# Competitive Equilibrium in the Long Run

Christopher Makler

Stanford University Department of Economics

Econ 50: Lecture 14

## Today's Agenda

Part 1: Taxes (from last time)

Part 2: Long-Run Competitive Eqm

Equilibrium quantity with a tax

Elasticity and tax incidence

Welfare effects of a tax

Externalities and Pigovian taxes

The "zero profit condition"

Firm entry and exit

Long-run industry "supply curve"

Increasing/decreasing/constant cost industries

# Effects of Taxes and Subsidies

D(p_C) = 10 - p_C
S(p_F) = 2p_F - 2

Solve for the equilibrium prices $$p_F$$ and $$p_C$$
and quantity $$Q = D(p) = S(p)$$,
as well as government revenue  if:

(1)\ \ \text{No tax: }p_C = p_F = p
(2)\ \ \text{Firms pay tax }t: p_C = p, \ \ \ p_F = p - t
(3)\ \ \text{Consumers pay tax }t: p_C = p + t, \ \ \ p_F = p
p_C = \text{price consumers pay}
D(p_C) = 10 - p_C
S(p_F) = 2p_F - 2
(1)\ \ \text{No tax: }p_C = p_F = p
p_C = \text{price consumers pay}
D(p_C) = 10 - p_C
S(p_F) = 2p_F - 2
(2)\ \ \text{Firms pay tax }t: p_C = p, \ \ \ p_F = p - t
p_C = \text{price consumers pay}
D(p_C) = 10 - p_C
S(p_F) = 2p_F - 2
(3)\ \ \text{Consumers pay tax }t: p_C = p + t, \ \ \ p_F = p
p_C = \text{price consumers pay}

# Elasticity and Tax Incidence

Tax burden for consumers:
the amount of the tax that results in an increase in the price paid by consumers,
relative to the equilibrium price

Tax burden for firms:
the amount of the tax that results in an decrease in the price received by firms,
relative to the equilibrium price

What is the burden in this case?

How does tax burden relate to the relative elasticities of demand and supply?

# Welfare Effects of a Tax

Why are taxes (generally) inefficient?

Competitive markets:
consumers set P = MB,
firms set P = MC,

therefore MB = MC

If consumers and producers face the same price, then MB = MC

If there is a tax or a subsidy, there is a mismatch between MB and MC

Caveat: what if what consumers and producers think is their MB is not?

# The "Zero Profit Condition"

\pi_1 = p_1y_1^* - wL_1^*-rK_1^*

Profits in industry 1 when profit maximizing

Profits in industry 2 when profit maximizing

A firm in industry 1 should remain in industry 1 as long as

\pi_1 > \pi_2
p_1y_1^* - wL_1^*-rK_1^* > \pi_2
p_1y_1^* - wL_1^*-rK_1^*- \pi(y_2^*)>0

"Positive economic profit"

SR fixed costs

\pi_2 = p_2y_2^* - wL_2^*-rK_2^*

LR fixed costs

# The Effect of Entry and Exit

Industry Short Run:

Number of Firms is Fixed

Industry Long Run:

Firms will enter an industry with positive economic profits; firms will leave an industry with negative economic profits.

# Calculating Long-Run Equilibrium

D(p) = S(p)
S(p) = Ny^*(p)

Market supply: Given an industry with N identical firms, short-run supply will equal the number of firms
times the quantity supplied by each firm.

Equilibrium: In any equilibrium, the quantity demanded must equal the quantity supplied.

p = c'(y^*)

Profit maximization: each firm chooses the $$y^*$$
such that MR = MC; for a competitive firm, this is:

Zero profit: exit and entry drive profit to zero,
or AR = AC: for a competitive firm, this is:

p = \frac{c(y^*)}{y^*}

Set MC = AC to find y* and therefore p

N = \frac{D(p)}{y^*(p)}

(you'll do the math in the homework)

# Increasing, Decreasing, and Constant Cost Industries

Market Supply Curve:

Quantity supplied by firms at every possible price

Industry "Supply Curve":

Locus of (quantity, price) combinations that could arise in long-run competitive equilibrium, given different demand conditions.

Market Supply and Demand

Typical Firm's Cost Curves

MC

y

$perunit P Q S 1. demand increases D' D AC What is the effect of an increase in demand if costs are unaffected by the number of firms? S' 3. firms enter $$S_{LR}$$ Market Supply and Demand Typical Firm's Cost Curves MC y$ perunit

P

Q

S

demand
increases

D'

D

AC

What is the effect of an increase in demand if costs decrease as firms enter?

S'

firms enter,
costs decrease

$$S_{LR}$$

MC'

AC'

firms enter,
costs decrease

## What happens to inputs as more firms enter an industry?

Industry too small to affect price of inputs

Inputs get cheaper/faster/better

Inputs are scarce, command higher prices

Story

Industry Type

Industry Supply Curve

"Constant Cost Industry"

Horizontal

"Decreasing Cost Industry"

Downward Sloping

"Increasing Cost Industry"

Upward Sloping

# Conclusions and Next Steps

In today's lecture we talked about how producers face tradeoffs between two goods.

In Part II we talked about how firms could switch industries to chase profits,
leading to the "equal profit condition" that in LR equilibrium,
firms must earn the same profits in all industries.

In Part I we talked about how PPF represents possible efficient allocations of resources.
We modeled the economy as two competitive firms, taking output and input prices as given,
and saw how profit-seeking leads them to choose the highest-value point along the PPF,
even though each firm is only responsible for choosing its own output.

Next time: we use preferences, as expressed by consumer demand,
to find the socially optimal point along the PPF.

By Chris Makler

# Econ 50 | Spring 2022 | 14 | LR Competitive Eqm

Bringing supply and demand together

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