UNIT 7: Firm Costs, Revenues, and Profits

UNIT 7:
Firm Costs,
Revenues, and
Profits
Key Topics
1.
Cost concepts
a.
b.
c.
d.
e.
2.
Revenue concepts
a.
b.
3.
Cash and Non Cash
Variable and Fixed
Total: TFC, TVC, TC
Average: AFC, AVC, ATC, AVC & AP
Marginal: MC, MC & MP
Total
Marginal
Profit concepts
a.
b.
Profit maximizing output
Firm & market supply
Key Topics - continued
4. SR production
a.
b.
c.
Profits in P, ATC graph
Shut down condition (loss min.)
Firm & industry supply curves
5. LR production
a.
b.
c.
Isocost lines & LR cost min. (Ch. 6 Appendix)
Returns to scale and LRAC
Equilibrium
Profit Overview (recall)
= 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
 Profit
Recent Examples of Firm ‘Cost’
Concerns
GM
1.
Spent $5 billion to  costs of producing Saturn cars
Labor costs per car for GM were 2x Toyota’s
-
United, Delta, & other airlines
2.
-
Southwest’s costs often 50% less
Sears, K-Mart, Target
3.
-
Trying to compete with Walmart on basis of costs
Georgia Pacific
4.
-
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
equipment
Lost interest and rent
Total Fixed vs. Total Variable Costs
TFC
TVC
TC
=
=
=
=
=
=
=
=
=
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
total variable costs
costs that DO vary with changes in output
0 if output = 0
total costs
TFC + TVC
Average Costs
AFC =
=
AVC =
=
ATC =
=
fixed costs per unit of output
TFC/q
variable costs per unit of output
TVC/q
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
L
 TVC = W ∙ L
W
 MC =  TVC W   L
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
1
0
4
0
4
0
4
0
8
0
2
0
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
0
20
40
60
80
100
Can you graph the cost functions (q on horizontal axis)?
MC
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
=
=
=
=
=
AR
=
=
=
=
=
=
MR
total revenue
gross income
total $ sales
PxQ = (price of output) (units of output)
AR x Q = (revenue per unit of output) (units of
output)
average revenue
revenue per unit of output
TR/Q
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
MR
Q
Q
$
P=AR
$
TR
TR
Q
Q
Specific Firm Revenue Examples
Perfectly Competitive
Firm
Imperfectly Competitive
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
q1
q
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 profitmaximizing 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
=
Market S =
MC curve above AVC
 (P=MR) > AVC
sum of individual firm
supplies
Graph of SR Shut Down Point
$
Short-run
Supply curve
MC
ATC
AVC
Market price
Shut-down point
Q
SR Profit Scenarios
1.
2.
3.
Produce, π > 0
Produce, π < 0 (loss less than –
TFC)
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 =
 K
=
rK + wL
TC1 – wL
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 =
r
=
w
=
10,000
100  max K = 10,000/100 = 100
10  max L = 10,000/10 = 1000
K
100
TC1 = 10,000
 K = 100 - .1L
L
1000
Increasing Isocost
K
TC3 > TC2 > TC1
TC1 TC2 TC3
L
Changing Input Prices
K
TC1
TC1
r
w
L
L
Different Ways (costs) of Producing q1
K
1
2
q1
3
TC1
TC2 TC3
L
Cost Min Way of Producing q1
K
K*
K* & L* are cost-min. combinations
Min cost of producing q1 = TC1
1
2
TC1
L*
q1
3
TC2 TC3
L
Cost Minimization
- Slope of isoquant = - slope of isocost line
MPL w


MPK r
r
w


 MCK  MC L
MPK MPL
MPK MPL


 additional q per additional $ spent same for both K and L
r
w
Average Cost and Output
1)
2)
SR
Avg cost will eventually increase due to law
of diminish MP ( MC will start to  and
eventually pull avg cost up)
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)


b)
Firms will enter
 mkt S   P
P < min LR AC (firm losses)


Firms will exit
 mkt S   P