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ECO 610-401

Monday, September 29

Topics: Costs & Decision Making: Level of Production & Mix of Resources

Readings:

Brickley et. al, Chapters 5,7; Chapter 19:562-574

Hoyt, Lecture 3:103-126 Handouts

Extended Assignment 1

Notes and Examples

Reading Changing the Formula: Seeking Perfect Prices, CEO Tears

Up the Rules (WSJ, March 27, 2007)

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Assignment for Monday, October 6th

Topics:

Decision Making: Make or Buy and Transfer Pricing

Double Marginalization and Vertical Integration

Relevant Costs Review for Exam 1

Readings:

Brickley et. al, Chapter 19:562-574;

Hoyt, Lecture 3:115-126

Extended Assignment 1 Due

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Some Terminology for Production

Total Product or Total Output(TP or Q)

Q

Total output produced by L workers

Average Product (AP)

TP/L

The amount produced by L workers divided by the numberof workers--"output per worker".

Marginal Product (MP)

Q/L

the increase in output with an increase in labor

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Total Product

Q1

TPL

LL1

L2

Q

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Marginal and Average Product

LL1 L2

MPL

APL

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Short Run Costs -- Some Terminology

Fixed Costs (FC)

Costs independent of the level of output

cost of capital-- machinery or rent of a building.

Average Fixed Cost (AFC)

FC/Q

Overhead per unit

Total Variable Costs (TVC)

The total variable costs of producing Q units of output

variable costs usually being labor and raw materials

Average Variable Costs (AVC)

TVC/Q

labor costs per unit".

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Cost Terminology (continued)

Total Cost (TC)

FC+TVC

Average Total Cost (ATC)

TC/Q=TVC/Q+FC/Q

cost per unit.

Marginal Cost (MC)

TVC/ Q or TC/ Q

the increase in costs with an increase in output at Q units ofoutput

the wages paid to the additional workers hired to producethe additional output".

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Total Costs

QQ1

TVC

TC

FC

$

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Unit Costs

ATC

AVC

MC

Q

$

Q1 Q2 Q3

AFC

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Relationship between Cost andProductivity

The cost curves appear to be flipped depictions of the productcurves. Why?

MC = VC/Q = wL/Q =w( L/Q) = w/MPL

AVC = VC/Q = wL/Q =w(L/Q) = w/APL

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Lesson in Cost Theory 1:

MC and AVC are determined by productivity of the variable inputs,generally labor.

Decreasing MC reflects increasing MPL Increasing MC reflects declining MPL.

From trends in MC and AVC we can infer trends in theproductivity of labor

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Productivity & Costs(Let Wage = $10 hour)

Labor(hours) Output MPL MC

1 4

2 10

3 15

4 19

5 22

6 24

4

6

5

4

3

2

10/4=2.50

10/6=1.67

10/5=2.00

10/4=2.50

10/3=3.33

10/2=5.00

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Input Demand (Short Run)

What is the profit-maximizing demand for inputs?

Let =P(Q)Q(L,K) - wL - rK

Q(L,K)= production function.

K is fixed (short run). Choose L to maximize

MRMPL =w or MRPL = w

MRPLis the marginal revenue product of labor

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Profit-Maximization and Labor Demand


At profit-maximizing amount of input:

additional revenue from Q associated with an additional unit

of the input (MRPL)=

additional cost of hiring that input (w).

If MRPL > w then more labor should be employed;

if MRPL < w, less labor should be employed.

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Production in the Long Run

What is long run?

No fixed inputs Both capital and labor can be adjusted to:

increase output

decrease the cost of producing a given level of

output. More generally all inputs used in production are variable.

Flexible Production Processes

For any level of output there are numerous combinationsof inputs to produce it.

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Why study long run?

Characterize conditions that ensure cost-minimization inproduction?

Develop a framework to explain changes in production processeswhen:

prices of inputs change

output increases or decreases

productivity of inputs changes

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Conditions for Cost-Minimization

What characterizes cost minimization in long run?

MPl/wadditional productivity of an additional $ spenton labor

MPk/radditional productivity of an additional $ spenton capital

So cost minimization -->

MPL/w = MPk/r

Q per additional $ in L = Q per additional $ in KOr MPL/MPK = w/r

relative productivity = relative cost

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Example

Worker costs $150 per day. Hiring (dismissing) at a print shop willincrease (decrease) revenues by $200 per day through specialorders

Leasing another copy machines at $50 will increase revenues by $75.

Does the shop have the correct mix of labor and capital (copymachines)?

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The Impact of Changes in Input Prices on

Input Use

At w=$10 & r=$20

cost minimizing at K= 7 and L=14

total cost of producing 100 units is $280.

Suppose w increases to $20.Then the cost of K=7 & L=14 is 20(14) + 20(7) = $420.

Is this the new cost of producing 100 units of output?

Answer: No.

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Input Price Changes and Cost Changes


Increases in costs based on current mix of inputs will alwaysoverestimate the cost increase.

With flexible production, a firm can substitute away from the inputthat has increased in price.

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Production with Multiple Plants and Products

Issues:

Multi-plant Production

Given multiple plants how should you allocateproduction between the plants?

When is it profitable to open another plant?

How does having multiple plants affects costs ofproduction and output decisions?

Multiple Products

How do we allocate inputs between products? How do we make production decisions when production

is joint?

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Example: Allocation of Production amongPlants

A manufacturer has a work force of 1,000 to allocate betweenthe production of a single product produces in 2 plants.

How should it allocate the workers to maximize output?

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L A QA LB QB

0 0 0 0100 1950 100 1575

200 3800 200 3100

300 5550 300 4575

400 7200 400 6000

500 8750 500 7375

600 10200 600 8700

700 11550 700 9975

800 12800 800 11200

900 13950 900 12375

1000 15000 1000 13500

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L A QA dQA LB QB dQB

0 0 0 0

100 1950 1950 100 1575 1575

200 3800 1850 200 3100 1525

300 5550 1750 300 4575 1475

400 7200 1650 400 6000 1425

500 8750 1550 500 7375 1375600 10200 1450 600 8700 1325

700 11550 1350 700 9975 1275

800 12800 1250 800 11200 1225

900 13950 1150 900 12375 1175

1000 15000 1050 1000 13500 1125

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Multiple Products

A firm produces 2 products with labor of 5

Product A

Price = $10

Cost of materials, $2

1st worker give 5 units an hour per worker

2nd worker give 4 units

3rd

worker gives 3 units 4th worker gives 2 units

5th worker gives 2 units

Product B

Price = $7

Cost of materials, $1 1st worker give 8 units an hour per worker

2nd worker give 6 units

3rd worker gives 4 units



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Rules for Allocating Inputs

For plants (A & B) we allocate the inputs so that

For products we allocate the inputs so that

B

L

A

LMPMP

YYXX MCMRMCMR

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Allocation of Scarce Inputs

Lesson in Cost Theory .

With limited inputs to be allocated in the production of a singleproduct among a number of plants, the profit-maximizingallocation of the input requires that the marginal product of the

input be equal in all plants.

For allocation of a limited input among a number of products itmust be the case that the marginal contribution of the input toprofits, marginal revenue product less the marginal cost of

product, should be equal for all products.

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Table 1: Output Al location and Costs with Two Plants

Q Plant A Plant B Combined Output Allocation

ATC MC ATC MC ATC MC Q1 Q2

10 16.20 6.40 16.10 8.20 24.20 6.40 10 020 11.40 6.80 12.20 8.40 15.40 6.80 20 0

30 9.93 7.20 10.97 8.60 12.60 7.20 30 0

40 9.30 7.60 10.40 8.80 11.30 7.60 40 0

50 9.00 8.00 10.10 9.00 10.60 8.00 50 0

60 8.87 8.40 9.93 9.20 10.18 8.13 53 7

70 8.83 8.80 9.84 9.40 9.90 8.27 57 13

80 8.85 9.20 9.80 9.60 9.70 8.40 60 20

90 8.91 9.60 9.79 9.80 9.56 8.53 63 27

100 9.00 10.00 9.80 10.00 9.47 8.67 67 33

110 9.11 10.40 9.83 10.20 9.40 8.80 70 40

120 9.23 10.80 9.87 10.40 9.36 8.93 73 47

130 9.37 11.20 9.92 10.60 9.33 9.07 77 53

140 9.51 11.60 9.97 10.80 9.31 9.20 80 60

150 9.67 12.00 10.03 11.00 9.31 9.33 83 67

160 9.83 12.40 10.10 11.20 9.32 9.47 87 73

170 9.99 12.80 10.17 11.40 9.33 9.60 90 80

180 10.16 13.20 10.24 11.60 9.35 9.73 93 87

190 10.33 13.60 10.32 11.80 9.37 9.87 97 93

200 10.50 14.00 10.40 12.00 9.40 10.00 100 100

210 10.68 14.40 10.48 12.20 9.43 10.13 103 107

220 10.85 14.80 10.56 12.40 9.47 10.27 107 113

230 11.03 15.20 10.65 12.60 9.50 10.40 110 120

240 11.22 15.60 10.73 12.80 9.54 10.53 113 127

250 11.40 16.00 10.82 13.00 9.59 10.67 117 133

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0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

0 25 50 75 100 125 150 175 200 225 250

Q

Cost($)

ATCA

MCA

ATCB

MCB

ATCCombined

MCCombined

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Multiple Plant Production

Lesson in Cost Theory.

A firm with multiple plants can always minimize its costs byallocating the production so that marginal cost is equal in allplants.

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Opportunity Costs

Notice: Fixed supplies of labor & material in examples with 2plants, 2 products. Then no costs for these? Correct?

What is meant by Opportunity Cost?

Opportunity Cost of an action is value of the foregone

alternative, the benefits sacrificed. Explicit costs are opportunity costs as price of input reflects

its value in alternative use.

But use of any input (labor, capital) that has no explicit cost

may have opportunity cost

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Opportunity Costs: Some Examples

Sole Proprietorship: Owner/Manager of Retail Outlet

Explicit Costs:

Rent: $20,000

Direct Labor: 60,000

Utilities: 3,000

Merchandise: 140,000

Total: $227,000

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Sole Proprietorship

Revenues: $260,000

Is profit = $260,000 - $227,000 = $33,000

Yes if we meanAccounting Profit

No if we meanEconomic Profit.

Why? Did not include the opportunity cost of owners time &effort.

Suppose that Owner could earn $50,000 as manager ofsimilar retail operation. Then full cost is explicit cost +

opportunity cost = $267,000 Economic Profit = $260,000 - $277,000 = (17,000)

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Planting a Crop

Agribusiness plants corn in a field that it owns. Costs include:

labor

storage, shipping

fertilizer, irrigation, seed depreciation of machinery (due to use)

What else should be included?

Foregone profits (contribution) on alternative crop.

Foregone rent from sale of land

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Machine Time

2 Product Lines share limited machine time

Product Line 1:

Unit Costs:DM (Direct Machine):2, DL(Direct Labor):1

1 Machine hour per unit

Price = 5

Product Line 2

Unit Costs: DM: 3 DL: 4

2 Machine hours per unit

Price = 10

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Machine Time (continued)

What is the economic cost of each product line (per unit)?

1 MH for product line 1 yields contribution of 5-2-1=2

2 MH for product line 2 yields contribution of 10-3-4=3 or1.5 per 1 MH

Then economic cost is

For 1, 2 + 1+ 1.5 = 4.5

For , 3 + 4 + 2 = 9

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Vertical Integration

The modern corporation is often organized into a number ofdifferent divisions that are vertically integrated.

Vertical integration implies a structure in which the productdeveloped in the "upstream" division is an input in

production in a "downstream" division.Examples:

Automobile production

Engines are produced in one division of GM and thenpurchased by another a division that assembles theautomobile.

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An Example with External Market

Company produces electronic control devices and specialty

microchips.ATC is $300 and Pc = 550.

Company uses chips in control devices.

ATC of device (ATCd) is $500 + 2*ATCc = $1100 and Pd

= $1,500. Assume the $500 is variable.Should the company produce control devices?

Consider 2 alternative situations:

Outside orders for chips were insufficient to keep capacity

utilized. Suppose that $200 of the devices costs are fixed and capacitycould be fully-utilized by outside orders. Should the firmproduce chips in the short run?

Wh h i l i i ?

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Why have vertical integration?

Enables a corporation to monitor and reward production more

easily by rewarding division based on the "profits" generatedby that division.

Upstream division that "sells" its products to downstreamdivision needs a price for its product. Reasons:

To accurately measure division profit and evaluate theoverall success of the firm.

To motivate divisions by giving them a chance to earnprofits based on their performance.

To ensure the proper production and allocation of"upstream" products to "downstream" divisions orexternal markets.

To minimize international tax liabilities.

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Choosing the Transfer Price

Example: 2 divisions upstream" and downstream.

The upstream produces a component by the downstreamdivision for sale on an external market.

What should the price of the component (pC) be?

To answer -- the overall objective of the corporation is to

maximize its profits, not the profits of any single division.Assume that each division operates independently given

the component price:

upstream division can decided how much to produce

downstream can decide how much to purchase and fromwhom (possibly outside the firm).

There are two general cases:

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No External Market

Price of the components (pc) should be set at the marginal cost ofproducing the component.

If at the pc = MC, the division is not earning positive profitsbecause of fixed costs, then the corporation must subsidize the

division by providing a payment to cover these fixed costs but itshould not change pc from MC.

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No External Market: An Example

2 divisions (downstream (d) and upstream (u)):

Demand for downstream (d) given by

Pd = 20 - (1/50)Q

MCd = 6 Mcu = 4 (1 unit of u for each unit of d)

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0

2

4

6

8

10

12

14

16

18

20

0 50 100 150 200 250 300 350 400 450 500

Q

$

D

MR

D

MR

MCd+Mc

u=MC

d+P

T

MCd

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An External Market for the Upstream

ComponentIn the case of perfect competition, the price of the component equal to

what the price is on the external market.

If the upstream division cannot produce them at that price then

it is more profitable for the corporation to purchase externallyand not have internal production.

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External Sales and Purchases

Upstream division may also want to sell externally as well.

If demand for component by the downstream division is less than Q atwhich pe = MC then:

Upstream division can increase its profits by selling components onthe external market.

If demand is greater than Q at which pc = MC then: Upstream division will not be willing to supply the entire demand for

downstream division and it will need to purchase the componentexternally.

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External Markets: An Example

2 cases:

Low Demand for downstream product in firm

Pd= 14 - (1/50)Qd

High Demand for downstream product in firm Pd= 20 - (1/50)Qd MCd = 6

Mcu = 2.5 + (1/100)Q

Pe=4 (external price for component)

Example A: External Sales/Low Demand

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p /

0

1

2

3

4

56

7

8

9

10

1112

13

14

15

16

1718

19

20

0 40 80 120 160 200 240 280 320 360 400

MCd

MCu+MC

u

D

MRd

Pe

External

Sales

0

4

Example B: External Purchases/High Demand

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0

1

2

3

4

56

7

8

9

10

1112

13

14

15

16

1718

19

20

0 40 80 120 160 200 240 280 320 360 400

MCd

MCu+MCu

D

MRd

Pe

External

Purchases

0

4

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An Example Problem (5.5)

Manufacturer of Toys has 2 lines (A&B)

Also produces chip used in both lines

Has capacity of 10,000

Chip can be sold externally (line C) External price is $20

Additional costs for external sale

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Demand for 3 products

PA QA PB QB PC QC

$60 1000 $50 2000 20 10,00040 2000 40 4000

20 3000 30 600020 8,000

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Variable Costs (excluding chip costs)

Product Variable Cost

(excluding chip costs)

A 20

B 25

C 3

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Transfer Pricing

What should the transfer price be?

What will production be?

Suppose that capacity for chip increases to 20,000.

What should transfer price be?

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