1

AGEC 603

Derived Demand for Land

Individual Demand Individual Demand

• Based on consumer choice • Utility theory and budget constraint

• Utility theory • Utility is the satisfaction one gets from

consuming a good or service

• Budget constraint – how much you have to spend

Marginal Utility Marginal Utility

• Change in utility derived from a change in consumption of a particular good holding other goods constant

• Law of Diminishing Marginal Utility - as consumption per unit of time increases, marginal utility decreases

• Examples

– M&Ms

– Texan Steak - Amarillo

2

Indifference / Isoutility Curves Indifference / Isoutility Curves

L1 L2

Land units

Bundle of goods

B1

B2

Negative slope

Nonintersecting

Everywhere dense

Convex to the origin

Consuming B1L1 provides the same utility

as consuming B2L2

Indifference Curves Indifference Curves

Which bundle would you

prefer … bundle M or

bundle B?

Which bundle would you

prefer … bundle M or

bundle B? M

B

1 2 3 4 5 6 7 8

Land Units

Bu

nd

les

of

go

od

s

1 2

3

4 5

6

7 8

The answer is that this we

would be indifferent

because they give us the

same utility. The ultimate

choice will depend on the

prices of these two

products.

The answer is that this we

would be indifferent

because they give us the

same utility. The ultimate

choice will depend on the

prices of these two

products.

Indifference Curves Indifference Curves

1 2 3 4 5 6 7 8

Land Units

B

un

dle

of

go

od

s

1 2

3

4 5

6

7 8

Which bundle would you

prefer more…bundle C or

bundle N?

Which bundle would you

prefer more…bundle C or

bundle N?

C N We would prefer bundle N

over bundle C because it

gives us more utility or

satisfaction. The question

is whether we can afford

to buy bundle N!

We would prefer bundle N

over bundle C because it

gives us more utility or

satisfaction. The question

is whether we can afford

to buy bundle N!

3

Marginal Rate of Substitution Marginal Rate of Substitution

• The rate at which the consumer is willing to substitute one good for another and maintain a constant utility level

• MRS of land for bundle with utility constant

• Notice - rise over run = the slope for a specific segment for a nonlinear curves

land

bundle

Marginal Rate of Substitution Marginal Rate of Substitution

• MRSland for bundle

going from 2 to 3

land units

1 2 3 4 5 6 7 8

1

Land Units

Bu

nd

le o

f g

oo

ds

1 2

3 4

5

6 7

8

-

1

This means the consumer

is willing to give up 1

bundle unit in exchange

for one land unit!

This means the consumer

is willing to give up 1

bundle unit in exchange

for one land unit!

11

1

_

land

bundle

Marginal Rate of Substitution Marginal Rate of Substitution

• MRSbundle for land

going from 2 to 3

bundle units

1 2 3 4 5 6 7 8

-2

Land Units

Bu

nd

le o

f g

oo

ds

1 2

3 4

5

6 7

8

1

502

1.-

-land

bundle

This means the consumer

is willing to give up 2 land

units for one additional

unit of bundle of goods!

This means the consumer

is willing to give up 2 land

units for one additional

unit of bundle of goods!

4

Marginal Rate of Substitution Marginal Rate of Substitution

• Why? – Utility must be constant

– What you give up with one, you must gain with the other!

bundle

land

MU

MU

land

bundleMRS

Budget Constraint Budget Constraint

• Represents the amount of income available for spending on the consumption bundles

• Example land / bundle budget

Pland x Qland + Pbundle x Qbundle Budget

where Pland and Pbundle represent the price of land and the bundle of goods

while Qland and Qbunlde represent the quantities you purchase during the

time period.

Budget Constraint – Graph

1 2 3 4 5 6 7 8 9 10 11

Land

B

un

dle

of

go

od

s

1 2

3

4 5

6

7 8

Apply all income to bundle

Apply all income to land Budget Constraint

Income = $200

Prices = $40 / unit bundle and $20 / unit land

5

Bundle Price Decreases by 1/2 Bundle Price Decreases by 1/2

1 2 3 4 5 6 7 8 9 10 11

Land

Bu

nd

le o

f g

oo

ds

1 2

3

4 5

6

7 8

9

1

0 Bundle price decreases by 1/2

Apply all income to land

Original price budget

constraint

After price change budget

constraint

Bundle Price Increases by 2 Bundle Price Increases by 2

1 2 3 4 5 6 7 8 9 10 11

Land

B

un

dle

of

go

od

s

1 2

3

4 5

6

7 8

9

1

0

Original price budget

constraint

Bundle price decreases by

1/2 budget constraint

Bundle price doubles budget

constraint

Land Price Changes Land Price Changes

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

Land

B

un

dle

of

go

od

s

1 2

3

4 5

6

7 8

9

1

0

Original price budget

constraint

Land price doubles

Land price decreases by 1/2

6

Income Changes Income Changes

1 2 3 4 5 6 7 8 9 10 11

Dozen corn ears consumed per week

Ste

ak

s (l

bs)

co

nsu

med

per

week

1 2

3

4 5

6

7 8

Budget Line at increased

income

Original Budget

Line

Budget Line

at ½ income

Note: parallel shifts

Objective - Maximize Utility

1 2 3 4 5 6 7 8 9 10 11

Land Units

B

un

dle

of

go

od

s

1 2

3 4

5

6 7

8

Indifference Curve – below budget constraint

Can increase utility by moving outward

Not Optimal

Indifference Curves and

points above the budget

Constraint exceeds your

budget - not feasible

Point Indifference Curve is Tangent

to Budget Constraint

Feasible – spends all budget

Maximizes Utility – highest curve obtainable

Slope Budget Constraint

1 2 3 4 5 6 7 8 9 10 11

Land Units

B

un

dle

of

go

od

1 2

3 4

5

6 7

8

Using x and y intercept points to calculate slope

land = 0, bundle = 5 and land = 10 and bundle = 0

Slope = rise / run = (5-0)/(0-10) = -0.5

These points obtained

Income / price of bundle = 5 and

Income / price of land = 10

bundle

land

land

bundle

land

bunlde

P

P

P

I

P

I

P

I

P

I

)0(

)0(

7

• Slope of indifference curve = slope of budget constraint

• Slope of indifference curve = MRS = - MUland / MUbundle

• Slope of budget constraint = -Pland / Pbundle

• Therefore,

Tangency Conditions

bundle

bundle

land

land

bundle

land

bundle

land

P

MU

P

MU

P

P

MU

MUMRS

• Point where utility is maximized subject to the budget constraint occurs at

MUland MUbundle

Pland Pbundle

• In other words, the marginal utility derived from the last dollar spent on each good is identical. This can be expanded to include all goods and services purchased by the consumer.

Consumer Equilibrium

=

Individual Demand Curve

1 2 3 4 5 6 7 8 9 10 11

Land units

B

un

dle

of

go

od

s

1 2

3 4

5

6 7

8

Original Price = $20 / unit

Consumption bundle

2.5 bundle units and

5 units land

What if price decreases to $15?

What happens to budget constraint?

8

Land Price Decreases

New x-intercept

Same Why

1 2 3 4 5 6 7 8 9 10 11 12 13 14

Land Units

B

un

dle

of

go

od

s

1 2

3 4

5

6 7

8

9

1

0 1

1

New equilibrium

= 2.75 bundle and 6 land

Why an increase in bundle

and increase in land?

Land Price Increases

New y-intercept same

Why?

1 2 3 4 5 6 7 8 9 10 11 12 13 14

Land Units

Bu

nd

le o

f g

oo

ds

1 2

3 4

5

6 7

8

9

1

0 1

1

New equilibrium

= 3.125 bundle and 1.5 land

Why an decrease in land

and increase in bundle?

Individual Demand Curve - Land

Demand Schedule

Price Quantity

Pincrease 1.5

Po 5

Pdecrease 6

9

Market Demand Curve - Land

+ =

The market demand curve is the horizontal

summation of the demand schedules

for all the consumers in the market.

The market demand curve is the horizontal

summation of the demand schedules

for all the consumers in the market.

Demand Curve Jargon - Review

• Specific terms to distinguish between

movement along a demand curve and a shift

in a demand curve

• Change in the quantity demanded is a

movement along a demand curve - Cause

• Change in demand is a shift in the demand

curve - Causes

World Population and Demand World Population and Demand

• Population one of the most important factors in

determining demand for land

• Trends

• Changing characteristics

• Future outlook

• Density

D

L1 L2 L3

Land Quantity

Price

P3

P2

P1

S

Increasing population leads to

1) increasing price and

2) increasing land use

assuming no change in supply curve

10

World Population World Population

Source: http://one-simple-idea.com/Environment1.htm

World Population World Population

Year Population Change

1 AD 200 million

1650 500 million

1804 1 billion Doubled in 313 years

1927 2 billion Doubled in 118 years

1960 3 billion Increased by 1 billion in

38 years

1999 6 billion Doubled in 39 years

2013 7.1 billion

2015 7.2 billion Source U.S. Census Bureau

http://geography.about.com/od/obtainpopulationdata/a/worldpopulation.htm

http://en.wikipedia.org/wiki/File:World_population_distribution.svg

World Population Distribution World Population Distribution

11

http://www.nationsonline.org/oneworld/world_population.htm

World Population by Country World Population by Country

http://en.wikipedia.org/wiki/World_population

Urban Areas >= million

inhabitants in 2006

Urban Areas >= million

inhabitants in 2006

http://www.worldometers.info/world-population/#region

•

World Population Density

(people/km2)

World Population Density

(people/km2)

12

http://www.census.gov/population/international/data/idb/worldgrgraph.php

© 2009 Population Reference Bureau. All rights reserved. www.prb.org

Source: United Nations Population Division, World Population Prospects, The 2008 Revision.

World Population Growth Is Almost Entirely

Concentrated in the World's Poorer Countries.

World Population (in Billions): 1950-2050

13

Year Population Area (sq. km.)

Density

(persons per

sq. km.)

Acres /

person

1950 2,557,628,654 132,061,547 19.4 14.10

1960 3,042,828,380 132,061,547 23.0 12.16

1970 3,712,338,708 132,061,547 28.1 9.86

1980 4,450,929,761 132,061,547 33.7 8.20

1990 5,287,869,228 132,061,547 40.0 6.88

2000 6,090,319,399 132,061,547 46.1 5.98

2010 6,866,054,281 132,061,547 52.0 5.31

2020 7,631,071,690 132,061,547 57.8 4.80

2030 8,315,758,309 132,061,547 63.0 4.40

2040 8,896,844,579 132,061,547 67. 4.10

2050 9,376,416,975 132,061,547 71.0 3.80

Population Density Projections

• http://www.census.gov/population/international/data/idb/informationGateway.php

Global Hunger Index

• The 2013 (GHI) ranks 88 countries using

three indicators: – The proportion of people who are calorie

deficient, or undernourished

– The prevalence of underweight in children

under the age of five

– The under-five mortality rate

• Takes into account the special vulnerability

of children to nutritional deprivation

• Ratings from 0 (best) to 100 (worst).

Global Hunger Index

• Countries are rated from 0 (best) to 100

(worst).

• Overall GHI scores improved from 18.7 in

the 1990 to 15.2 in the 2008.

• Sub-Saharan Africa and South Asia have

the worst scores on the 2008 GHI.

Policy Research Institute, http://www.ifpri.org

14

2008 Global Hunger Index

GHI-Winners and Losers 1990 - 2008

Global Hunger Index http://www.ifpri.org/ghi/2013

Policy Research Institute, http://www.ifpri.org

15

U.S. Population

http://www.census.gov/popest/data/maps/11maps.html

U.S. Population

16

U.S. Population

U.S. Population

One birth every 8 seconds

One death every 12 seconds

One international migrant (net) every 40 seconds

Net gain of one person every 17 seconds

Components of Population Change

http://www.census.gov/popclock/embed.php?component=counter

State Population,

2013

Pop. per sq. mi.,

2013 2030 Poplation

California 38,332,521 246.1 46,444,861

Texas 26,448,193 101.2 33,317,744

New York 19,651,127 417.0 28,685,769

Florida 19,552,860 364.6 19,477,429

Illinois 12,882,135 232.0 13,432,892

Pennsylvania 12,773,801 285.5 12,768,184

Ohio 11,570,808 283.2 12,227,739

Georgia 9,992,167 173.7 10,712,397

Michigan 9,895,622 175.0 12,017,838

North Carolina 9,848,060 202.0 10,694,172

http://www.census.gov/popclock/#populous-counties

10 Most Populous States

17

Fastest Growing Cities 2010- 2011

http://www.census.gov/newsroom/releases/archives/population/cb12-117.html

Percent

Increase

2011 Total

Population

1. New Orleans 4.9 360,740

2. Round Rock,

Texas 4.8 104,664

3. Austin, Texas 3.8 820,611

4. Plano, Texas 3.8 269,776

5. McKinney, Texas 3.8 136,067

6. Frisco, Texas 3.8 121,387

7. Denton, Texas 3.4 117,187

8. Denver 3.3 619,968

9. Cary, N.C. 3.2 139,633

10. Raleigh, N.C. 3.1 416,468

11. Alexandria, Va. 3.1 144,301

12. Tampa, Fla. 3.1 346,037

13. McAllen, Texas 3.0 133,742

14. Carrollton, Texas 3.0 122,640

15. Atlanta 3.0 432,427

http://www.census.gov/newsroom/releases/archives/population/cb11-215.html

The 10 Fastest Growing States from April

1, 2010, to July 1, 2011

Percent

change

1. District of Columbia 2.70

2. Texas 2.10

3. Utah 1.93

4. Alaska 1.76

5. Colorado 1.74

6. North Dakota 1.69

7. Washington 1.57

8. Arizona 1.42

9. Florida 1.36

10. Georgia 1.32

The 10 States with the Largest Numeric

Increase from April 1, 2010, to July 1, 2011

Numeric

change

1. Texas 529,000

2. California 438,000

3. Florida 256,000

4. Georgia 128,000

5. North Carolina 121,000

6. Washington 105,000

7. Virginia 96,000

8. Arizona 90,000

9. Colorado 88,000

10. New York 87,000

Fastest Growing States 2010- 2011

http://www.census.gov/dataviz/visualizations/051

U.S. Population Movement

18

Births Deaths

2015 321,363 2,471 0.77 1,677 4,290 2,613 794

2020 333,896 2,521 0.76 1,612 4,380 2,768 909

2025 346,407 2,478 0.72 1,453 4,413 2,959 1,024

2030 358,471 2,364 0.66 1,225 4,433 3,208 1,139

2035 369,662 2,159 0.59 1,002 4,505 3,503 1,156

2040 380,016 2,022 0.53 848 4,612 3,765 1,174

2045 389,934 1,969 0.51 778 4,729 3,951 1,191

2050 399,803 1,985 0.50 781 4,820 4,038 1,204

Vital eventsNet

international

migration1

Table 1. Projections of the Population and Components of Change for the United States: 2015 to 2060

Year PopulationNumeric

change

Percent

change

Natural

increase

http://www.census.gov/population/projections/data/national/2012/summarytables.html

U.S. Population Projections

thousands

29.2

7.6 9.5

42.9

45.8

0.0

5.0

10.0

15.0

20.0

25.0

30.0

35.0

40.0

45.0

50.0

United States Northeast Midwest South West

Interim Projections: Percent Change in Population by Region of the United States, 2000 to 2030

Source: U.S. Census Bureau, Population Division, Interim State Population Projections, 2005

Texas Population Projections

Low – zero migration

High – 2000-2010

migration rate

http://txsdc.utsa.edu/

19

Texas Population Projections

http://txsdc.utsa.edu/

Growth

rates vary

by year

and area

Changing Demographics

Aging Population

20

Changing Race Make-up

Changing Demographics Changing Demographics

Mean Commute travel

times

Year Minutes

1980 21.7

1990 22.4

2000 25.5

2009 25.1

Back to Demand Theory

• How does above fit into our simple

theoretical aggregated demand

– Changing demographic

• Aging – usually lower disposable income

• Work at home – lower travel expenses – increase

income to spend elsewhere

– Change in taste and preferences

• Change in indifference curve

• Only time will tell?

21

Changing Income and Utility Max

Land Units

B

un

dle

of

go

od

s

Increase in income

increase budget

constraint

Increase in budget

constraint move

equilibrium

Changing Income

Land Units

L

an

d P

rice

Increase in demand

D new

D original

World GDP – Increase - Projected

22

U.S. & Texas Income

Non Ag Land Resource Needs

• Increasing Population – mineral and energy

needs increasing

• Urbanization

• Increased incomes – increase demand for land

• Increased incomes – increase in recreational /

leisure activities

• All increasing demand for land

• Changing taste and preferences

Competition between Land Uses

• Highest and best use

• Conflicts of interest arise

– Many land uses are not compatible with each

other

– Owners have different objectives

– Conflicts of interest between owners and

society