Firm Costs, Revenues, and Profits

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UNIT 7

• Firm Costs, Revenues, and Profits

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Key Topics

• Cost concepts
• Cash and Non Cash
• Variable and Fixed
• Total TFC, TVC, TC
• Average AFC, AVC, ATC, AVC AP
• Marginal MC, MC MP
• Revenue concepts
• Total
• Marginal
• Profit concepts
• Profit maximizing output
• Firm market supply

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Key Topics - continued

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

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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

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Recent Examples of Firm Cost Concerns

• GM
• Spent 5 billion to ? costs of producing Saturn
  cars
• Labor costs per car for GM were 2x Toyotas
• United, Delta, other airlines
• - Southwests costs often 50 less
• Sears, K-Mart, Target
• - Trying to compete with Walmart on basis of
  costs
• Georgia Pacific
• Started using thinner saws
• Less saw dust
• 800 more rail cars of lumber per year

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Cost Concepts

• Cash and Non Cash
• Fixed and Variable
• Total, Average, and Marginal

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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
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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

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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

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Marginal Cost

• MC additional cost per unit of additional
  output

slope of TC and slope of TVC curves
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MC, AVC, and ATC Relationships

• If MC gt AVC ? AVC is increasing
• If MC lt AVC ? AVC is declining
• If MC gt ATC ? ATC is increasing
• If MC lt ATC ? ATC is declining

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Product and Cost Relationships

• Assume variable input labor
• MP ?Q/?L AP
• TVC W L
• MC
• note MC ? is opposite of MP ?
• AVC
• note AVC ? is opposite of AP ?

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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.

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• 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
?TVC/?q w/MP
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Another Cost of Production Example

• Assume a production process has the following
  costs
• TFC 120
• TVC .1q2
• MC .2q

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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)?
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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)

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TFC in AFC graph

• AFC TFC/q ? TFC AFC x q

AFC1
TFC
AFC
q
q1
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TVC in AVC graph

• AVC TVC/q ? TVC AVC x q

AVC
AVC1
TVC
q
q1
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TC in ATC graph

• ATC TC/q ? TC ATC x q

ATC
ATC1
TC
q
q1
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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
• ?TR/?Q

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General Types of Firms (based on the D for their
product)

• Perfectly Competitive
• D curve for their product is flat
• P is constant (? can sell any Q at given P
  determined by SD)
• AR MR P (all constant)
• TR P x Q (? linear, upward sloping given P is
  constant)
• 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 gt0 to lt0)

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General Graphs of Revenue Concepts
Perfectly Competitive Firm
Imperfectly Competitive Firm


PRARMR
PAR
MR
Q
Q


TR
TR
Q
Q
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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
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TR in P graph (competitive firm)

• TR P x q

P
P
TR
q
q1
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Revenue-Cost Concepts

• Profit TR TC
• Operating profit TR - TVC

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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.

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General Graph of Perfectly Competitive Firm
Profit Max

MC
MR
Q

TR
TC
Q
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Perfectly Competitive Firm Profit Max (Example)

• P MR 10
• MC .2Q
• TR 10Q
• TC 120 .1Q2
• ? Max Q ?
• MR MC
• ? 10 .2Q
• ? Q 50
• ?Max p TR-TC (at Q 50)
• 10(50) 120 .1(50)2
• 500 120 250
• 130

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General Graph of Imperfectly Competitive Firm
Profit Max

MC
MR
Q

TR
TC
Q
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Imperfectly Competitive Firm Profit Max (example)

• P 44-Q
• MR 44-2Q
• TR 44Q-Q2
• MC .2Q
• TC 120 .1Q2
• ? Max Q ?
• MRMC
• ? 44-2Q .2Q
• ? 2.2Q 44
• ? Q 20
• Max p TR-TC (at Q 20)
• 44(20)-(20)2 120 .1(20)2
• 480 160
• 320

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Fixed Costs and Profit Max

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

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Q. Should a firm shut down in SR?

• Profit if produce
• TR TVC TFC
• Profit if dont produce or shut down
• -TFC
• ? Shut down if
• TR TVC TFC lt -TFC
• TR TVC lt 0
• TR lt TVC

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Perfectly Competitive Firm Market Supply

• Firm S MC curve above AVC
• ? (PMR) gt AVC
• Market S sum of individual firm supplies

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Graph of SR Shut Down Point

MC
Short-run Supply curve
ATC
AVC
Market price
Shut-down point
Q
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SR Profit Scenarios

1. Produce, p gt 0
2. Produce, p lt 0 (loss less than TFC)
3. Dont produce, p -TFC

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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, p TR TC
• ? to max p of producing given q, need to min. TC

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Budget Line

• maximum combinations of 2 goods that can be
  bought given ones income
• combinations of 2 goods whose cost equals ones
  income

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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

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Isocost Line Equation

• TC1 rK wL
• rK TC1 wL
• K TC1/r w/r L
• Note slope inverse input price ratio
• ?K / ?L
• rate at which capital can be exchanged
• for 1 unit of labor, while holding costs
• constant

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• Equation of TC1 10,000 (r 100, w 10)

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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
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Increasing Isocost
K
TC3 gt TC2 gt TC1
L
TC1
TC2
TC3
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Changing Input Prices
K
TC1
TC1
?r
?w
L
L
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Different Ways (costs) of Producing q1
K
1
2
q1
3
TC3
TC2
TC1
L
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Cost Min Way of Producing q1
K
K L are cost-min. combinations Min cost of
producing q1 TC1
1
K
2
q1
3
TC3
TC2
TC1
L
L
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Cost Minimization

• - Slope of isoquant - slope of isocost line

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Average Cost and Output

• 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

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LR Equilibrium ? P of output min LR AC

• LR Disequilibrium
• P gt min LR AC (from profits)
• Firms will enter
• ? mkt S ? ? P
• P lt min LR AC (firm losses)
• Firms will exit
• ? mkt S ? ? P