# Profit Maximization by ewghwehws

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```									Profit Maximization

Lecture 13
Today’s Topics
• Long Run Profit Maximization
– Should I be in this market?
– How much should I produce?

• Short Run Profit Maximization
– Should I shut down?
– How much should I produce?
Profit Maximization
•   Firms are organized to produce a profit (surplus) for the owners of the
organization. Remember in the long run, the opportunity costs of the
manager as well as the owners of capital are included in the total costs
of the firm. Total costs represent minimum costs.

•   Profits are the difference between Total Revenues (TR) and Total
Costs (TC)
Profits =  = TR - TC

•   Assume that
– Firms are risk neutral
– Market is competitive, output sold by the firm will not affect the price of the
good
Revenue
•   Average Revenue:

AR = TR/Q = PQ/Q = P

•   Marginal Revenue:

 
TR  PQ PQ
        P
Q   Q   Q


•   If the average is constant then the marginal must be equal to average.
Profit Maximization
Managers will want to consider the following condition when choosing their output.

0
Q

The change in profits given a change in output equals:


 
  TR TC


TR TC
     P  MC
Hence                    Q     Q      Q   Q

P MC  0 or P  MC

The only difference between Long Run and Short Run pertains to the relevant costs:

LR or SR. Note this ‘first order’ condition only states that at what level of output one
should produce to maximize (or minimize) profits. One has to determine ‘second
order’ conditions to determine whether one is making profits or not.
Long Run
LRMC   LRAC   If the price is Po, will the firm produce?
\$

At Q* and Q**, Po = MC, however, at
both output levels, the firm is not
covering their costs

Po < LRAC

The firm won’t produce at this price and
Po                            won’t produce until

P ≥ min LRAC

Q*   Q**           Q
Long Run
LRMC   LRAC   If the price is P, will the firm produce?
\$

At Q* and Q**, P = MC, however, at Q*
the firm is not covering their costs

P < LRAC

P
But at Q**, the firm will make a profit
and will produce at this level if the price
is P.

Q*   Q**           Q
Long Run Supply
LRMC
LRAC
\$    LRS
The portion of the LRMC where Q
exceeds the level of output associated
with minimum LRAC.

In the LR, will a firm produce in the
increasing returns to scale portion of
their technology?

If the market is competitive, what price
should the firm expect if all firms have
face the same input prices?

Q
Long Run Price Expectations
If all firms (existing and potential competitors) have access to the same
technology then they will have the same cost structure. In the long run, if
the price exceeds the min LRAC then the profits should attract competitors
and hence drive down the price until no profits exist. Hence if these
conditions exist then the firm should expect

P = min LRAC

In general, the firm should expect the long run price to equal the minimum
of the minimum LRAC of its competitors. If the firm can expect to maintain
a long run cost advantage over its competitors then the firm can expect in
the long run to make a surplus (revenues will exceed the firm’s opportunity
costs)
What Will the Firm do in the SR?
LRMC
LRAC
\$              LRS
In the long run, the firm will expect the
price (PE) to equal minimum LRAC and
consequently put in place a capital
stock (KLR) that is both technically and
cost efficient to produce QLR.

What if price deviates from PE? How
will the firm change its decision of how
much to produce?
PE

Remember in the short run, the firm
can’t change its capital stock. It can
only change its output and work force.

QLR                 Q
A Higher Price than PE
LRMC
LRAC
\$            LRS

If the price exceeds PE, the firm will
P                               want to expand its output but will it
expand its output until

P = LRMC?
PE

QLR    Q
A Price HIGHER than PE

LRMC
LRAC   At Q=QLR:
\$
SRATC   SRMC
SRATC = LRAC
SRMC = LRMC

At Q>QLR:
P

SRATC > LRAC
SRMC > LRMC

PE                                   Produce at P = SRMC(Q) ==> QSR

Note, output rises but not as much as it would
in the long run.

QSR            Q
A Price LOWER than PE

LRMC
LRAC
\$
SRATC         SRMC

Will they produce at P = SRMC(Q) ==> QSR?

Note in the LR, they would choose not to
produce and ‘get out’ of the business if P
remained at this level.
PE
P

QSR                  Q
A Price LOWER than PE
LRMC
LRAC   In the short run, what is their opportunity cost
\$                                           of being this market? Their total costs or just
SRATC         SRMC                  their labor costs? It is just their labor costs
because their capital is ‘fixed’ in this business
in the short run. Hence they will remain in
business and operating at QSR if they can
cover their opportunity costs (variable costs)

P ≥ min SRAVC

They will shut down in the short run if
PE
P                                                       P < min SRAVC
SRAVC

QSR                   Q
SRS and LRS
LRMC
LRAC
\$
SRATC   SRMC
In the LR, if the firm expects P = min LRAC
then the LRS is the ‘inverse’ of the LRMC
above min LRAC.

LRS is the ‘green’ relationship.
SRAVC
In the SR (given the firm’s LR expectations)
the SRS is the ‘inverse’ of the SRMC above
min SRAVC. This is the ‘black’ relationship in
the picture.

responsiveness than the SRS?

Q

How will the firm respond to a permanent decline in average
revenues (P) if it continues to operate in both the SR and LR?

If the price declines, the firm will reduce its output in the short run
by laying off workers until P = SRMC or P = w/MPL. In the long run
if the price remains low, the firm will restrict its output even further
by shedding capital and perhaps even more labor (effect on labor is
unclear).
More or Less Labor?
K

IsoCost reflecting w/r

Initial QLR

QSR

L