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Profit Maximization

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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
                         access to the same technology and
                         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.

                                   Why is the LRS show more price
                                   responsiveness than the SRS?

                             Q
    Question about Firm Behavior


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
  Questions about Firm Behavior

Is it possible for the firm in response to a permanent
decline in average revenues to
   Continue to operate in SR but shut down in LR?

          Yes if min LRAC > P > min SRAVC

  Shut down in SR and reopen in LR?

          Yes if min SRAVC > P > min LRAC

								
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