bài giảng kinh tế vi mô tiếng anh ch7 minimising cost

economic costs • business costs: only explicit costs out of pocket • economic costs: explicit cost + implicit cost = opportunity cost • opportunity cost • value of best alternative use

Chapter 7

Minimizing Costs

1 measuring costs

2 short-run cost minimization

3 long-run cost minimization

4 costs are lower in long run

5 costs of producing multiple goods simultaneously

Key issues

Applications & problems

• taxes and depreciation

• labor only firm

• allocating time on an exam

• demolishing buildings

• agricultural subsidies and land restrictions

• tomato harvester

Two-step procedure to choose

technology

1 pick all technologically efficient production processes

2 from these technologically efficient production processes, pick the one that is economically efficient (minimizes cost)

Two reasons to study costs

1 understanding relationship between costs of

inputs and production helps us determine

least costly way to produce

2 relationship between output and costs

determines nature of an industry

• how many firms are in the industry

• how high price is relative to cost

Business vs economic costs

• business costs: only explicit costs (out of pocket)

• economic costs: explicit cost + implicit cost =

opportunity cost

• opportunity cost

• value of best alternative use of the resource

• classic example: "There's no such thing as a free lunch"

• “What have you given up to study opportunity costs”

Cost of running your own firm

• explicit cost: $40,000 per year (rent, materials,

wage payments)

• instead of paying yourself a salary, you keep any

profit at year's end

• your labor opportunity cost = $25,000/year you

could have earned working for another firm

• business cost = $40,000

• economic cost = $65,000 = $40,000 + $25,000

Capital costs

• capital is a durable good: a product that is usable for years

• capital may be rented or purchased

If capital is rented

• rental payment is the opportunity cost

• using the rental rate avoids 2 measurement

problems

• don't have to worry how to allocate the initial

purchase cost over time

• any adjustment in the cost of capital over time

is reflected in the rental rate

If capital is purchased

• firm's bookkeeper may

• expense cost by recording purchase price when it's made, or

• amortize cost by spreading it over life of capital according to IRS's arbitrary rules

• economists amortize capital cost based on its opportunity cost at each moment of time:

• amount that firm could charge others to rent capital

• thus, economists always use rental rate

Depreciate a business vehicle

• Toyota Land Cruiser (sports utility vehicle) and

Cadillac Seville (car) both cost $45,000

• tax law let’s you depreciate Land Cruiser in 6

years vs 23 for Seville

• after 5 years depreciated $42,408 for Land Cruiser

vs $14,460 for Seville

• “reason”

• Land Cruiser weighs more than 6,000 pounds and

Seville doesn't

• Congress uses 6,000 pounds as a criterion to distinguish

between trucks and cars

Short-run cost measures

• fixed cost (F): production expense that does

not vary with output

• variable cost (VC): production expense that

changes with quantity of output produced

• total cost (C):

C = VC + F

Sunk fixed cost

• usually assume fixed cost is sunk: expenditure that

you cannot be recovered

• opportunity cost of capital is zero

• because you can't get this expenditure back no matter

what you do, so ignore it when making decisions

• example: walk out of a bad movie early,

regardless of what you paid to attend

• otherwise, fixed cost is called avoidable

Marginal cost (MC)

• cost of producing the last unit

• change in cost, ∆C, when output changes by

∆q

• ∆C/∆q (or dC/dq)

Average cost concepts

• average fixed cost:

AFC = F /q

• average variable cost:

AVC = VC /q

• average (total) cost:

AC = C/q = AFC + AVC

Figure 7.1

Short-Run Cost Curves

120 216 400

48

10

4

Quantity, q, Units per day

Quantity, q, Units per day

6

b a

B A

4

C

F

1 1 27 20

VC

MC

AC AVC

AFC

Cost, $

Cost per unit, $ (a)

(b) 60

28 20

8 0

MC curve cuts AC and AVC at

their minimum points

• AC and AVC curves fall when MC is below

them, and rise when MC is above them

• therefore, MC cuts AC and AVC curves at

their minimum points

Production function determines

shape of cost curve

• production function shows how many inputs

needed to produce a given level of output

• firm's cost: multiply quantity of each input

by its price and sum

Norwegian printing firm

• short-run AC curve is U-shaped even though AVC is strictly upward sloping

• firm's capital is fixed at 100

Application Short-Run Cost Curves for a Printing Firm

Cost, kroner

q, Units per year

AFC AVC AC MC

0

20

30

40

50

10

Cost effects of $10 specific tax

• affects variable but not fixed cost

• after-tax (a) cost = before-tax (b) cost + 10q:

C a = C b + 10q

• at every quantity, AVC, AC, and MC curves shift

up by $10:

AVC a = AVC b+ $10

AC a = AC b+ $10

MC a = MC b+ $10

Figure 7.3 Effects of a Specific Tax on Cost Curves

Costs per

unit, $

15

0

q, Units per day

80

37

27

$10

AC a = AC b+ 10

AC b

MC b

MC a = MC b+ 10

$10

Cost effects of lump-sum tax

• affects fixed cost but not variable cost

• after-tax (a) cost = before-tax (b) cost plus lump-sum tax (L):

C a = C b+ L

• thus

AC a = AC b+ L/q

MC a = MC b

Solved Problem 7.1

Costs per

unit, $

/q

q, Units per day

AC b

q a

C

q b

AC a = AC b + /q

M

Lump-sum tax: California

$800-per-year tax is levied “for the privilege

of doing business in California”

Lump-sum tax: New York

$900,600 for three-year license to sell hot

dogs in front of NY City's Metropolitan

Museum of Art

Long-run costs

• firm adjusts all its inputs so its cost of production is as low as possible

• if capital and other variable can be varied,

no LR fixed costs (F = 0)

• then LR total cost = LR variable cost:

C = VC

Input choice

choose from all technologically efficient

combinations of inputs, the economically

efficient combination of inputs

Costs of input bundles

• isocost: all combinations of inputs that

require the same (iso) total expenditure (cost)

• if cost is C = wL + rK

• then isocost is

• where is a fixed level of cost

,

C wL rK= +

C

Figure 7.4 A Family of Isocost Lines

K, Units of

capital per year

a b

d e

c

$150 isocost

$100 isocost

$50 isocost

$100

———$5 = 20 $150———$5 = 30

$50

——$5— = 10

$100

———$10

10 =

$50

— ——

5 =

$150

———$10

15 =

L, Units of labor per year

Properties of isocost lines

1 where isocost line hits axes depends on and factor prices

• intersects capital axis at

• intersects labor axis at

2 isocosts farther from origin have higher costs:

3 slope of each isocost line is the same:

∆K/∆L = -w/r

/

C r

/

C w

C w

r r

= −

Figure 7.5 Cost minimization for Norweigian printing firm

K, Units of

capital per year

y

x

z

116 50

24 0

L , Units of labor per year

100

303

28

q = 100 isoquant

3,000-kr

isocost

2,000-kr

isocost

1,000-kr

isocost

Equivalent cost-minimizing rules

to pick lowest-cost combination of inputs to produce a given level of output when isoquants are smooth:

• lowest-isocost rule: pick bundle of inputs where

lowest isocost line touches isoquant

• tangency rule: isoquant is tangent to isocost line:

MRTS = |ratio of the input prices| = w/r

• last-dollar rule: last dollar spent on one input

produces as much extra output as last dollar spent on any other input

Derivation of last dollar rule

L K

MRTS

Cost minimizing vs output

maximizing

with smooth isoquants: firm determines best factor proportions by either

• cost minimizing: what is the lowest cost, C*, at which the firm can produce output q*?

• output maximizing: What is the most output,

q*, that can be produced at cost C*?

Relative factor price changes

• cause firm to change the mix of inputs used

• firm substitutes relatively less expensive

inputs for more expensive ones

• In Figure 7.6, r = 8 kr

• original wage = 24 kr, so w/r = 3

• new wage = 8 kr, so w/r = 1

Figure 7.6 Change in Factor Price

K, Units of

capital per year

v x

77 50

0 L, Workers per year

100

52

q = 100 isoquant

Original

2,000 kr

New isocost, 1,032 kr

LR cost varies with output

• examine lowest-cost factor combination for

various levels of output

• expansion path:

• cost-minimizing combination of labor and capital for

each output level

• curve through tangency points is LR expansion path

• expansion path shows same relationship between

LR cost and output as the LR cost curve

Figure 7.7a Expansion Path and Long-Run cost Curve

K, Units of

capital per year

x y z

100 75 50

0 L, Workers per year

150 200

100

Expansion path

(a) Expansion Path

3,000-kr isocost

2,000-kr isocost 4,000-kr isocost

100 isoquant

200 isoquant

Figure 7.7b Expansion Path and Long-Run cost Curve

C, Cost, kroner

X Y Z

0 q, Units per year

4,000

3,000

2,000

Long-run cost curve (b) Long-Run Cost Curve

200

100 150

Solved Problem

• suppose that the wage rate falls (while the rental rate of capital remains unchanged)

• what happens to the expansion path?

Shape of LR cost curves

• reason why LR AC is U-shaped different than SR

• SR:

• SR AC initially downward sloping because AFC is

downward sloping

• SR AC later upward sloping because of diminishing

returns

• LR

• no fixed cost in LR (usually)

• production function returns to scale determine shape

Figure 7.8 Long-Run Cost Curves Cost, $

q* q, Quantity per day

(a) Cost Curve

C

Cost per unit, $

q* q, Quantity per day

MC

AC

(b) Marginal and Average Cost Curves

Economies of scale

AC rises when output increases

diseconomies of scale

AC does not change as output

increases

no economies of scale

AC falls as output expands

economies of scale

Causes of economies of scale

• returns to scale in production function

• sufficient condition for AC economies of scale

• not necessary condition

• in LR, firm may change ratio of K/L as it

expands output, so could have economies of

scale in costs without increasing returns to

scale in production

Costs lower in long run

• in LR, firm chooses optimal plant size level

to minimize its LR cost given q

• because the firm cannot vary its capital in

SR but can in LR

• SR cost ≥ LR cost

• SR cost > LR cost if the "wrong" level of capital is used in SR

Figure 7.9 Long-Run Average Cost as the Envelope of

Short-Run Average Cost Curves

Average cost, $

a

b

d

e

SRAC1 SRAC2

SRAC3

SRAC3LRAC

c

q2

q1 q, Output per day

10

0

12

Long-Run Cost Curves in Printing and Oil Pipelines

(a) Norwegian Printing Firm Cost, kroner

q, Output per year

0

20 30 40

10

SRAC1

SRMC1

SRAC2

SRMC2

LRAC = LRMC

Long-Run Cost Curves in Printing and Oil Pipelines

(b) Oil Pipelines

2000 1000 400 200

0

Thousand barrels per day

Cost per barrel-mile

150

100

50

10

8" SRAC 10" SRAC 16" SRAC 12" SRAC

26" SRAC 20" SRAC

40" SRAC

LRAC

• firms have more flexibility in long run

• technical progress may lower cost over time

• learning by doing: productive skills and knowledge of better ways to produce that workers and managers gain from experience

Figure 7.11a Learning by Doing

Labor costs

per plane, $

250

50 0

C-141 planes

(a) Learning by Doing on C-141 Aircraft

500

400

300

200

100

Average labor cost

Figure 7.11b Learning by Doing

Average cost

A B C b c

q, Output per period

(b) Economies of Scale and Learning by Doing

Learning by doing

Economies of scale

q2 q3

AC3

AC2

AC1

q1

Cost of producing multiple goods

• outputs are linked if a single input is used to

produce all of them

• mutton and wool both come from sheep

• beef and hides come from cattle

• heating fuel and gasoline come from oil

• it is less expensive to produce goods jointly

than separately (beef & hides)

Joint production

• Laura spends one day collecting mushrooms and wild strawberries in the wood

• economies of scope (PPF1 )

• picking only mushrooms: 8 pints

• pick only strawberries: 6 pints

• pick some of each: 6 pints of mushrooms and 4 pints of strawberries

• no economies of scope (PPF2 )

• mushrooms grow in one section and strawberries in another

• PPF 2 is a straight line

Figure 7.12 Joint Production

Mushrooms,

Pints per day

PPF2

PPF1

6 4 Wild strawberries, Pints per day

8

6

0

Measuring scope (SC)

• C(q1, 0) = cost of producing q1units of first good by itself

• C(0, q2) = cost of producing only q2units of second good

• C(q1, q2) = cost of producing both goods together

1 2

( , )

C q C q C q q SC

C q q

=

Scope

cheaper to produce separately

SC < 0

diseconomies of scope

cost same either way

SC = 0

no economies of scope

cheaper to produce goods jointly

SC > 0

economies of scope

Economies of scope

• refining: cheaper to produce motor gasoline, distillate fuels, and other refined products together

• auto manufacturing: four automobile manufacturers

• 25% less expensive (SC = 0.25) to produce large cars

together with small cars and trucks than to produce large cars separately and small cars and trucks together

• no economies of scope from producing trucks together with small and large cars

Diseconomies of scope

using railroads to transport freight and passengers

together

• 41% less expensive (SC = -0.41) to transport

passengers and freight separately than together

• in early 1970s: passenger service was transferred

from the private railroad companies to Amtrak,

and services are separate

Summary

cost minimization from all technologically efficient production processes, choose one that is economically efficient

1 Measuring costs

• use economic cost: explicit + implicit costs

• opportunity cost: value of next best

alternative use includes both explicit and

implicit costs

2 Short-run costs

• some factors are fixed in the SR

• costs vary with only variable (nonfixed) inputs

3 Long-run costs

• all factors can be varied, so all costs are variable

• AC = AVC

• costs minimized where

• lowest isocost touches the relevant isoquant

• isocost is tangent to the isoquant

• last dollar spent on any input increases output by as

much as last dollar spent on any other input

4 Costs are lower in long run

• more flexibility in LR

• technological progress

• learning by doing

5 Costs of producing multiple

goods

• economies of scope: less expensive to

produce goods jointly rather than separately

• diseconomies of scope: less expensive to

produce separately