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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)
4) Market equilibrium is Pareto-efficient.
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.
4) Market equilibrium is Pareto-efficient.
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.
Equilibrium & Efficiency
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.
Equilibrium & Efficiency
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
Equilibrium & Efficiency
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
Equilibrium & Efficiency
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*
Producer Surplus
The total difference between the firms’
marginal cost of production and the
market price
PS = (- FC)
CS
PS
Equilibrium & Efficiency
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*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
Now consider the firm’s problem:
Profit ( = Total Revenue(TR) – Total Cost(TC)
TR = PW TC(Q) = rK + wL
P Price L LaborW Widgets K Capital
w Wage Rater Rate on Capital
General Equilibrium
Now consider the firm’s problem:
Profit ( = Total Revenue(TR) – Total Cost(TC)
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
Now consider the firm’s problem:
Profit ( = Total Revenue(TR) – Total Cost(TC)
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
We know that in a market equilibrium, both consumers and firms are optimizing, and we used these conditions to derive Demand and Supply curves.
Welfare
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
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
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
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
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
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
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
Q* Q
P
Po
P*
Supply
Represents total marginal cost
of production
mc = firm’s
S = Market SupplyS = mc
Welfare
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
Q* Q
P
Po
P*
Supply
Represents marginal social cost
of production
mc = firm’s
S = Market SupplyS = MC
Welfare
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*
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: