UNIT II:Firms & Markets

UNIT II: Firms & Markets

• Theory of the Firm• Profit Maximization• Perfect Competition• Review• 7/14 MIDTERM

7/7

Perfect Competition

Is it true that the rational pursuit of private interests produces coherence rather than chaos, and if so, how is it done?

-- Frank Hahn

Adam Smith described a world in which market competition weed-outs inefficient behavior, so that the ‘pursuit of private interests’ is led, as if by an invisible hand, to promote the general welfare of society.

Today, we will solve for a competitive equilibrium and consider its welfare implications. We will also construct a general equilibrium model of Smith’s vision.

Perfect Competition

• Assumptions and Implications (from last time)• Solving for the Competitive Equilibrium• Equilibrium and Efficiency• General Equilibrium• Welfare Analysis

Perfect Competition

Assumptions

• Firms are price-takers: can sell all the output they want at P*; can sell nothing at any price > P*.

• Homogenous product: e.g., wheat, t-shirts, long-distance phone minutes.

• Perfect factor mobility: in the long run, factors can move costlessly to where they are most productive (highest w, r).

• Perfect information: firms know everything about costs, consumer demand, other profitable opportunities, etc.

Perfect Competition

Implications

1) Firms produce at minimum average cost, i.e., “efficient scale.” (AC = ACmin)

2) Price is equal to marginal cost. (P = MC)

3) Firms earn zero (economic) profits. ( = 0)

4) Market equilibrium is Pareto-efficient.

Perfect Competition

In the Long-run…

1) Firms produce at minimum average cost, i.e., “efficient scale.” (AC = ACmin)

2) Price is equal to marginal cost. (P = MC)

3) Firms earn zero (economic) profits. ( = 0)


Perfect Competition

The Short-run & the Long-run

In the short-run, firms adjust to price signals by varying their utilization of labor (variable factors).

In the long-run, firms adjust to profit signals by – varying plant size (fixed factors); and – entering or exiting the market.

We can use this account to understand (and solve for) the long-run competitive equilibrium.

Short-run equilibrium with three firms. Firm A is making positive profits, Firm B is making zero profits, and Firm C is making negative profits (losses).

Firm A Firm B Firm C q q q

$

P

MC MC MCAC

ACAC

q: firm

Q: market

Perfect Competition

Short-run equilibrium with three firms. Firm A is making positive profits, Firm B is making zero profits, and Firm C is making negative profits (losses).

Firm A Firm B Firm C q q q

$

P

In the long run,Firm C will exit the market.

MC

AC

MC

AC

Perfect Competition

In the long-run, inefficient firms will exit, and new firms will enter, as long as some firms are making positive economic profits.

Firm A Firm B Firm D q q q

$

P

MC MC

AC

MC

ACAC

Perfect Competition

In the long-run, if there are no barriers to entry, then new firms have access to the most efficient production technology. We call this the efficient scale.

Firm A Firm D Firm E q* q q* q q* q

$

P*

MC MC

AC

MC

ACAC

Perfect Competition

Long-run equilibrium. Firms are producing at the efficient scale. P* = ACmin; = 0.

$

P*

q* q Q* Q

$

LRS

MC

AC

D

Perfect Competition

Perfect Competition

Consider a perfectly competitive industry characterized by the following total cost and demand functions:

TC = 100 + q2 QD = 1000 – 20P

Find the market equilibrium in the long-run. How many firms are in the market?

Perfect Competition

TC = 100 + q2 QD = 1000 – 20P

q* = 10 q 600 Q

$

LRS

MC = 2q

AVC = q

AC = 100/q + q

Firms produce at ACmin

i) AC = MC 100/q + q = 2q 100 + q2 = 2q2

q2 = 100; q* = 10

ii) AC’ = 0 -100/q2 + 1 = 0 q2 = 100; q* = 10

$

P* = 20

q* is the efficient scale

Perfect Competition

TC = 100 + q2 QD’ = 1500 – 20P

q.n = (MC/2)n = (P/2)n => QS = 30P SRS$

P* = 20

q’ = 15 q Q’ = 900 Q

$

LRS

MC = 2q

AVC = q

AC = 100/q + q

n = 60

SRS

D

D’

P’ = 30

Perfect Competition

TC = 100 + q2 QD’ = 1500 – 20P

$

P* = 20

q* = 10 q Q** = 1100 Q

$

LRS

MC = 2q

AVC = q

AC = 100/q + q

n = 110

D

D’

Perfect Competition

In the Long-run …

1) Firms produce at minimum average cost, i.e., “efficient scale.”

2) Price is equal to marginal cost.

3) Firms earn zero (economic) profits.


Equilibrium & Efficiency

Is it true that the rational pursuit of private interests produces coherence rather than chaos, and if so, how is it done?

-- Frank Hahn

Equilibrium: most generally, an equilibrium is a state of the market in which decision plans are mutually consistent and therefore can be implemented.

In the market, coordination takes place via prices: at a given price, all the output firms want to produce can be sold and all the goods consumers want to purchase can be bought.


Pareto Efficiency: an economic situation is Pareto efficient if no one can be made any better off without making someone else worse off.

Pareto efficiency is a “good” thing, but it says nothing about equity; income distribution; economic justice.

Competitive markets produce Pareto efficient equilibria (Q*), because at Q* the price someone is willing to pay for an additional unit of the good is equal to the price that someone must be paid to sell that unit.


The market equilibrium is Pareto efficient because at Q* the price someone is willing to pay for an additional unit of the good is equal to the price that someone must be paid to sell that unit.

D

Q Q* Q

P At Q < Q*, a buyer and seller can exchange and

both be better off Willing to pay Pb

Pb = Ps

Willing to sell for Ps

S


We know that in a market equilibrium, both consumers and firms are optimizing, and we used these conditions to derive Demand and Supply curves.

D: MRS = Px/Py

S: MR = MC

Q* Q

P

Po

P*

Consumer Surplus

The total difference between what

consumers are willing to pay and

the market price

CS = ½(Po- P*)Q*

CS



D: MRS = Px/Py

S: MR = MC

Q* Q

P

Po

P*

Producer Surplus

The total difference between the firms’

marginal cost of production and the

market price

PS = (- FC)

CS

PS



D: MRS = Px/Py

S: MR = MC

Q* Q

P

Po

P*CS

PS

Social Surplus

The sum of consumer and

producer surplus

SS = CS + PS

Greatest at Q*

Pure Exchange

An Edgeworth Box

Indifference curves for Person 1.

X

Y

1

Pure Exchange

An Edgeworth Box

Indifference curves for Person 1 and Person 2. The dimensions of the box represent the total amounts of X and Y in the economy.

1

2Y

X

Pure Exchange

An Edgeworth Box

Contract Curve: the set of Pareto efficient allocations, where each person is at the highest possible indifference curve, given the indifference curve of the other person.

1

2Y

X

Pure Exchange

An Edgeworth Box

The initial endowment is shown in the graph, above. Both are better off at a point in the shaded area.

1

2Y

X

Endowment

Pure Exchange

An Edgeworth Box

Exchange (trade) should occur until they reach a point on the contract curve.

1

2Y

X

Endowment

Pure Exchange

An Edgeworth Box

1

2Y

X

Endowment

Exchange (trade) should occur s.t., MRS1= MRS2 = Px/Py.

Pure Exchange

An Edgeworth Box

1

2Y

X

Endowment

Efficient Allocation

Exchange leads to a Pareto Efficient Allocation.

General Equilibrium

Consider an economy with 2 consumers and 1 producer. Despite their small numbers, all behave as price-takers. Consumers consume leisure (X) and widgets (W), and widgets require only labor (L) to produce, according to the following production function:

W = LConsumers’ preferences are described by:

U1 = X11/3W1

2/3; and U2 = X22/3W2

1/3

Also, L + X = 24 (hrs/day) and the wage (w) is $1/hr.

Find: X1,2, W1,2, P

General Equilibrium

Start by constructing the market demand curve

W = W1 + W2 => W = 24/Pw

U1 = X11/3W1

2/3 U2 = X22/3W2

1/3

MUx = 1/3X-2/3W2/3 MUx = 2/3X-1/3W1/3

MUw = 2/3X1/3W-1/3 MUw = 1/3X2/3W-2/3

MRS1 = W/(2X) = Px/Pw MRS2 = 2W/X = Px/Pw

Px=1 => X = 1/2PwW => X = 2PwW

BC: I = PxX + PwW BC: I = PxX + PwW

24 = 3/2 PwW 24 = 3PwW

=> W1 = 16/Pw => W2 = 8/Pw

General Equilibrium

Now consider the firm’s problem:

Profit ( = Total Revenue(TR) – Total Cost(TC)

TR(Q) = PQ TC(Q) = rK + wL

P Price L LaborQ Quantity K Capital

w Wage Rater Rate on Capital

General Equilibrium



TR = PW TC(Q) = rK + wL

P Price L LaborW Widgets K Capital

w Wage Rater Rate on Capital

General Equilibrium



TR = PW TC(Q) = rK + wLMR = P MC = w

since w =1, we know: P = 1; W = 24 W1 = 16; W2 = 8 X1 = 8; X2 = 16

also L + X = 24, so: L1 = 16; L2 = 8; L = 24 rRate on Capital

From the Demand curve: W = 24/Pw

General Equilibrium



TR = PW TC(Q) = rK + wLMR = P MC = w

since w =1, we know: P = 1; W = 24 W1 = 16; W2 = 8 X1 = 8; X2 = 16

also L + X = 24, so: L1 = 16; L2 = 8; L = 24 rRate on Capital

General Equilibrium

The Market for Widgets r Rate on

Capital

W* = 24 W

P

P*= 1

Demand: W = 24/Pw

Supply: P = 1

Welfare

First Theorem of Welfare Economics: All competitive equilibria are Pareto-efficient.

Second Theorem of Welfare Economics: Any allocation (of wealth or goods) can be

sustained in a competitive equilibrium.

Welfare

D = d

Q

P Demand

Represents the horizontal sum of

individual consumers’

demand curves

d = consumer

D = Market Demand


Welfare


D: MRS = Px/Py

Q

P Demand

Since all consumers are optimizing at

the same output prices

(Px/Py)

MRS1 = MRS2

Consumption Efficiency

d = consumer

D = Market Demand

Welfare


D: MRS = Px/Py

P = mc: MRTS = w/r

Q* Q

P

Po

P*

Supply

Represents individual firm’s

optimal factor proportion, given

factor prices

(w/r)

mc = individual firm’s marginal cost

Welfare


D: MRS = Px/Py

P = mc: MRTS = w/r

Q* Q

P

Po

P*

Supply

Since all firms are optimizing

(minimizing cost) at the same factor

prices (w/r)

MRTSx = MRTSy

mc = individual firm’s marginal cost

Production Efficiency

Welfare


D: MRS = Px/Py

Q* Q

P

Po

P*

Supply

Represents total marginal cost

of production

mc = firm’s

S = Market SupplyS = mc

Welfare


D: MRS = Px/Py

Q* Q

P

Po

P*

Supply

Represents marginal social cost

of production

mc = firm’s

S = Market SupplyS = MC

Welfare


D: MRS = Px/Py

S: MR = MC

Q* Q

P

Po

P*

Supply

Since relative prices fully reflect

relative costs

MRSyx = MRTyx (MRTyx = MCx/MCy)

Product mix is optimal

Marginal Rate of Transformation

MRTyx = MCx/MCy

Allocative Efficiency

Welfare

Consumption Efficiency: All consumers are optimizing at given output prices (Px/Py)

MRS1 = MRS2

Production Efficiency: All firms are optimizing (minimizing cost) at given factor prices (w/r) MRTSx = MRTSy

Allocation Efficiency: Product mix will be optimal; relative prices fully reflect relative costs

MRSyx = MRTyx (where MRTyx = MCx/MCy)

Welfare

The raison d'être of Welfare Economics is simple. How desirable it would be if we were able to pronounce as a matter of scientific demonstration that such and such a policy was good or bad(Robbins 1984, p. xx).

Next Time

7/12

UNIT III:

UNIT II:Firms & Markets

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