UNIT 7:

Firm Costs, Revenues, and

Profits

Key Topics

1. Cost conceptsa. Cash and Non Cashb. Variable and Fixedc. Total: TFC, TVC, TCd. Average: AFC, AVC, ATC, AVC & APe. Marginal: MC, MC & MP

2. Revenue conceptsa. Totalb. Marginal

3. Profit conceptsa. Profit maximizing outputb. Firm & market supply

Key Topics - continued

4. SR productiona. Profits in P, ATC graph

b. Shut down condition (loss min.)

c. Firm & industry supply curves

5. LR productiona. Isocost lines & LR cost min. (Ch. 6 Appendix)

b. Returns to scale and LRAC

c. Equilibrium

Profit Overview (recall)

Profit = TR – TCTR depends on P of output, Q of

outputTC 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 CashFixed and VariableTotal, 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 = 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

q

TVC

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 = TVC = W ∙ L MC =

note: MC Δ is opposite of MP Δ

AVC =

note: AVC Δ is opposite of AP Δ

TVC

Q

W L

Q

W

MP

TVC

Q

W L

Q

W

AP

Q

L

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

q1

q

AFCTFC

TVC in AVC graph

AVC = TVC/q TVC = AVC x q

AVC1

q

AVC

TVC

$

q1

TC in ATC graph

ATC = TC/q TC = ATC x q

ATC1

q

ATC

TC

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 CompetitiveD 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 CompetitiveD 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

$

$

$

$

Q

Q

Q

Q

TR

PR=AR=MR

MRP=AR

TR

Perfectly Competitive Firm Imperfectly Competitive Firm

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

q

TR

q1

$

P

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

$

$

Q

Q

TR

TC

MC

MR

Perfectly Competitive Firm Profit Max (Example)

P = MR = 10MC = .2QTR = 10QTC = 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

$

$

TCTR

Q

QMR

MC

Imperfectly Competitive Firm Profit Max (example)

P = 44-QMR = 44-2QTR = 44Q-Q2

MC = .2QTC = 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

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

Q. 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.

Fixed Costs and Profit Max

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

q

TVC

qP AVC

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

$

Q

MC

ATC

AVC

Shut-down pointMarket price

Short-runSupply curve

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)

KTC

r

w

rL

K L

K L

1

1 0 0 0 0

1 0 0

1 0

1 0 0

1 0 0 1

,

.

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

1000

L

TC1 = 10,000 K = 100 - .1L

Increasing Isocost

K

TC1 TC2 TC3

L

TC3 > TC2 > TC1

Changing Input Prices

K

L

w

TC1TC1

r

L

Different Ways (costs) of Producing q1

K

L

12 3 q1

TC1

TC2TC3

Cost Min Way of Producing q1

K

L

12 3 q1

TC1

TC2TC3

K*

L*

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

Cost Minimization

- Slope of isoquant = - slope of isocost line

MP

MP

w

r

r

M P

w

MPMC MC

MP

r

M P

wadditiona l q per add itiona l spen t sam e for bo th K and L

L

K

K LK L

K L $

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 scalea) If increasing LR AC will with qb) If constant LR AC does not change with qc) 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