Chapter 27 Demand in the Factor Market 27-1 Copyright 2002 by The McGraw-Hill Companies, Inc. All rights reserved.

Chapter 27

Demand in the Factor Market

27-1Copyright 2002 by The McGraw-Hill Companies, Inc. All rights reserved.

Chapter Objectives

• Derived demand

• Productivity

• Marginal revenue product

• Changes in resource demand

• The substitution and output effects

• Optimum resource mix for the firm

27-2Copyright 2002 by The McGraw-Hill Companies, Inc. All rights reserved.

Derived Demand

• Derived demand is the demand for resources• There are four resources: land, labor, capital,

and entrepreneurial ability• The demand for these resources is derived from

the demand for the final products– The demand for land on which to grow corn is

derived from the demand for corn

– The demand for labor with which to produce cars is derived from the demand for cars

27-3Copyright 2002 by The McGraw-Hill Companies, Inc. All rights reserved.

Productivity

• Productivity is output per unit of input– Productivity is measured by what is produced– Inputs measure the four economic resources

• The more productive a resource is, the more it will be in demand– This is reflected in in both their prices and their

rents• Sally can get higher wages than John because she is more

productive• An acre of land that produces more cotton than another

acre of land will command a higher rent

27-4Copyright 2002 by The McGraw-Hill Companies, Inc. All rights reserved.

Prices of Substitute Goods

• A given good or service can usually be produced in many different ways

• Every country or organization uses the cheapest production method– When wages rise, many companies seek to substitute

machinery for relatively expensive labor– If land becomes more expensive, farmers would

work each acre more intensively, substituting labor and capital for more expensive land

• The demand for a resource is its marginal revenue product schedule (MRP)

27-5Copyright 2002 by The McGraw-Hill Companies, Inc. All rights reserved.

Marginal Revenue Product (MRP)

• How much of a resource is purchased depend on three things– The price of that resource– The productivity of that resource– The selling price of the final product that the

resource helps to produce

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Hypothetical Output of Labor Hired by a Firm

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Units of Labor Output Marginal Physical Product 1 15 15 2 29 14 3 41 12 4 51 10 5 58 7 6 62 4 7 63 1 8 63 0 9 62 -1 10 60 -2

Note: The marginal physical product we are computing here is identical to computing marginal output in diminishing returns

Hypothetical Output of Labor Hired by a Firm

27-8Copyright 2002 by The McGraw-Hill Companies, Inc. All rights reserved.

Units of Labor Output Marginal Physical Product 1 15 15 2 29 14 3 41 12 4 51 10 5 58 7 6 62 4 7 63 1 8 63 0 9 62 -1 10 60 -2

Note: No business firm would hire more than seven workers under these circumstances, even if the wage rate was a penny an hour.

Hypothetical Marginal Revenue Product Schedule

27-9Copyright 2002 by The McGraw-Hill Companies, Inc. All rights reserved.

(1) (2) (3) (4) (5) (6) Units Marginal Total Marginal of Physical Revenue Revenue Land Output Product Price Product Product* 1 20 20 2 38 18 3 53 15 4 65 12 5 73 8 6 78 5 7 80 2 8 80 0 9 79 -1

Hypothetical Marginal Revenue Product Schedule

27-10Copyright 2002 by The McGraw-Hill Companies, Inc. All rights reserved.

(1) (2) (3) (4) (5) (6) Units Marginal Total Marginal of Physical Revenue Revenue Land Output Product Price Product Product* 1 20 20 $10 2 38 18 10 3 53 15 10 4 65 12 10 5 73 8 10 6 78 5 10 7 80 2 10 8 80 0 10 9 79 -1 10

This is a perfect competitor because the firm can sell its entire output at the same price of $10

Hypothetical Marginal Revenue Product Schedule

27-11Copyright 2002 by The McGraw-Hill Companies, Inc. All rights reserved.

(1) (2) (3) (4) (5) (6) Units Marginal Total Marginal of Physical Revenue Revenue Land Output Product Price Product Product* 1 20 20 $10 $200 $200 2 38 18 10 380 180 3 53 15 10 530 150 4 65 12 10 650 120 5 73 8 10 730 80 6 78 5 10 780 50 7 80 2 10 800 20 8 80 0 10 800 0 9 79 -1 10 790 -10

*You should use the Total Revenue Product column to calculate the Marginal Revenue Product (MRP) because this method works for both the perfect competitor and the imperfect competitor

Hypothetical Marginal Revenue Product Schedule

27-12Copyright 2002 by The McGraw-Hill Companies, Inc. All rights reserved.

(1) (2) (3) (4) (5) (6) Units Marginal Total Marginal of Physical Revenue Revenue Land Output Product Price Product Product* 1 20 20 $10 $200 $200 2 38 18 10 380 180 3 53 15 10 530 150 4 65 12 10 650 120 5 73 8 10 730 80 6 78 5 10 780 50 7 80 2 10 800 20 8 80 0 10 800 0 9 79 -1 10 790 -10

How many units of land would you hire if you needed to pay $200 rent per unit?

Hypothetical Marginal Revenue Product Schedule

27-13Copyright 2002 by The McGraw-Hill Companies, Inc. All rights reserved.

(1) (2) (3) (4) (5) (6) Units Marginal Total Marginal of Physical Revenue Revenue Land Output Product Price Product Product* 1 20 20 $10 $200 $200 2 38 18 10 380 180 3 53 15 10 530 150 4 65 12 10 650 120 5 73 8 10 730 80 6 78 5 10 780 50 7 80 2 10 800 20 8 80 0 10 800 0 9 79 -1 10 790 -10

How many units of land would you hire if you needed to pay $200 rent per unit?

You would hire just one unit of land because only the first unit is worth $200

Hypothetical Marginal Revenue Product Schedule

27-14Copyright 2002 by The McGraw-Hill Companies, Inc. All rights reserved.

(1) (2) (3) (4) (5) (6) Units Marginal Total Marginal of Physical Revenue Revenue Land Output Product Price Product Product* 1 20 20 $10 $200 $200 2 38 18 10 380 180 3 53 15 10 530 150 4 65 12 10 650 120 5 73 8 10 730 80 6 78 5 10 780 50 7 80 2 10 800 20 8 80 0 10 800 0 9 79 -1 10 790 -10

How many units of land would you hire if you needed to pay $150 rent per unit?

Hypothetical Marginal Revenue Product Schedule

27-15Copyright 2002 by The McGraw-Hill Companies, Inc. All rights reserved.

(1) (2) (3) (4) (5) (6) Units Marginal Total Marginal of Physical Revenue Revenue Land Output Product Price Product Product* 1 20 20 $10 $200 $200 2 38 18 10 380 180 3 53 15 10 530 150 4 65 12 10 650 120 5 73 8 10 730 80 6 78 5 10 780 50 7 80 2 10 800 20 8 80 0 10 800 0 9 79 -1 10 790 -10

How many units of land would you hire if you needed to pay $150 rent per unit?You would hire 3 units of land

Hypothetical Marginal Revenue Product Schedule

27-16Copyright 2002 by The McGraw-Hill Companies, Inc. All rights reserved.

(1) (2) (3) (4) (5) (6) Units Marginal Total Marginal of Physical Revenue Revenue Land Output Product Price Product Product* 1 20 20 $10 $200 $200 2 38 18 10 380 180 3 53 15 10 530 150 4 65 12 10 650 120 5 73 8 10 730 80 6 78 5 10 780 50 7 80 2 10 800 20 8 80 0 10 800 0 9 79 -1 10 790 -10

How many units of land would you hire if its price were $90. Assume the land is indivisible.

You would hire 4 units because the fifth unit is only worth $80

Hypothetical Marginal Revenue Product Schedule

27-17Copyright 2002 by The McGraw-Hill Companies, Inc. All rights reserved.

(1) (2) (3) (4) (5) (6) Units Marginal Total Marginal of Physical Revenue Revenue Land Output Product Price Product Product* 1 20 20 $10 $200 $200 2 38 18 10 380 180 3 53 15 10 530 150 4 65 12 10 650 120 5 73 8 10 730 80 6 78 5 10 780 50 7 80 2 10 800 20 8 80 0 10 800 0 9 79 -1 10 790 -10

In case you haven’t yet realized it the MRP schedule is the firm’s demand schedule for land

The Marginal Revenue Product (MRP) Curve

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200

180

160

140

120

100

80

60

40

20

Units of land

Rent

1 2 3 4 5 6 7 8 9

MRP

This curve represents the firm’s demand for land. It slopes downward to the right. The lower the rent the greater the quantity of land demanded. The higher the rent the lower the quantity of land demanded

If the rent is $120 how many units of land are demanded?

Four units

The Marginal Revenue Product (MRP) Curve

27-19Copyright 2002 by The McGraw-Hill Companies, Inc. All rights reserved.

200

180

160

140

120

100

80

60

40

20

Units of land

Rent

1 2 3 4 5 6 7 8 9

MRP

If the rent is $120 how many units of land are demanded?

Four units

How much rent is collected?Total Rent is (4 X $120) = $480

The Marginal Revenue Product (MRP) Curve

27-20Copyright 2002 by The McGraw-Hill Companies, Inc. All rights reserved.

200

180

160

140

120

100

80

60

40

20

Units of land

Rent

1 2 3 4 5 6 7 8 9

MRP

Four units

The producer’s surplus is the triangular area above the rent line. This is the difference between how much this land is worth to the firm and how much it actually had to pay in rent

How much the firm actually paid in rent is shown in the rectangular area below the triangle

Hypothetical MRP Schedule of the Imperfect Competitor

27-21Copyright 2002 by The McGraw-Hill Companies, Inc. All rights reserved.

(1) (2) (3) (4) (5) (6) Units Marginal Total Marginal of Physical Revenue Revenue Labor Output Product Price Product Product 1 18 18 $12 $216 $216 2 34 16 11 374 258 3 48 14 10 480 106 4 59 11 9 531 51 5 68 9 8 544 13 6 74 6 7 518 -26 7 77 3 6 462 -56 8 78 1 5 390 -72

How do we know this firm is an imperfect competitor?

The firm has to lower price to sell more.

Hypothetical MRP Schedule of the Imperfect Competitor

27-22Copyright 2002 by The McGraw-Hill Companies, Inc. All rights reserved.

(1) (2) (3) (4) (5) (6) Units Marginal Total Marginal of Physical Revenue Revenue Labor Output Product Price Product Product 1 18 18 $12 $216 $216 2 34 16 11 374 258 3 48 14 10 480 106 4 59 11 9 531 51 5 68 9 8 544 13 6 74 6 7 518 -26 7 77 3 6 462 -56 8 78 1 5 390 -72 How many workers would the firm hire if the wage rate were $150?Two workers would be hired. You would not hire the third worker because you would be paying $150 for something worth only $106.

The wage bill would be (2 X $150) = $300

Hypothetical MRP Schedule of the Imperfect Competitor

27-23Copyright 2002 by The McGraw-Hill Companies, Inc. All rights reserved.

(1) (2) (3) (4) (5) (6) Units Marginal Total Marginal of Physical Revenue Revenue Labor Output Product Price Product Product 1 18 18 $12 $216 $216 2 34 16 11 374 258 3 48 14 10 480 106 4 59 11 9 531 51 5 68 9 8 544 13 6 74 6 7 518 -26 7 77 3 6 462 -56 8 78 1 5 390 -72 How many workers would the firm hire if the wage rate were $51?Four workers would be hired. You would not hire the fifth worker because you would be paying $51 for something worth only $13 .

The wage bill would be (4 X $51) = $204

The Marginal Revenue Product Curve of the Perfect and Imperfect Competitors

27-24Copyright 2002 by The McGraw-Hill Companies, Inc. All rights reserved.

Units of labor

MRP

MRP(perfectcompetitor)

MRP(imperfectcompetitor)

220

200

180

160

140

120

100

80

60

40

20

Ð20

0

Ð40

Ð60

Ð8010 2 3 4 5 6 7 8 9

The MRP curve of the imperfect competitor declines more steeply than that of the perfect competitor because the imperfect competitor must lower price to sell additional output

A Shift in the Marginal Revenue Product Curve

27-25Copyright 2002 by The McGraw-Hill Companies, Inc. All rights reserved.

Units of capital

MRP

MRP1

MRP2

1 2 3 4 5 6 7 8 9

70

60

50

40

30

20

10

Remember, the MRP schedule is a firm’s demand schedule. Therefore a shift in the MRP schedule is the same as a shift in the demand schedule

Four things can cause a shift from MRP1 to MRP2

Changes in demand for the final product

Productivity changes

Changes in the price of other resources

Complementary factors

Changes in the Demand for the Final Product

• This is by far the most important influence on the demand for a factor of production– If the demand for the final product increased

so much that the price doubled, the MRP schedule of the firm would increase

– This means the MRP schedule changed and the MRP curve would shift to the right because the MRP increased

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A Shift in the Marginal Revenue Product Curve

27-27Copyright 2002 by The McGraw-Hill Companies, Inc. All rights reserved.

Units of land

MRP

MRP1

MRP2

Total rent

ProducerÕs

Rent

400

380

360

340

320

300

280

260

240

220

200

180

160

140

120

100

80

60

40

20

1 2 3 4 5 6 7 8 9

Productivity Changes

• Productivity is output per unit of input• If output per unit of input increases then

the MPP schedule also increases. This increases the MRP and the MRP curves shifts to the right

• Nearly all of any productivity increase comes from either better capital or better trained and educated labor or both

27-28Copyright 2002 by The McGraw-Hill Companies, Inc. All rights reserved.

Changes in the Prices of Other Resources• There are four factors of production

– Sometimes one factor is substituted for another• When a new machine replaces several workers, we are

substituting capital for labor

– The substitution effect• If the price of a resource is raised, other resources will be

substituted for it. If the price of a resource is lowered, it will be substituted for other resources

– The output effect• If the price of a resource rises, output of the final product

will decline, thereby lowering the employment of all resources. If the price of a resource falls, output of the final product will rise, thereby increasing the employment of all resources

– The two effects are contradictory• Sometime the substitution effect is stronger and sometime

the output effect is stronger

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Complementary Factors

• Although resources are usually substitutable at least to some degree, they also work well together– You need at least some labor to produce virtually

every good or service

• Two factors are complements in production if an increase in the use of one requires an increase in the use of the other

• When the price of a resource rises, the demand for a complementary resource will fall

• When the price of a resource falls, the demand for a complementary resource rises

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Optimum Resource Mix for the Firm

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A firm will use increasing amounts of a resource until the MRP of that resource equals its price.

We would hire workers until the MRP of labor equals the price of labor

MRP of labor = Price of labor

MRP of labor Price of labor=

Price of labor Price of laborMRP of laborPrice of labor

= 1

Optimum Resource Mix for the Firm

27-32Copyright 2002 by The McGraw-Hill Companies, Inc. All rights reserved.

A firm will use increasing amounts of a resource until the MRP of that resource equals its price.

We would hire units of land until the MRP of land equals the price of land

MRP of land = Price of land

MRP of land Price of land=

Price of land Price of landMRP of landPrice of land

= 1

Optimum Resource Mix for the Firm

27-33Copyright 2002 by The McGraw-Hill Companies, Inc. All rights reserved.

A firm will use increasing amounts of a resource until the MRP of that resource equals its price.

We would buy units of capital until the MRP of capital equals the price of capital

MRP of capital = Price of capital

MRP of capital Price of capital=

Price of capital Price of capitalMRP of capitalPrice of capital

= 1

Hypothetical MRP Schedules for a Firm

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Units of MRP of Units of MRP of Units of MRP of Land Land Capital Capital Labor Labor 1 $12 1 $15 1 $30 2 10 2 13 2 26 3 8 3 10 3 21 4 6 4 7 4 15 5 4 5 3 5 8 6 2 6 0 6 1

If the rent is $8 how many of units of land will you hire?

Answer: 3

Hypothetical MRP Schedules for a Firm

27-35Copyright 2002 by The McGraw-Hill Companies, Inc. All rights reserved.

Units of MRP of Units of MRP of Units of MRP of Land Land Capital Capital Labor Labor 1 $12 1 $15 1 $30 2 10 2 13 2 26 3 8 3 10 3 21 4 6 4 7 4 15 5 4 5 3 5 8 6 2 6 0 6 1

If the interest is $3 how many of units of capital will you hire?

Answer: 5

Hypothetical MRP Schedules for a Firm

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Units of MRP of Units of MRP of Units of MRP of Land Land Capital Capital Labor Labor 1 $12 1 $15 1 $30 2 10 2 13 2 26 3 8 3 10 3 21 4 6 4 7 4 15 5 4 5 3 5 8 6 2 6 0 6 1

If the wage rate is $15 how many of units of labor will you hire?

Answer: 4

Hypothetical MRP Schedules for a Firm

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Units of MRP of Units of MRP of Units of MRP of Land Land Capital Capital Labor Labor 1 $12 1 $15 1 $30 2 10 2 13 2 26 3 8 3 10 3 21 4 6 4 7 4 15 5 4 5 3 5 8 6 2 6 0 6 1

A firm will keep hiring more and more of a resource up to the point at which the MRP is equal to its price