Profits, Shutdown, Long Run
and FC
© 1998,2010 by Peter Berck
Profits
• We know that a firm maximizes its profits
when p = mc or when q = 0.
• But which?
• Profits are Revenues less Costs
– Profits are PQ – C(Q)
– = Q { P – AC(Q) }
P - AC(q*)
P
MC
AC
AVC
$/unit
P - AC(q*)
AC(q*)
q*
Q
Profit Box
P
MC
AC
AVC
$/unit
P - AC(q*)
AC(q*)
Box is P - AC(q*) high and q* wide
q* {P - AC(q*) = Pq* - C(q*) = p
q*
Q
Categorizing Cost
• VC are costs exclusive of fixed capital
• FC is the financial obligation to pay for fixed
capital
Shutdown
• Let q* given by mc(q*) = p be quantity that
maximizes profit among those quantities that
are nonzero.
• if q = 0, shutdown, profit is -FC
• if pq* - vc(q*) < 0 then profit is
– {pq* - vc(q*)} - FC < -FC
– firm maximizes profits by setting q = o
– called shutdown
Shutdown Point
• pq* - vc(q*) = q* (p - avc(q*) )
– so shutdown if p - avc(q*) <0
– but the minimum point of the U shaped avc curve
comes where mc(q) = avc(q), so
– the least price at which the firm operates is the
minimum point of avc.
Shutdown Point, Ps
$/unit
At Ps p = {Ps - AC(q*)} q*. By construction,
Ps=AVC(q*) so p = {AVC(q*) - AC(q*)} q*
and by definition of AFC
AC
MC
p = {-AFC(q*)} q* = -FC.
AVC
For any lower price, profit is less so Ps gives minimum
point at which production is not zero.
Ps
q*
Q
Firm’s Supply Curve
• A firm’s supply curve is its marginal
cost curve above average variable
cost
Are all costs Present and Accounted
for?
• Suppose firm uses clean air as part of
production process and doesn’t pay for it???
• suppose value of clean air used is t per unit of
output. (value of lost breathing!)
• t is the external cost of making the output
• mc are the private or internal costs of making
output
• where external (jargon: externality) means
external to the firm
Case for regulation
• firm sets p = mc
– doesn’t account for t cause doesn’t pay t
• social cost is private + external = mc +t
– correct answer is mc + t = p
• Charging a tax of t, the costs borne by society
and not paid by firm, “internalizes the
externality” (yuck) and makes the firm pay all
the costs of its operation
The picture
p
What happens to quantity of polluting output?
Price to consumers, to firm?
Tax revenue? Firms’ profits?
mc + t
mc
pc
p1
pfirm
D
q2
q1
q
Long Run
• Each firm with U-shaped cost curves has a
particular fixed capital stock
• In short run, capital stock is fixed and so is
number of firms
• Long run, number of firms (hence capital)
varies.
Entry and Exit
• If profits are positive, firms enter
• If profits are negative firms exit
– Each firm is the same as the other firms
– Each firm has U shaped cost curves
• We define Long run supply and Long Run
Competitive Equilibrium
Supply from 4 Firms
Supply from N identical firms is
SN(p) = N S(p) where S is the supply curve
for a single firm.
S4
$/unit
MC AC
AVC
Q
Short run supply
$/unit
when there are 2, 3 or 4 firms
MC AC
AVC S2
S3
S4
Q
Short Run Equilibrium
Three firms, so supply is S3
D = S3 determines price, P
Output per firm is q*, total output 3 q*
Profits per firm are green box
$/unit
•
•
•
•
MC AC
S3
P
D
q*
3q*
Q
Positive Profit means Entry
$/unit
• Firm enters; New supply S4
• S4 = D at new lower price, p’
• Profits = 0
MC AC
S3
S4
p’
q’
Q
Long Run Supply
$/unit
• Since firms enter at prices above p’ and leave
at prices below, p’ is the price in the long run
and by adjusting number of firms any amount
of output will be made at this price. Q= any
and p = p’ is the long run supply curve
MC
S3
S4
p’
q’
Q
Long Run Competitive Equilibrium
$/unit
• P = MC(q’) for each firm (and p’ > AVCmin)
• P = D(N q’)
• Profits = 0
MC
S3
S4
p’
q’
Q
Who pays for pollution in the long run
model?
• Recall: C(Q with a tax) > C(Q with TBES) >C(Q)
– Tax and TBES are set to use same technique, but
with tax have to pay for remaining pollution
• So AC(Q with a tax) > AC(Q with TBES) >AC(Q)
Who pays?
Which is more effective
tax
$/unit
tbes
p’
q’
Q