐶 curves.
DEMAND FACED BY
FIRM IS HORIZONTAL…
• In perfect competition (see very first lecture!) we
usually treat each firm as a very small part of the market. $ Market
• Market equilibrium is (𝑌, 𝑝∗ ) where 𝑌 is huge relative to Demand

the scale of the firm’s cost curves we’ve studied.

𝑀𝐶(𝑦)

• In perfect competition, firm is a price-taker.

𝐴𝐶(𝑦)
• 𝑌 is so large compared 𝐴𝐶(𝑦): If we try to cut/raise
𝑝∗
production enough to move market price, costs explode. “Demand curve”
(as perceived by our
• To an individual firm, it’s as if the demand curve is tiny little firm)

horizontal at the market price 𝑝∗ . 𝑦

𝑌
…WHICH MEANS 𝑀𝐶(𝑦) IS
THE FIRM’S SUPPLY CURVE.
• Profit maximizing firm faces flat demand curve at 𝑝∗ .
𝜋 𝑦 = 𝑝𝑦 − 𝑐 𝑦 Profit maximizing $
quantity 𝑦 ∗ satisfies
𝑀𝐶(𝑦)
𝑑𝜋
= 𝑝 − 𝑀𝐶 𝑦 = 0 𝑝 = 𝑀𝐶 𝑦∗
𝑑𝑦
𝑝∗ 𝐴𝐶(𝑦)
• This means 𝑀𝐶(𝑦) is the firm’s supply curve… almost.
𝑑2 𝜋 𝐴𝑉𝐶(𝑦)
• At a maximum, must have < 0.
𝑑𝑦 2
..as long as
𝑑2 𝜋 𝑝∗
= −𝑀𝐶 ′ (𝑦) <0 𝑀𝐶 ′ 𝑦 >0 Firm supply curve
𝑑𝑦 2
𝑦
• Geometrically, this means the firm’s supply curves is the 𝑦∗
increasing portion of its marginal cost curve.
PROFITS

• Now that we know the optimal quantity 𝑦 ∗ , how much

profit does the firm actually make? $

𝜋 𝑦 ∗ = 𝑝∗ 𝑦 ∗ − 𝑐 𝑦 ∗ = 𝑦 ∗ 𝑝∗ − 𝐴𝐶(𝑦 ∗ ) 𝑀𝐶(𝑦)
Note: 𝑐 𝑦 ∗ = 𝑦 ∗ 𝐴𝐶(𝑦 ∗ )
𝑝∗ 𝐴𝐶(𝑦)
Area=Profit
• Geometrically, this is the area of a rectangle: height
𝐴𝐶(𝑦 ∗ ) 𝐴𝑉𝐶(𝑦)
𝜋 𝑦∗ = 𝑦∗ 𝑝∗ − 𝐴𝐶(𝑦 ∗ )
Area = base × height

𝑦
𝑦∗
base
NEGATIVE PROFITS AND SHUTDOWN

• When 𝑝∗ < 𝐴𝐶 𝑦 ∗ , the firm makes negative profits.

• Will a firm making negative profits continue to produce? Why
$
not simply shut down (𝑦 = 0) instead?
𝑀𝐶(𝑦)
• As long as 𝑝∗ > 𝐴𝑉𝐶 𝑦 ∗ , the firm makes enough revenue
to cover its variable costs of production.
𝐴𝐶(𝑦)
• This net operating revenue allows the firm to recoup a portion of
its fixed costs (which we assume are already paid).
𝐴𝑉𝐶(𝑦)
• If 𝑝∗ stays below 𝐴𝐶 𝑦 ∗ , the firm eventually shuts down 𝑝∗ Profit < 0

(presumably the next time fixed costs come due). Revenue - VC

𝑜 𝑝𝑜
• The price 𝑝 = min(𝐴𝑉𝐶) is the shutdown point.
• Below this, the firm makes negative net operating revenue and 𝑦
𝑦∗
will cease its day-to-day operations entirely (shut down).
PROFITS VS PRODUCER SURPLUS

• As argument on last slide suggests, in microeconomics we

generally treat fixed costs as sunk costs. $
• Sunk costs have already been incurred. That money is gone. 𝑀𝐶(𝑦)
• Think gambling/poker: “Don’t throw good money after bad.”
𝑝∗ 𝐴𝐶(𝑦)
• Producer surplus ignores fixed costs. It can be written Area=Profit

𝑷𝑺 = 𝑦 ∗ 𝑝∗ − 𝐴𝑉𝐶(𝑦 ∗ ) = 𝜋 𝑦 ∗ + 𝐹 𝑷𝑺 𝐴𝑉𝐶(𝑦)

• We can show using calculus that this is equivalent to our

old definition of PS (area above the supply curve).
𝑦
𝑦∗
EXAMPLE

• From last lecture: Fixed

cost 100
𝑐 𝑦 = 𝑦 2 + 100 𝐴𝐶 𝑦 = 𝑦 + $
𝑦
𝑑𝑐(𝑦)
𝑀𝐶 𝑦 = = 2𝑦 𝐴𝑉𝐶 𝑦 = 𝑦
𝑑𝑦
• Suppose market price is 𝑝∗ = $30 𝑀𝐶(𝑦) 𝐴𝐶(𝑦)
• 𝑀𝐶 𝑦 ∗ = 2𝑦 ∗ = 30 𝑦 ∗ = 15 pink area = $125
100 𝑝∗ = $30
• 𝐴𝐶 𝑦∗ = 15 + 15
= $21.67 𝐴𝐶(𝑦 ∗ ) = $21.67
𝐴𝐶(𝑦 𝑚𝑖𝑛 ) = $20
𝐴𝑉𝐶
• 𝜋 𝑦 ∗ = 30 − 21.67 15 = $125 green area = $225

• PS (method #1): 𝑦 ∗ 𝑝∗ − 𝐴𝑉𝐶(𝑦 ∗ ) = 15 30 − 15 = $225

• Difference between PS and profit = 225 − 125 = $100 𝑦
𝑦 𝑚𝑖𝑛 = 10 𝑦 ∗ = 15
1 1
• PS (method #2): Area of =
2
𝑏𝑎𝑠𝑒 ℎ𝑒𝑖𝑔ℎ𝑡 =
2
30 15 = $225
LONG RUN EQUILIBRIUM:
ENTRY AND EXIT
• To move from firm to industry supply we make two more
simplifying assumptions: $
i. Firms are all identical
𝑀𝐶(𝑦)
ii. There are no barriers to entry (beyond fixed costs)

• Suppose that, in a ‘short run equilibrium’ market price is 𝑝∗ . 𝑝∗ 𝐴𝐶(𝑦)

• Firms are able to cover FC and make a moderate profit (pink).
𝑝𝑚𝑖𝑛 𝐴𝑉𝐶(𝑦)
• If a new firm can set up and enter the industry next year by
paying the same fixed cost, more firms will enter.
• More firms entering shifts industry supply out, lowering 𝑝∗ .
• This continues until 𝑝∗ = 𝑝𝑚𝑖𝑛 (minimum of AC) 𝑦
• At this price, there is no incentive for new firms to enter.
INDUSTRY SUPPLY

• “But I thought individual firms couldn’t affect price?”

• They can’t… at least not by themselves $ Market
Demand
• Each firm produces a very small part of total output, 𝑌
𝑀𝐶1 (𝑦) 𝑀𝐶𝑛 (𝑦)
• If any of them individually tried to raise price, they’d sell zero. 𝑀𝐶2 (𝑦)
𝑀𝐶3 (𝑦)
𝑀𝐶𝑛+1 (𝑦)

• But if profits are positive, one or more firms will enter. 𝐴𝐶(𝑦)
• That will shift total output and effect the equilibrium price. 𝑝∗
𝑝′
• And that will continue until all firms make zero profit
(equivalently, just enough revenue to cover fixed costs).
• More specifically, with discrete # of firms, entry continues until 𝑦
𝑌 𝑌′
one more firm entering would cause price to fall below 𝑝𝑚𝑖𝑛 .
SHORT VS LONG RUN
INDUSTRY SUPPLY
• We now have a coherent theory of market (industry) supply and
how it arises from individual firms’ decisions. $ Market
• An individual firm’s supply curve is simply MC. Demand
Market
• (More precisely the upward sloping portion of the MC curve.) Supply Market
𝑀𝐶1 (𝑦) (short run)
𝑀𝐶2 (𝑦) Supply
• In the short run, market supply is the horizontal sum of (long run)

individual firm’s supply curves.

• It still slopes upward, but is much flatter (simple geometry!)

• Long run market supply is even flatter.

• If prices rise in the short run, firm-level profits increase.
• In the long run, this means new firms enter, and prices fall. 𝑦
• Can show supply always slopes up (no ‘Giffen goods’ for producers).
RESTRICTED ENTRY AND
ECONOMIC RENT
• Consider what happens when total supply is capped at some level 𝑌ത
$ $ This occurs, for example,
when some factors of
𝑀𝐶(𝑦) production are in fixed
𝑀𝐶1 (𝑦) 𝑀𝐶𝑛 (𝑦)
supply (oil deposits) or are
𝑀𝐶2 (𝑦)
𝑀𝐶3 (𝑦)
𝑀𝐶𝑛+1 (𝑦)
𝑝∗ 𝐴𝐶(𝑦) regulated (taxi licenses).

𝐴𝐶(𝑦) 𝑝ҧ In these cases, entry is

Rent
𝑝∗
𝐴𝑉𝐶(𝑦) effectively limited, so firms
𝑝ҧ earn economic rents in
equilibrium (payments to a
factor of production in
excess of what is necessary
𝑦 𝑦
𝑌ത for it to be supplied).
Industry Individual firm
RENT SEEKING

• Most situations where supply is capped involve government regulation.

• Either directly, as in the case of taxi medallions/licenses…
• …or ‘indirectly’ as in the case of factors of production that are in fixed supply, like oil deposits.
• Government may also limit entry to incentivize firms to innovate (R&D expenditures/patents).
• So the problem becomes as much about political science as economics.
• Firms that lobby lawmakers to protect/increase their profits = rent seeking behavior.
• Varian’s take (Chapter 24): Rent seeking is 100% deadweight loss, since the resources that
firms/industries spend on PACs/lobbying/campaign contributions aren’t generating any surplus.
• This may be a little short-sighted (patents obviously have benefitted society!).
• But for many industries these days it’s hard to argue with.