Ch 7

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					UNIT 7:


           Firm Costs,
          Revenues, and
              Profits
Key Topics

1.    Cost concepts
     a.   Cash and Non Cash
     b.   Variable and Fixed
     c.   Total: TFC, TVC, TC
     d.   Average: AFC, AVC, ATC, AVC & AP
     e.   Marginal: MC, MC & MP
2.    Revenue concepts
     a.   Total
     b.   Marginal
3.    Profit concepts
     a.   Profit maximizing output
     b.   Firm & market supply
Key Topics - continued

4. SR production
  a.   Profits in P, ATC graph
  b.   Shut down condition (loss min.)
  c.   Firm & industry supply curves
5. LR production
  a.   Isocost lines & LR cost min. (Ch. 6 Appendix)
  b.   Returns to scale and LRAC
  c.   Equilibrium
       Profit Overview (recall)

 Profit= TR – TC
 TR depends on P of output, Q of
  output
 TC depends on P of inputs, Q of
  inputs, productivity of inputs,
  production technology used
          Recent Examples of Firm ‘Cost’
                    Concerns

1.       GM
     -     Spent $5 billion to  costs of producing Saturn cars
     -     Labor costs per car for GM were 2x Toyota’s
2.       United, Delta, & other airlines
     -     Southwest’s costs often 50% less
3.       Sears, K-Mart, Target
     -     Trying to compete with Walmart on basis of costs
4.       Georgia Pacific
     -     Started using ‘thinner’ saws
     -     Less saw dust
     -     800 more rail cars of lumber per year
          Cost Concepts


 Cash  and Non Cash
 Fixed and Variable
 Total, Average, and Marginal
    Opportunity Cost Examples

Activity                Opportunity Cost
Operate own business   Lost wages and
                       interest

Own and farm land      Lost rent and interest

Buy and operate        Lost interest and rent
equipment
 Total Fixed vs. Total Variable Costs

TFC   =   total fixed costs
      =   costs that have to be paid even if output = 0
      =   costs that do NOT vary with changes in
                   output
      =   ‘overhead’ and ‘sunk’ costs
TVC   =   total variable costs
      =   costs that DO vary with changes in output
      =   0 if output = 0
TC    =   total costs
      =   TFC + TVC
          Average Costs


AFC =   fixed costs per unit of output
    =   TFC/q
AVC =   variable costs per unit of output
    =   TVC/q
ATC =   total costs per unit of output
    =   TC/q = AFC + AVC
Marginal Cost

MC =   additional cost per unit of
       additional output
   =     TC  TVC
            
         q    q
   =   slope of TC and slope of TVC
       curves
MC, AVC, and ATC Relationships


If MC > AVC  AVC is increasing
If MC < AVC  AVC is declining
If MC > ATC  ATC is increasing
If MC < ATC  ATC is declining
    Product and Cost Relationships

Assume variable input = labor
 MP = ΔQ/ΔL       AP = Q
 TVC = W ∙ L             L
 MC =  TVC W   L      W
                            
             Q        Q        MP
    note: MC Δ is opposite of MP Δ
   AVC =     TVC W  L W
                      
               Q   Q     AP
    note: AVC Δ is opposite of AP Δ
A ‘Janitor’ Production Example

 Assume the only variable input a janitorial
 service firm uses to clean offices is workers
 who are paid a wage, w, of $8 an hour. Each
 worker can clean four offices in an hour. Use
 math to determine the variable cost, the
 average variable cost, and the marginal cost
 of cleaning one more office.
Assume: q = TP = 4L
w = $8

 L     TP    AP     MP      TVC   AVC   MC

 0     0      0       0      0     0    0
 1     4      4       4      8     2    2
 2     8      4       4     16     2    2
 3     12     4       4     24     2    2
 4     16     4       4     32     2    2

NOTE: AVC = TVC/q = w/AP
      MC = ΔTVC/Δq = w/MP
Another Cost of Production Example

 Assume a production process has the
 following costs:
 TFC = 120
 TVC = .1q2
 MC = .2q
Complete the following table:

 Q      TFC     TVC       TC      AFC      AVC      ATC    MC
 0
 20
 40
 60
 80
100

Can you graph the cost functions (q on horizontal axis)?
Total Costs of Production


TFC = AFC x q
    = (fixed cost per unit of output) (units of output)
TVC = AVC x q
    = (variable cost per unit of output) (units of output)
TC = ATC x q
   = (total cost per unit of output) (units of output)
TFC in AFC graph

AFC = TFC/q  TFC = AFC x q

     $




   AFC1
          TFC          AFC
                         q
                q1
TVC in AVC graph

AVC = TVC/q  TVC = AVC x q

     $


                              AVC

  AVC1
         TVC

                          q
                     q1
TC in ATC graph

ATC = TC/q  TC = ATC x q

     $


                            ATC

   ATC1
          TC

                            q
                     q1
Revenue Concepts

TR   =   total revenue
     =   gross income
     =   total $ sales
     =   PxQ = (price of output) (units of output)
     =   AR x Q = (revenue per unit of output) (units of
         output)
AR   =   average revenue
     =   revenue per unit of output
     =   TR/Q
MR   =   marginal revenue
     =   additional revenue per unit of additional output
     =   ΔTR/ΔQ
General Types of Firms (based on the
D for their product)

1.   Perfectly Competitive
     D curve for their product is flat
     P is constant ( can sell any Q at given P determined by S&D)
     AR = MR = P (all constant)
     TR = P x Q ( linear, upward sloping given P is constant)
2.   Imperfectly Competitive
     D curve for their product is downward sloping
     P depends on Q sold ( must lower P to sell more Q)
     AR = P (= firm D curve)
     TR = PxQ (nonlinear, inverted U shape given P is not constant)
     MR = slope of TR (decreases with ↑Q, also goes from >0 to <0)
General Graphs of Revenue Concepts

Perfectly Competitive Firm       Imperfectly Competitive Firm

$                            $
                  PR=AR=MR
                                           P=AR
                                      MR
                                                   Q
                       Q


 $                TR         $

                                                  TR


                       Q                               Q
Specific Firm Revenue Examples


Perfectly Competitive   Imperfectly Competitive
         Firm                    Firm

    P = AR = 10             P = AR = 44 – Q

   TR = PQ = 10Q          TR = PQ = 44Q – Q2

      MR = 10                MR = 44 – 2Q
TR in P graph (competitive firm)

TR = P x q

     $



     P                 P


             TR

                           q
                  q1
Revenue-Cost Concepts


Profit = TR – TC

Operating profit = TR - TVC
    Comparing Costs and Revenues to
            Maximize Profit

   The profit-maximizing level of output for all
    firms is the output level where MR = MC.
   In perfect competition, MR = P, therefore, the
    firm will produce up to the point where the
    price of its output is just equal to short-run
    marginal cost.
   The key idea here is that firms will produce
    as long as marginal revenue exceeds
    marginal cost.
General Graph of Perfectly Competitive
           Firm Profit Max

  $
                  MC

                 MR


                       Q
 $
                      TR

                 TC



                       Q
Perfectly Competitive Firm Profit Max
(Example)

P = MR = 10
MC = .2Q
TR = 10Q
TC = 120 + .1Q2
Π Max Q 
  MR = MC
   10 = .2Q
   Q = 50
Max π       =    TR-TC (at Q = 50)
             =    10(50) – [120 + .1(50)2]
             =    500 – 120 – 250
             =    130
    General Graph of Imperfectly
    Competitive Firm Profit Max

$
                  MC


             MR
                       Q

$
                       TR
             TC


                       Q
Imperfectly Competitive Firm Profit
Max (example)

P = 44-Q
MR = 44-2Q
TR = 44Q-Q2
MC = .2Q
TC = 120 + .1Q2
Π Max Q 
   MR=MC
    44-2Q = .2Q
    2.2Q = 44
    Q = 20
 Max π        = TR-TC (at Q = 20)
               = [44(20)-(20)2] – [120 + .1(20)2]
               = [480] – [160]
               = 320
         Fixed Costs and Profit Max

Q.   True or False?
     Fixed costs do not affect the profit-
     maximizing level of output?

A.   True.
     Only, marginal costs (changes in variable
     costs) determine profit-maximizing level of
     output. Recall, profit-max output rule is to
     produce where MR = MC.
Q. Should a firm ‘shut down’ in SR?

A.   Profit if ‘produce’
     = TR – TVC – TFC
     Profit if ‘don’t produce’ or ‘shut down’
     = -TFC
      Shut down if
         TR – TVC – TFC < -TFC
         TR – TVC < 0
         TR < TVC
            TR TVC
                   P  AVC
             q   q
 Perfectly Competitive Firm & Market
              Supply


Firm S   =   MC curve above AVC
              (P=MR) > AVC

Market S =   sum of individual firm
             supplies
      Graph of SR Shut Down Point

        $
                Short-run            MC
               Supply curve               ATC

                                              AVC


Market price
                   Shut-down point


                                          Q
SR Profit Scenarios


1.   Produce, π > 0
2.   Produce, π < 0 (loss less than –
     TFC)
3.   Don’t produce, π = -TFC
SR vs LR Production if q = f(K,L)

SR:    K is fixed
              only decision is q which determines L
LR: K is NOT fixed
              decisions =
               1) q and
               2) what combination of K & L to use to
                      produce q
Recall, π = TR – TC
        to max π of producing given q, need to min. TC
Budget Line



= maximum combinations of 2 goods
  that can be bought given one’s
  income
= combinations of 2 goods whose
  cost equals one’s income
Isocost Line


= maximum combinations of 2 inputs
  that can be purchased given a
  production ‘budget’ (cost level)
= combinations of 2 inputs that are
  equal in cost
Isocost Line Equation

TC1 =        rK + wL
 rK =       TC1 – wL
 K  =       TC1/r – w/r L

Note: ¯slope = ‘inverse’ input price ratio
      =     ΔK / ΔL
      =     rate at which capital can be exchanged
            for 1 unit of labor, while holding costs
            constant
Equation of TC1 = 10,000 (r = 100, w = 10)


     TC1 w
 K       L
      r   r

     10,000 10
 K            L
      100    100

 K  100  .1L
Isocost Line (specific example)

TC1 =         10,000
r   =         100  max K = 10,000/100 = 100
w   =         10  max L = 10,000/10 = 1000
         K
        100

                          TC1 = 10,000
                               K = 100 - .1L
                              L
                       1000
Increasing Isocost

    K




             TC3 > TC2 > TC1




                               L
           TC1 TC2 TC3
Changing Input Prices

K

    TC1                 TC1


                              r
            w




                 L                 L
Different Ways (costs) of Producing q1

  K




              1
                   2     3             q1


                             TC2 TC3
                       TC1
                                       L
Cost Min Way of Producing q1

  K
          K* & L* are cost-min. combinations
          Min cost of producing q1 = TC1



  K*        1
                    2      3             q1


                               TC2 TC3
                        TC1
           L*                            L
Cost Minimization

- Slope of isoquant = - slope of isocost line

  MPL w
    
  MPK r


   r   w
         MC K  MC L
  MPK MPL


  MPK MPL
         additional q per additional $ spent same for both K and L
   r   w
Average Cost and Output

1)   SR
     Avg cost will eventually increase due to law
     of diminish MP ( MC will start to  and
     eventually pull avg cost up)
2)   LR economics of scale
     a) If increasing  LR AC will  with  q
     b) If constant  LR AC does not change with  q
     c) If decreasing  LR AC will  if  q
LR Equilibrium  P of output = min LR
AC

LR Disequilibrium
a) P > min LR AC (from profits)
        Firms will enter
         mkt S   P
b)   P < min LR AC (firm losses)
        Firms will exit
         mkt S   P

				
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