# 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
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
=     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
=   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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