Transcript Perfect Competition & Welfare

Perfect Competition
& Welfare
Outline
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Derive aggregate supply function
Short and Long run equilibrium
Practice problem
Consumer and Producer Surplus
Dead weight loss
Practice problem
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Focus on profit maximizing behavior of firms
Take as given the market demand curve
$/unit
Equation:
P = A - B.Q
linear
demand
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Inverse demand
function:
willingness to pay
Maximum willingness
to pay
A
Constant
slope
P1
Demand
Q1
A/B Quantity
At price P1 a consumer
will buy quantity Q1
Perfect Competition
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Firms and consumers are price-takers
Firm can sell as much as it likes at the ruling market price
 do not need many firms
 do need the idea that firms believe that their actions will not
affect the market price
Therefore, marginal revenue equals price
To maximize profit a firm of any type must equate marginal
revenue with marginal cost
So in perfect competition price equals marginal cost
MR = MC
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Profit is p(q) = R(q) - C(q)
Profit maximization: dp/dq = 0
This implies dR(q)/dq - dC(q)/dq = 0
But dR(q)/dq = marginal revenue
dC(q)/dq = marginal cost
So profit maximization implies MR = MC
Perfect competition: an illustration
With market price PC
$/unit
the firm maximizes
profit by setting
MR (= PC) = MC and
producing quantity qc
With market demand D2
• The supply curve moves to the right
andmarket
marketdemand
supplyDS11
(a) The Firm
(b)With
The
Industry
• Price falls
and
market supply
S1P1
equilibrium
price is
equilibrium
price isis Q
P1C
$/unitprofits exist
and quantity
• Entry continues while
and quantity
is QCthat
Now assume
•Existing
Long-run
equilibrium
is
restored
MC
firms maximize
demand
atprofits
price Pby
supply curve S2
increasing
C and
S1 to
increases
D1
output
AC to q1
D2
P1
S2
P1
Excess profits induce
PC
new firms to enter
the market
PC
qc q1
Quantity
D2
QC
Q1 Q´C
Quantity
Perfect competition: additional points
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Derivation of the short-run supply curve
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this is the horizontal summation of the individual firms’
marginal cost curves
$/unit
Example 1: Three firms
Firm 3
Firm 1
Firm 2
Firm 1: qMC
= MC/4
= 4q +- 82
q1+q2+q3
Firm 2: qMC
= MC/2
= 2q +- 84
Firm 3: qMC
= MC/6
= 6q +- 84/3
Invert these
8
Aggregate: Q= q1+q2+q3
= 11MC/12 - 22/3
MC = 12Q/11 + 8
Quantity
Example 2: Eighty firms
$/unit
Firm i
Each firm: qMC
= MC/4
= 4q +- 82
Invert these
Aggregate: Q= 80q
= 20MC - 160
MC = Q/20 + 8
Aggregate
8
Quantity
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Definition of normal profit
 not the same as zero profit
 implies that a firm is making the market return on the assets
employed in the business
Practice problem
Dem a n d: Q
D
6 0 00 5 0P

9
90 D
In verseDem a n d: P  1 2 0 
Q
50
TC q   1 0 0  q 2  1 0q
Initial number of firms = 20
1) Find short run equilibrium
2) Find long run equilibrium
Short run
6 0 0 0 5 0P
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TC q   1 0 0  q 2  1 0q
QD 
m c  2q  1 0
p 10
s
q 
2
Qs  10p  200
D  S 1 0 p  2 0 0 
p 
7800
 5 5.7
140
6 0 0 0 5 0 p
9
Long run
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P = min avg cost
Point at which MC=AC
m c  2q  10
ac 
100
 q  10
q
100
m c  ac  2q  10 
 q  10
q
q  10
p  30
6000 50 p
4500

 500
9
9
nq  Q  n  Q / q  500/ 10  50
Q
Exercise
Competitive Industry – 2 types of firms
1. Low cost firms:
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Constant marginal cost 10 cents per unit – no fixed cost.
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Total capacity of group = 1000 units
2. High cost firms:
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marginal cost of 20 cents per unit
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When producing at full capacity average cost = 30 cents
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total group capacity of 2000 units
a) Draw the long run supply curve of this industry and the short run
supply curve assuming all firms are active.
(b) After a fall in demand, there has been an initial price reduction in
the short run, followed by a price increase in the long run. Draw
demand curves before and after the fall in demand that would lead
to this situation. Explain.
(c) Consider again the initial situation and suppose the low cost firms
discover extra capacity (e.g. new oil wells) at the same marginal cost
of 10 cents per unit and that in the short run this lead to a reduction
in price but in the long run the price returned to its previous level.
Draw a picture for the supply function of this industry prior and
after the change and the demand function that would explain this
situation.
Efficiency and Surplus
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Can we reallocate resources to make some individuals better off
without making others worse off?
Need a measure of well-being
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consumer surplus: difference between the maximum
amount a consumer is willing to pay for a unit of a good
and the amount actually paid for that unit
aggregate consumer surplus is the sum over all units
consumed and all consumers
producer surplus: difference between the amount a
producer receives from the sale of a unit and the
amount that unit costs to produce
aggregate producer surplus is the sum over all units
produced and all producers
total surplus = consumer surplus + producer surplus
Efficiency and surplus: illustration
$/unit
The demand curve measures the
willingness to pay for each unit
Consumer surplus is the area
between the demand curve and the
equilibrium price
The supply curve measures the
marginal cost of each unit
Producer surplus is the area
between the supply curve and the
equilibrium price
Competitive
Supply
PC
Consumer
surplus
Equilibrium occurs
where supply equals
demand: price PC
quantity QC
Producer
surplus
Demand
Aggregate surplus is the sum of
consumer surplus and producer surplus
The competitive equilibrium is
efficient
QC
Quantity
Illustration (cont.)
Assume that a greater quantity QG
is traded
Price falls to PG
$/unit
The net effect is a
reduction in total
surplus
Competitive
Supply
Producer surplus is now a positive
part
and a negative part
PC
Consumer surplus increases
PG
Part of this is a transfer from
producers
Part offsets the negative producer
surplus
Demand
QC
QG
Quantity
Output restricted to QM
$/unit
Suppose output is restricted to QM
The market clearing price is PM
Consumer surplus is given by this
area
And producer surplus is given by
this area
This is the deadweight
loss of monopoly
Competitive
Supply
PM
PC
There are mutually beneficial
trades that do not take place:
between QM and QC
Demand
QM
QC MR
Quantity
Exercise
Consider a competitive industry where all firms are identical with cost
function: C = 200 +q2/2 + 10q.
Market demand is given by: p = 55 -Q/20
Find the long run equilibrium (price, quantity and number of firms.)
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Mc=q+10, AC=200/q+q/2+10
Equating get: q/2=200/q  q2 = 400  q=20
p=mc=30
Substituting in demand function: 30=55-Q/20  Q=500
Number of firms nq=Q  n=Q/q=500/20=25
Exercise (continued)
Suppose now the government introduces a regulation that
limits the size of firms to no more than 10 units. Will there be
exit or entry of firms? Find the new long run equilibrium.
AC=200/q+q/2+10
AC
AC(10)=35
P=35=55-Q/20
35
30
Q=400
10
20
n=40
q
Exercise (continued)
Suppose now the government introduces a regulation
that forces firms to produce no less than 40 units. Find
the new long run equilibrium.
AC=200/q+q/2+10
AC
AC(40)=35
P=35=55-Q/20
35
30
Q=400
20
40
n=10
q
Exercise (continued)
Welfare loss:
5*400+100*5/2
Welfare cost:
=2,250
Original Surplus:
55
500*25/2=6,250
% loss = 36%
35
30
Qs
Welfare loss
400
500
Q