fcprofitetc

7/31/2019 FCprofitetc

1/22

Profits, Shutdown, Long Run

and FC

1998 by Peter Berck


2/22

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) }


3/22

P - AC(q*)

AC

AVCMC

Q

$/unit

P

q*

AC(q*)

P - AC(q*)


4/22

Profit Box

AC

AVCMC

Q

$/unit

P

q*

AC(q*)

P - AC(q*)

Box is P - AC(q*) high and q* wide

q* {P - AC(q*) = Pq* - C(q*) =


5/22

Categorizing Cost

VC are costs exclusive of fixed capital

FC is the financial obligation to pay for

fixed capital FCB is the portion of FC financed with

bonds. (includes interest costs)

FCE is the portion financed with equity


6/22

Shutdown

Let q* given by mc(q*) = p be quantity thatmaximizes profit among those quantitiesthat 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


7/22

Shutdown Point

pq* - vc(q*) = q* (p - avc(q*) )

so shutdown if p - avc(q*)


8/22

Bankrupt

legal term: cant pay bills.

pq* - vc(q*) < 0

bankrupt; cant pay for any of FC. shutdown

FCB< pq* - vc(q*) < FC

not bankrupt. pay loans and some or all of equity.

0 < pq* - vc(q*) < FCB

bankrupt: should operate; can pay some of loans. Court

allows this. point of bankruptcy


9/22

Shutdown Point, Ps

AC

AVCMC

Q

$/unit

Ps

q*

At Ps = {Ps - AC(q*)} q*. By construction,

Ps=AVC(q*) so = {AVC(q*) - AC(q*)} q*

and by definition of AFC

= {-AFC(q*)} q* = -FC.

For any lower price, profit is less so Ps gives minimum

point at which production is not zero.


10/22

Firms Supply Curve

A firms supply curve is its

marginal cost curve above average

variable cost


11/22

Are all costs Present and

Accounted for? Suppose firm uses clean air as part of

production process and doesnt pay for it???

suppose value of clean air used is t per unitof output. (value of lost breathing!)

t is the external cost of making the output

mc are the private or internal costs ofmaking output

where external (jargon: externality) means

external to the firm


12/22

Case for regulation

firm sets p = mc doesnt account for t cause doesnt pay t

social cost

is private + external = mc +t correct answer is mc + t = p

Charging a tax of t, the costs borne bysociety and not paid by firm, internalizes

the externality (yuck) and makes the firmpay all the costs of its operation


13/22

The picture

D

q

p

mc

mc + t

What happens to quantity of polluting output?Price to consumers, to firm?

Tax revenue? Firms profits?

q1q2

p1

pc

pfirm


14/22

Long Run

Each firm with U-shaped cost curves has a

particular fixed capital stock

In short run, capital stock is fixed and so isnumber of firms

Long run, number of firms (hence capital)

varies.


15/22

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


16/22

Supply from 4 Firms

ACAVC

MC

Q

$/unit

S4

Supply from N identical firms is

SN(p) = N S(p) where S is the supply curve

for a single firm.


17/22

Short run supply

ACAVC

MC

Q

$/unit

S4

when there are 2, 3 or 4 firms

S2 S3


18/22

Short Run Equilibrium

ACMC

Q

$/unit

S3P

D

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

q* 3q*


19/22

Firm enters; New supply S4

S4 = D at new lower price, p

Profits = 0

Positive Profit means Entry

ACMC

Q

$/unit

S4S3

p

q


20/22

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 firmsany amount of output will be made at this

price. Q= any and p = p is the long run

supply curve

Long Run Supply

MC

Q

$/unit

S4S3

p

q


21/22

P = MC(q) for each firm (and p > AVCmin)

P = D(N q)

Profits = 0

Long Run Competitive

Equilibrium

MC

Q

$/unit

S4S3

p

q


22/22

Another LR-SR story

A single firm can adjust its K only in long

run

Never appears in the literature Always appears in text books

Chapter 9 in LC covers this. I wont

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