MBA201a: Economic Costs & Costs of Production

Professor Wolfram MBA201a - Fall 2009 Page 2

Economic categorizations of costs: cost functions

• We have seen how economic costs include opportunity costs and exclude sunk costs.

• Once we’ve got the right costs, what do we do with them?

Cost functions

– Cost functions relate some cost to the quantity a firm

produces.

– Cost functions represent ideal rather than actual costs.

– A firm’s cost function may change over time.

Professor Wolfram MBA201a - Fall 2009 Page 3

T-shirt factory example

You run a t-shirt factory for Fruit-of-the-Loom.

You’re currently producing 45 t-shirts a week, and selling them to headquarters for $1.80 each, for total revenues of $80/week.

Your division manager tells you that if you’re making 45 t-shirts a week, your total costs are $71/week, so your average cost per t-shirt is $1.58.

Are you happy?

Professor Wolfram MBA201a - Fall 2009 Page 4

Categorizing the costs

Upon further investigation, you learn that your cost structure looks like this:

To produce t-shirts:

• You must lease one machine at $20 / week.

• The machine requires one worker.

• The machine, operated by the worker, produces one t-shirt per hour.

• Worker is paid $1/hour on weekdays (up to 40 hours), $2/hour on Saturdays (up to 8 hours), $3 on Sundays (up to 8 hours).

Are you still happy?

Professor Wolfram MBA201a - Fall 2009 Page 5

The Average Cost Fallacy

• The first 40 t-shirts cost:

C(n) = F + V(n) = $20 + $1*40 = $60

At a price of $1.80, profits on these is $12.

• The next 5 t-shirts cost:

$2*5 = $10

At a price of $1.80, they generate revenue of $9.

You’re losing $1 by producing up to 45! You should have stopped at 40.

fixed variable

Professor Wolfram MBA201a - Fall 2009 Page 6

We will talk about 6 types of cost functions

Total cost (C): total cost of inputs the firm needs to produce output q. Denoted C(q).

Fixed cost (FC): the cost that does not depend on the output level, C(0) [or really C(0.00001)]

Variable cost (VC): that cost which would be zero if the output level were zero, C(q) – C(0) [or really C(q) – C(0.00001)].

Average total cost (ATC) (aka simply “average cost” (AC)): total cost divided by output level, C(q)/q.

Average variable cost (AVC): variable cost divided by output level, VC(q)/q.

Marginal cost (MC): the unit cost of a small increase in output. – Derivative of cost with respect to output, dC/dq– Approximated by C(q)-C(q-1), e.g. C(40)-C(39)

Professor Wolfram MBA201a - Fall 2009 Page 7

A total cost function graphically

An example: C(Q) = 10 + .5Q

0

5

10

15

20

25

30

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31

Q

C(Q

)

C(Q)

Professor Wolfram MBA201a - Fall 2009 Page 8

The average total cost function

ATC(Q) = C(Q)/Q = 10/Q + .5

0

2

4

6

8

10

12

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

Q

AT

C(Q

)

ATC(Q)

Professor Wolfram MBA201a - Fall 2009 Page 9

Marginal costs

0

2

4

6

8

10

12

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

Q

AT

C(Q

)/M

C(Q

)

ATC(Q) MC(Q)

MC(Q) = dC(Q)/dQ = .5

Professor Wolfram MBA201a - Fall 2009 Page 10

T-shirts: costs

Suppose output level is 40 t-shirts per week. Then,

– Fixed cost: FC = $20.

– Variable cost: VC = 40 x $1 = $40.

– Average total cost: ATC = (20+40)/40 = $1.5

– Average variable cost: AVC = (40)/40 = $1

– Marginal cost: MC = $1.

(Note that producing an extra T-shirt would imply working on

Saturday, which costs more: MC(41) = $2.)

Similar calculations can be made for other output levels, leading to the cost functions …

Professor Wolfram MBA201a - Fall 2009 Page 11

T-shirt factory cost functions

Cost ($)

ATC

10

3

1

20 30 40 50

1.5

2

MC

48 T-shirts

Professor Wolfram MBA201a - Fall 2009 Page 12

Marginal and average cost curves: generic shape

Cost ($)

ATC

q1

MC

q2

p1

p2

Marginal cost always crosses average cost at its minimum.

Professor Wolfram MBA201a - Fall 2009 Page 13

More average cost and marginal cost in Excel

C(Q) = 10 + .2Q2; ATC = 10/Q +.2Q; AVC= .2Q; MC = .4Q

0

2

4

6

8

10

12

14

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

Q

AT

C(Q

)/M

C(Q

)

ATC(Q) MC(Q)

Professor Wolfram MBA201a - Fall 2009 Page 14

Economies of scale

Economies of scale describe how the firm’s average costs change as output increases.

– ATC with quantity = “diseconomies of scale”

– ATC with quantity = “economies of scale”

Note: a cost function can exhibit economies of scale at some

output levels and diseconomies of scale at other output

levels.

Professor Wolfram MBA201a - Fall 2009 Page 15

T-shirt factory profits

Cost ($)

ATC

10

3

1

20 30 40 50

1.5

2

MC

48 T-shirts

1.8

Profits

Professor Wolfram MBA201a - Fall 2009 Page 16

What if Fruit-of-the-LoomTM offers a lower price?

Scenario B: Fruit-of-the-Loom™ offers p = $1.3 per t-shirt.

No matter how much factory produces, price is below per-unit cost; i.e., no matter how much factory produces, it will lose money: 

p < AC implies q x p < q x AC

implies Revenue < Cost

Optimal decision is not to produce at all.

Professor Wolfram MBA201a - Fall 2009 Page 17

General lessons on output decisions

There is a general lesson from the factory example.

What to produce: Firms should produce every unit for which the income on that unit (in this case the price) is greater than the cost.

What not to produce: Firms should not produce any unit for which the income on that unit is less than the cost.

Note that AC(q) is not playing a role in determining how much to produce, only whether to produce at all.

Marginal cost: how much to produceAverage Cost: whether to produce

Professor Wolfram MBA201a - Fall 2009 Page 18

Output decisions in the generic case

Cost ($)

ATC

q1

MC

p1

p2

Professor Wolfram MBA201a - Fall 2009 Page 19

Output decisions in the generic case

Cost ($)

q1

MC

q2

p2 =

lost profits

Professor Wolfram MBA201a - Fall 2009 Page 20

Supply curve

Supply curve: how much a firm produces at each price.

Generalizing from previous example:

Firm can sell all it wants at given price (we say market is

“perfectly competitive”).

If price is below minimum average cost, p0, then firm is better

off by shutting down.

If price is greater than P0, say P’, then firm should sell output q’

such that MC=P’.

Supply curve is given by MC curve for values of P greater than the minimum of AC, zero for values of p below minimum of AC.

Professor Wolfram MBA201a - Fall 2009 Page 21

Quantity

Price

AC

q0

S

q’

p0

p’

Supply curve for a competitive (price-taking) firm

MC

Professor Wolfram MBA201a - Fall 2009 Page 22

Next week

– Next week, we’ll talk about how to take a supply curve for a

single firm producing a perfectly competitive industry (what

we just saw for the t-shirt example)…

– and derive the aggregate industry supply curves that we’ve

been drawing since the first lecture.

– We’ll also begin talking about monopoly pricing, which you’ll

see is an extension of the ideas we’ve introduced today.

Professor Wolfram MBA201a - Fall 2009 Page 23

Takeaways

We defined a number of economic cost functions.

We discussed how fixed costs do not include sunk costs.

Similarly, fixed and variable costs do include opportunity costs.

We saw how cost functions help firms make decisions about how much to produce and whether to produce at all.

If a firm is facing a fixed price, it will:

– Use ATC to decide whether to produce or shut down

(produce if p > ATC, otherwise shut down).

– Use MC to decide how much to produce (produce as long as

p > MC). In fact, MC defines the firm’s supply function if it is

producing.