CFO Ch 8

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8Short-Run Costs and

Output DecisionsCHAPTER OUTLINECosts in the Short Run

Fixed CostsVariable CostsTotal CostsShort-Run Costs: A Review

Output Decisions: Revenues, Costs, and Profit Maximization

Perfect CompetitionTotal Revenue and Marginal RevenueComparing Costs and Revenues to

Maximize ProfitThe Short-Run Supply Curve

Looking Ahead

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fixed cost Any cost that does not depend on the firms’ level of output. These costs are incurred even if the firm is producing nothing. There are no fixed costs in the long run.

variable cost A cost that depends on the level of production chosen.

total cost (TC) Total fixed costs plus total variable costs.

TC = TFC + TVC

Costs in the Short Run

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total fixed costs (TFC) or overhead The total of all costs that do not change with output even if output is zero.

TABLE 8.1 Short-Run Fixed Cost (Total and Average) of a Hypothetical Firm

(1)q

(2)TFC

(3)AFC (TFC/q)

012345

$1,0001,0001,0001,0001,0001,000

$ −1,000

500333250200


Fixed Costs

Total Fixed Cost (TFC)

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average fixed cost (AFC) Total fixed cost divided by the number of units of output; a per-unit measure of fixed costs.

TFCAFCq

=

spreading overhead The process of dividing total fixed costs by more units of output. Average fixed cost declines as quantity rises.


Fixed Costs

Average Fixed Cost (AFC)

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Average Fixed Cost (AFC)

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total variable cost (TVC) The total of all costs that vary with output in the short run.

total variable cost curve A graph that shows the relationship between total variable cost and the level of a firm’s output.


Variable Costs

Total Variable Cost (TVC)

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(9 x $2) + (6 x $1) = $24

(6 x $2) + (14 x $1) = $26

6

14

9

6

A

B

3 units ofoutput

(7 x $2) + (6 x $1) = $20

(4 x $2) + (10 x $1) = $18

6

10

7

4

A

B

2 units ofoutput

4

6

(4 x $2) + (4 x $1) = $12

(2 x $2) + (6 x $1) = $10

4

2

A

B

1 unit of output

Total Variable Cost Assuming PK = $2, PL = $1

TVC = (K x PK) + (L x PL) Using

Technique

Units of Input Required(Production Function)

K LProduce

TABLE 8.2 Derivation of Total Variable Cost Schedule from Technology and Factor Prices


Variable Costs


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Variable Costs


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marginal cost (MC) The increase in total cost that results from producing 1 more unit of output. Marginal costs reflect changes in variable costs.

TABLE 8.3 Derivation of Marginal Cost from Total Variable CostUnits of Output Total Variable Costs ($) Marginal Costs ($)

0123

0101824

1086


Variable Costs

Marginal Cost (MC)

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Variable Costs

The Shape of the Marginal Cost Curve in the Short Run

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In the short run, every firm is constrained by some fixed input that (1) leads to diminishing returns to variable inputs and (2) limits its capacity to produce. As a firm approaches that capacity, it becomes increasingly costly to produce successively higher levels of output. Marginal costs ultimately increase with output in the short run.


Variable Costs

The Shape of the Marginal Cost Curve in the Short Run

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MCTVCTVCq

TVCTVC =∆=∆

=∆

=1Δ

of slope


Graphing Total Variable Costs and Marginal Costs

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TVCAVCq

=

average variable cost (AVC) Total variable cost divided by the number of units of output.


Variable Costs

Average Variable Cost (AVC)

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TABLE 8.4 Short-Run Costs of a Hypothetical Firm

(1)q

(2)TVC

(3)MC

(∆ TVC)

(4)AVC

(TVC/q)(5)

TFC

(6)TC

(TVC + TFC)

(7)AFC

(TFC/q)

(8)ATC

(TC/q or AFC + AVC)

0 $ 0 $ − $ − $1,000 $ 1,000 $ − $ −

1 10 10 10 1,000 1,010 1,000 1,010

2 18 8 9 1,000 1,018 500 509

3 24 6 8 1,000 1,024 333 341

4 32 8 8 1,000 1,032 250 258

5 42 10 8.4 1,000 1,042 200 208.4

− − − − − − − −

− − − − − − − −

− − − − − − − −

500 8,000 20 16 1,000 9,000 2 18


Variable Costs

Average Variable Cost (AVC)

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f FIGURE 8.6 More Short-Run CostsWhen marginal cost is below average cost, average cost is declining. When marginal cost is aboveaverage cost, average cost is increasing.Rising marginal cost intersects average variable cost at the minimum point of AVC.


Variable Costs

Graphing Average Variable Costs and Marginal Costs

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Total Costs

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average total cost (ATC) Total cost divided by the number of units of output.

qTCATC =

AVCAFC ATC +=


Total Costs

Average Total Cost (ATC)

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f FIGURE 8.8 Average Total Cost = Average Variable Cost + Average Fixed Cost

To get average total cost, we add average fixed and average variable costs at all levels of output.Because average fixed cost falls with output, an ever-declining amount is added to AVC. Thus, AVC and ATC get closer together as output increases, but the two lines never meet.


Total Costs

Average Total Cost (ATC)

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If marginal cost is below average total cost, average total cost will decline toward marginal cost. If marginal cost is above average total cost, average total cost will increase. As a result, marginal cost intersects average totalcost at ATC’s minimum point for the same reason that it intersects the average variablecost curve at its minimum point.

The relationship between average total cost and marginal cost is exactly the same as the relationship between average variable cost and marginal cost.


Total Costs

The Relationship Between Average Total Cost and Marginal Cost

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TABLE 8.5 A Summary of Cost Concepts

Term Definition Equation

Accounting costs Out-of-pocket costs or costs as an accountant would define them. Sometimes referred to as explicit costs.

-

Economic costs Costs that include the full opportunity costs of all inputs. These include what are often called implicit costs.

-

Total fixed costs (TFC) Costs that do not depend on the quantity of output produced. These must be paid even if output is zero.

-

Total variable costs (TVC) Costs that vary with the level of output. -Total cost (TC) The total economic cost of all the inputs used

by a firm in production.TC = TFC + TVC

Average fixed costs (AFC) Fixed costs per unit of output. AFC = TFC/qAverage variable costs (AVC)

Variable costs per unit of output. AVC = TVC/q

Average total costs (ATC) Total costs per unit of output. ATC = TC/q ATC = AFC + AVCMarginal costs (MC) The increase in total cost that results from

producing 1 additional unit of output.MC = DTC/Dq


Short-Run Costs: A Review

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Costs in DollarsStudents Total Fixed Cost Total Variable Cost Total Cost Average Total Cost

500 $60 million $ 20 million $ 80 million $160,0001,000 60 million 40 million 100 million 100,0001,500 60 million 60 million 120 million 80.0002,000 60 million 80 million 140 million 70,0002,500 60 million 100 million 160 million 64,000

Average and Marginal Costs at a College

E C O N O M I C S I N P R A C T I C E

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perfect competition An industry structure in which there are many firms, each small relative to the industry, producing identical products and in which no firm is large enough to have any control over prices. In perfectly competitive industries, new competitors can freely enter and exit the market.

homogeneous products Undifferentiated products; products that are identical to, or indistinguishable from, one another.


Perfect Competition

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c FIGURE 8.9 Demand Facing a Single Firm in a Perfectly Competitive Market If a representative firm in a perfectly competitive market raises the price of its output above $6.00, the quantity demanded of that firm’s output will drop to zero.Each firm faces a perfectly elastic demand curve, d.


Perfect Competition

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qP TR ×=×= quantity pricerevenue total

total revenue (TR) The total amount that a firm takes in from the sale of its product: the price per unit times the quantity of output the firm decides to produce (P x q).

marginal revenue (MR) The additional revenue that a firm takes in when it increases output by one additional unit. In perfect competition, P = MR.


Total Revenue and Marginal Revenue

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Comparing Costs and Revenues to Maximize Profit

The Profit-Maximizing Level of Output

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As long as marginal revenue is greater than marginal cost, even though the difference between the two is getting smaller, added output means added profit. Whenever marginal revenue exceeds marginal cost, the revenue gained by increasing output by 1 unit per period exceeds the cost incurred by doing so.

The profit-maximizing perfectly competitive firm will produce up to the point where the price of its output is just equal to short-run marginal cost—the level of output at which P* = MC.

The profit-maximizing output level for all firms is the output

level where MR = MC.



The Profit-Maximizing Level of Output

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TABLE 8.6 Profit Analysis for a Simple Firm

(1)

q

(2)

TFC

(3)

TVC

(4)

MC

(5)

P = MR

(6)TR

(P x q)

(7)TC

(TFC + TVC)

(8)Profit

(TR − TC)

0 $ 10 $ 0 $ − $ 15 $ 0 $ 10 $ −10

1 10 10 10 15 15 20 −5

2 10 15 5 15 30 25 5

3 10 20 5 15 45 30 15

4 10 30 10 15 60 40 20

5 10 50 20 15 75 60 15

6 10 80 30 15 90 90 0



A Numerical Example

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An analysis of fixed costs; variable costs; marginal costs; revenues; marginal revenues; and profits were used by this ice cream parlor to determine whether to stay in business.

Case Study in Marginal Analysis: An Ice Cream Parlor

E C O N O M I C S I N P R A C T I C E

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The Short-Run Supply Curve

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Annex: Firms in Perfect

Competition

Based on Mankiw Ch. 12

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Characteristics of Perfect Competition

1. Many buyers and many sellers.

2. The goods offered for sale are largely the same.

3. Firms can freely enter or exit the market.

� Because of 1 & 2, each buyer and seller is a “price taker” – takes the price as given.

� Because of 3, economic profit is zero.

� ∏ >0 will cause entry

� ∏ < 0 will cause exit

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The Revenue of a Competitive Firm

• Total revenue (TR)

• Average revenue (AR)

• Marginal revenue (MR):The change in TR from selling one more unit.

∆TR∆Q

MR =

TR = P x Q

TRQ

AR = = P

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Profit Maximization• What Q maximizes the firm’s profit? • To find the answer, “think at the margin.”

If increase Q by one unit,revenue rises by MR,cost rises by MC.

• If MR > MC, then increase Q to raise profit. • If MR < MC, then reduce Q to raise profit.

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MR = P for a Competitive Firm

• A competitive firm can keep increasing its output without affecting the market price.

• So, each one-unit increase in Q causes revenue to rise by P, i.e., MR = P.

MR = P is only true for

firms in perfectly competitive

markets.

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Profit Maximization

505

404

303

202

101

45

33

23

15

9

$5$00

∆Profit =

MR – MCMCMRProfitTCTRQAt any Q with

MR > MC,

increasing Qraises profit.

5

7

7

5

1

–$5

10

10

10

10

–2

0

2

4

$6

12

10

8

6

$4$10

At any Q with

MR < MC,

reducing Qraises profit.

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For any firm (whether PC or not), MR = MC

determines profit maximization.

For the PC firm, the key difference is that

P = MRAnd therefore P = MR = MC

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P1

MR

MC and the Firm’s Supply Decision

At Qa, MC < MR.

So, increase Qto raise profit.

At Qb, MC > MR.

So, reduce Qto raise profit.

At Q1, MC = MR.

Changing Qwould lower profit. Q

Costs

MC

Q1

Qa

Qb

Rule: MR = MC at the profit-maximizing Q.

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P1

MR

P2

MR2

MC and the Firm’s Supply Decision

If price rises to P2,

then the profit-maximizing quantity rises to Q

2.

The MC curve determines the firm’s Q at any price.

Hence,

Q

Costs

MC

Q1

Q2

the MC curve is the

firm’s supply curve.

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Shutdown vs. Exit

• Shutdown: A short-run decision not to produce anything because of market conditions.

• Exit: A long-run decision to leave the market.

• A key difference: – If shut down in SR, must still pay FC.– If exit in LR, zero costs.

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A Firm’s Short-run Decision to Shut Down

• Cost of shutting down: revenue loss = TR

• Benefit of shutting down: cost savings = VC(firm must still pay FC)

• So, shut down if TR < VC

• Divide both sides by Q: TR/Q < VC/Q

• So, firm’s decision rule is:

Shut down if P < AVC

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The firm’s SR supply curve is the portion of its MC curve above AVC.

Q

Costs

A Competitive Firm’s SR Supply Curve

MC

ATC

AVC

If P > AVC, then

firm produces Qwhere P = MC.

If P < AVC, then

firm shuts down

(produces Q = 0).

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A Firm’s Long-Run Decision to Exit

• Cost of exiting the market: revenue loss = TR

• Benefit of exiting the market: cost savings = TC(zero FC in the long run)

• So, firm exits if TR < TC

• Divide both sides by Q to write the firm’s decision rule as:

Exit if P < ATC

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A New Firm’s Decision to Enter Market

• In the long run, a new firm will enter the market if it is profitable to do so: if TR > TC.

• Divide both sides by Q to express the firm’s entry decision as:

Enter if P > ATC

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The firm’s LR supply curve is the portion of its MC curve above LRATC.

Q

Costs

The Competitive Firm’s Supply Curve

MC

LRATC

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profit

A Firm With Profits

Q

Costs, P

MC

ATCP MR

Q

ATC

profit per unit = P – ATC

revenue per unit =

cost per unit =

profit-maximizing quantity

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ATCloss

A Firm With Losses

Q

Costs, P

MC

ATC

P MR

Q

loss per unit

revenue per unit =

cost per unit =

loss-minimizing quantity

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Market Supply: Assumptions

1) All existing firms and potential entrants have identical costs.

2) Each firm’s costs do not change as other firms enter or exit the market.

3) The number of firms in the market is – fixed in the short run

(due to fixed costs)– variable in the long run

(due to free entry and exit)

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The SR Market Supply Curve

• As long as P ≥ AVC, each firm will produce its profit-maximizing quantity, where MR = MC. • Recall from Chapter 4:

At each price, the market quantity supplied is the sum of quantities supplied by all firms.

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The SR Market Supply Curve

MC

P2

Market

Q

P

(market)

One firm

Q

P

(firm)

SP3

Example: 1000 identical firmsAt each P, market Qs = 1000 x (one firm’s Qs)

AVCP2

P3

30

P1

2010

P1

30,00010,000 20,000

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Entry & Exit in the Long Run

• In the LR, the number of firms can change due to entry & exit. • If existing firms earn positive economic profit,

– new firms enter, SR market supply shifts right. – P falls, reducing profits and slowing entry.

• If existing firms incur losses,

– some firms exit, SR market supply shifts left. – P rises, reducing remaining firms’ losses.

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The Zero-Profit Condition

• Long-run equilibrium: The process of entry or exit is complete –remaining firms earn zero economic profit.

• Zero economic profit occurs when P = ATC.

• Since firms produce where P = MR = MC, the zero-profit condition is P = MC = ATC.

• Recall that MC intersects ATC at minimum ATC.

• Hence, in the long run, P = minimum ATC.

– Recall significance of minimum ATC

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S1

Profit

D1

P1

long-run

supply

D2

SR & LR Effects of an Increase in Demand

MC

ATC

P1

Market

Q

P

(market)

One firm

Q

P

(firm)

P2

P2

Q1

Q2

S2

Q3

A firm begins in

long-run eq’m…

…but then an increase

in demand raises P,……leading to SR

profits for the firm.

Over time, profits induce entry,

shifting S to the right, reducing P…

…driving profits to zero

and restoring long-run eq’m.

A

B

C

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CONCLUSION:The Efficiency of a Competitive Market• Profit-maximization: MC = MR

• Perfect competition: P = MR

• So, in the competitive eq’m: P = MC• Recall, MC is cost of producing the marginal unit.

P is value to buyers of the marginal unit. • So, the competitive eq’m is efficient, maximizes total

surplus. • In the next chapter, monopoly: pricing & production

decisions, deadweight loss, regulation.

59 of 34FIRMS IN COMPETITIVE MARKETS 59

profit

A Firm With Profits

Q

Costs, PMC

ATCP MR

Q

ATCprofit per unit = P –

ATC

revenue per unit =

cost per unit =

profit-maximizing quantity

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ATCloss

A Firm With Losses

Q

Costs, PMC

ATC

P MR

Q

loss per unitrevenue per unit

=

cost per unit =

loss-minimizing quantity

CFO Ch 8

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