Firm behaviour
Profit Maximization
in Competitive Markets
Finding the Supply Function
To explain firm behaviour we separated the
decision process artificially into two steps:
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Herbert Stocker
[email protected]
Institute of International Studies
University of Ramkhamhaeng
&
Department of Economics
University of Innsbruck
Firm behaviour
Technological restrictions are already
incorporated in the cost function
(remember that the cost function was derived by
cost minimization under constraint of the
production function!).
However, there were no assumptions for the
output market necessary, we just assumed that
factor prices are exogeneously given.
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Cost Minimization: firms look for a way to produce
any (given) output as cheap as possible.
→ optimal factor allocation!
As a result we get factor demand functions and the
cost function C ∗ = C (w , r , Q).
This happened in the last chapter.
Profit Maximization: next firms have to decide
what output to produce.
They face technological and market restrictions.
Firm behaviour
Market restrictions differ between market
structures. Therefore, we have to examine the
process profit maximization for different market
structures separately.
In this chapter we’ll focus on perfect competitive
markets, in the next chapter we’ll examine
imperfect competition.
Market restrictions refer market conditions, that
is, how output price is determined.
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Perfect Competition
Firms are price-takers! A firm cannot influence
the price of its product, thus it can sell any
amount of output at the market price. This is
because . . .
A large number of firms in the market.
An undifferentiated product.
Complete information available to all market
participants.
In the long run competition between firms pushes
economic profits (measured with opportunity cost)
down to zero. This is because . . .
Perfect Competition
Free Entry and Exit:
There is free entry and exit into and from an
industry when new producers can easily enter into
or leave that industry.
Free entry and exit ensure:
that the number of producers in an industry can adjust
to changing market conditions, and,
that producers in an industry cannot artificially keep
other firms out.
Free market entry and exit.
Profit Maximization
Assumption:
firms maximize economic profits!
Economic profits are the difference between total
revenue and total opportunity cost:
π = PQ − C (Q)
Maximization under constraints:
Technological restrictions: incorporated in cost
function C = C (Q);
Market restrictions: perfect competition ⇒ P, w and
r are given by the market (price-takers)!
Revenue and Marginal Revenue
Remember, total revenue R = P × Q.
Average revenue: AR ≡ R/Q = (PQ)/Q = P;
average revenue always equals the price!
Marginal Revenue (MR) is the additional
revenue that a firm takes in from selling one
additional unit of output;
or, the change in revenue divided by the change in
output
MR =
dR
d(PQ)
∆R
Change in Revenue
=
≈
=
dQ
dQ
∆Q
Change in Output
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Revenue and Marginal Revenue
Under perfect competition a firm can sell any
output for the market price! Therefore . . .
Marginal Revenue (MR) for a perfectly
competitive firm is a horizontal line, because it
can sell any further unit of output for the same
price. Therefore, for a perfectly competitive firm
price equals marginal revenue:
MR =
Perfect Competition
Since firms are small relative to the market managers
‘perceive’ relevant market demand as perfectly elastic!
P
MCi
representative
Firm
Market demand
ACi
P is ‘perceived’
Market demand
Marketsupply
d(PQ)
=P
dQ
(this is true only for perfect competition, this is not true for
other market structures!)
Profit Maximization
Q
Profit Maximization
Decision problem for exogeneous P:
max : π = PQ − C (w , r , Q)
P
MC
Q
A necessary condition for an optimum is (quantity Q is
the only choice variable)
Lost
Profit
P∗
∂C !
∂π
=P−
=0
∂Q
∂Q
When marginal cost is
P = MR smaller than marginal
AC
revenue
the firm
should produce more!
⇒ ⇐
or “price equal marginal cost”
MR = P =
∂C
≡ MC
∂Q
MC
MR= P
Why gives quantity
where P = MC highest
possible profits?
MC
When marginal revenue
is is smaller than
Q marginal cost the firm
should produce less!
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Profit Maximization
Profit Maximization
Profits :
P
The firm can increase
profits until revenue for
the last unit sold equals
cost of this last unit,
i.e. until marginal revenue is equal marginal
cost:
MC
P∗
P
bc
AC
bc
Q∗
Q
P = MR = MC
Profit Maximization
A profit maximizing firm should choose the output
quantity where marginal cost is equal to the
exogenous price:
MC(Q) = P
Always?
No! This will not be the case when . . .
. . . marginal cost decrease
. . . P < AC
π = PQ
−C C
Q
= P−
Q
= (P − AC) Q
P
MC
P
P∗
bc
π∗
AC
Profits are highest,
when the firm chooses
the quantity Q at
which
bc
Q∗
Q
MC(Q) = P
Profit Maximization
What happens, when P < AC?
Remember
π = PQ − C (Q)
C (Q)
Q
= P−
Q
= (P − AC) Q
When P < AC the firm would incur losses!
In this cases profits are not maximized, but losses
minimized.
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Profit Maximization
P
MC
PA
Supply Function of a Firm
AC
AVC
bc
A
PB
bc
B
bc
AFC
bc
QB QA
Q
1) When P = PA :
QA → Minimum Efficient Size
2) When P < PA :
long-run → market
exit → A:
‘exit
point’
3) When P < PB :
stop
production
immediately → B:
‘shut-down point’
Supply Function of a Firm
When the price falls below the minimum of the
average variable cost curve (PB ) the firm will stop
production immediately −→ shutdown point.
When the price falls only for a short time below
the minimum of the average total cost curve, but
the firm expects the price to increase again, the
firm will continue production, since she still can
cover at least a part of the fixed costs (price
between PA and PB ).
Only when the firm expects the price will remain
permanently below the minimum of the average
total cost curve she will decide to leave the
market permanently −→ exit point.
Supply Function of a Firm
The short-run supply function (S) of a firm on a
perfect competitive market is the increasing part of the
marginal cost curve, that lies above the minimum of
the average (variable) cost curve.
Short-Run Supply Curve
Short-Run Supply
Curve of a Firm:
P
Ssr
AC
AVC
PA
PB
bc
B
QB
AFC
Q
The portion of its
marginal cost curve
(MC) that lies above
average
variable
cost.
When market price
is between PA and
PB firm runs losses,
but can at least cover
some of the fixed
costs.
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Long-Run Supply Curve
P
PA
Slr
AC
AVC
bc
A
AFC
QA
Q
Irrelevance of Fixed Costs
Long-Run Supply
Curve of a Firm:
The marginal cost
curve (MC) above
the minimum point
of its average total
cost curve.
If market price is
above PA firm makes
profits.
Managerial decisionmaking
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2
Managers on competitive markets have to watch
market price and its development closely, and
to organize and monitor production efficiently!
Management on perfectly competitive markets
Two simple rules:
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2
Shut down if AVC > P,
or exit the market if ATC > P.
If AVC < P produce the quantity where MC = P.
Fixed costs are irrelevant in the decision how
much to produce!
Level of fixed cost has no effect on marginal cost
or minimum average variable cost.
Thus no effect on optimal level of output.
However, fixed cost are included in ATC, and
therefore may indirectly influence the long-run
decision of a firm to exit the market.
Sunk cost should have no influence whatsoever for
any decision of a firm!
Market Supply
Market supply equals the sum of the quantities
supplied by the individual firms in the market.
The market supply function (S) for a perfect
competitive market is the horizontal sum of the
individual supplies (aggregate quantities).
Since quantities can never be negative only
positive numbers may be added.
for a market with N firms:
S=
N
X
Qi
for all Qi > 0
i=1
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Profit Maximization and Competition
Example
Firm
Perfect competition implies free market entry and
exit.
If the market price is above the minimum of the
average total cost curve some firms earn economic
profits (opportunity cost!), therefore new firms
will enter the market.
This entry of new firms pushes prices in the long
term down to the minimum of the minimum of
the average total cost curve!
Example
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ACi
Marketentries!
π
Sk =
i=1
3
Qi
2
i=1
Qi
2
b
b
1
0
P5
3
ACi
1
0
1
2
3
4 Qi
0
Q D = 40 − 10P
10 20 30 40 S
0
P10
i=1
Qi
1
Reaction of
Firm
2
3
4 Qi
0
b
Q D = 40 − 10P
0
10 20 30 40 S
b
1
Reaction of
Firms
0
2
b
1
0
Marketentries!
1
2
3
4 Qi
0
P5
i=1
Qi
longrun market supply
P
Sl = 25
i=1 Qi
3
ACi
π=0
Sk =
4
MCi
3
b
Shortrun market supply
P
2
b
Total Market
P
4
2
1
1
P5
Sm =
b
0
π
Sk =
4
MCi
3
Shortrun market supply
P
Firm
Shortrun market supply
P
4
MCi
3
0
4
Total market
Ci = 0.75Qi2 + 0.75
2
Ci = 0.75Qi2 + 0.75
P
Example: long-run
Firm
P
Total Market
b
Q D = 40 − 10P
0
10 20 30 40 S
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Profit Maximization
Long-run Market Supply Curve
Short-run: Firms choose output quantity Q where
marginal cost equals the market price, because
this gives them the highest possible profit
MC(Q) = P
Long-run: However, in the long run competition
and market entries force the market price down to
the minimum of the average cost curve
MC(Q) = P = AC
Because of free market entry and exit the long run
market supply curve is horizontal at the minimum
of the average cost curve of a firm.
Long-run Market Supply Curve
Market entries (exits) shift the market supply
curve to the right (left).
In the long run firms will enter or exit the market
until market supply curve intersects the market
demand curve at the ‘smallest possible price’, i.e.
where market price is equal to the minimum of
average cost.
Therefore, markets entries and exits drive
economic profits down to zero!
Long-run Market Supply
In the long run firms will enter or exit the market
until profit is driven to zero, therefore the number
of firms in an industry is endogenous.
In the long run, price equals the minimum of
average total cost.
The long-run market supply curve is horizontal
(perfectly elastic) at price P = ACmin :
P
long-run market supply
The long-run market supply curve can still be
increasing if
it is an increasing cost industry (diseconomies of scale
or decreasing returns to scale).
factors are scarce and become more expensive with
increasing demand.
firms are differently efficient or own unique factors.
In this case market price will reflect the minimum
average cost of the marginal firm.
The marginal firm is the firm that would exit the market
if the price were any lower.
Q
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Short-Run Producer Surplus
Short-Run Producer Surplus
Short-Run Producer Surplus: the area above
the short-run supply curve that is below market
price over the range of output supplied.
Short-run producer surplus is the amount by
which total revenue (TR) exceeds total variable
cost (TVC).
Short-run producer surplus exceeds economic
profit by the amount of total fixed cost (TFC).
Attn: Short-Run Producer Surplus is based on the AVC curve, not TAC!
Economic Rent
Economic Rent
Economic Rent: Payment to the owner of a
scarce, superior resource in excess of the
resource’s opportunity cost.
In long-run competitive equilibrium firms that
employ such resources earn zero economic profit.
Potential economic profit is paid to the resource
as economic rent.
In increasing cost industries, all long-run producer
surplus is paid to resource suppliers as economic
rent.
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Summery
Managers on perfectly competitive markets have
little or no control over product price.
They compete on basis of lowering costs of
production.
One way of reducing cost is finding the ‘Minimum
Efficient Scale’ for the industry.
Perfectly competitive firms earn zero economic
profit because entry of other firms compete away
excess profit.
Long Run Strategies for Managers
Managers in competitive industries are in a difficult
situation, since they can only control cost. In the long
run they can try to gain market power by . . .
Differentiating products.
Forming producer association to change consumer
preferences and increase demand for output of the
entire industry.
Merging with other companies.
Any Questions?
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