Download AGEC 603 Individual Demand Marginal Utility

AGEC 603
Derived Demand for Land
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
• 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
1
Indifference / Isoutility Curves
Bundle of goods
Negative slope
Nonintersecting
Everywhere dense
Convex to the origin
B1
B2
L1
L2
Land units
Consuming B1L1 provides the same utility
as consuming B2L2
Bundles of goods
1 2 3 4 5 6 7 8
Indifference Curves
Which bundle would you
prefer … bundle M or
bundle B?
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.
M
B
1
2
3 4 5 6
Land Units
7
8
Indifference Curves
Bundle of goods
1 2 3 4 5 6 7 8
Which bundle would you
prefer more…bundle C or
bundle N?
C
1
2
3
N
4 5 6 7
Land Units
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!
8
2
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
constant
 bundle
 land

with utility
• Notice - rise over run = the slope for a specific segment for a
nonlinear curves
Marginal Rate of Substitution
Bundle of goods
3 4 5 6 7 8
-1
• MRSland for bundle
going from 2 to 3
land units
 bundle _ 1

 1
 land
1
1 2

1
2
3
4
5
6
7
8
1
Land Units
This means the consumer
is willing to give up 1
bundle unit in exchange
for one land unit!
Marginal Rate of Substitution
Bundle of goods
3 4 5 6 7 8
1
• MRSbundle for land
going from 2 to 3
bundle units
 bundle 1

 -0.5
 land
-2
1 2

1
2
3
4
5
6
-2
Land Units
7
8
This means the consumer
is willing to give up 2 land
units for one additional
unit of bundle of goods!
3
Marginal Rate of Substitution
MRS 
MU land
 bundle

 land
MU bundle
• Why?
– Utility must be constant
– What you give up with one, you must gain with the
other!
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
Bundle of goods
1 2 3 4 5 6 7 8
Income = $200
Prices = $40 / unit bundle and $20 / unit land
Apply all income to bundle
Budget Constraint
1
2
3
4
5 6
Land
7
8 9
Apply all income to land
10 11
4
Bundle Price Decreases by 1/2
Bundle of goods
4 5 6 7 8 9 10
Bundle price decreases by 1/2
Original price budget
constraint
After price change budget
constraint
1 2 3
Apply all income to land
1
2
3
4
5 6
Land
7
8 9
10 11
Bundle Price Increases by 2
Bundle of goods
4 5 6 7 8 9 10
Original price budget
constraint
Bundle price decreases by
1/2 budget constraint
1 2 3
Bundle price doubles budget
constraint
1
2
3
4
5 6
Land
7
8 9
10 11
Original price budget
constraint
Land price doubles
Land price decreases by 1/2
1 2 3
Bundle of goods
4 5 6 7 8 9 10
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
5
Steaks (lbs) consumed per week
1 2 3 4 5 6 7 8
Income Changes
Original Budget
Line
Budget Line at increased
income
Budget Line
at ½ income
Note: parallel shifts
1
2 3 4 5 6 7 8 9 10 11
Dozen corn ears consumed per week
Objective - Maximize Utility
Bundle of goods
3 4 5 6 7 8
Indifference Curve – below budget constraint
Can increase utility by moving outward
Not Optimal
1 2
Point Indifference Curve is Tangent
to Budget Constraint
Feasible – spends all budget
Maximizes Utility – highest curve obtainable
1
2
3
4
Indifference Curves and
points above the budget
Constraint exceeds your
budget - not feasible
5 6 7 8 9 10 11
Land Units
Slope Budget Constraint
Using x and y intercept points to calculate slope
land = 0, bundle = 5 and land = 10 and bundle = 0
Bundle of good
3 4 5 6 7 8
Slope = rise / run = (5-0)/(0-10) = -0.5
These points obtained
Income / price of bundle = 5 and
Income / price of land = 10
I
I
 0)
Pbunlde
Pbundle
P

  land
I
I
Pbundle
(0 
)
Pland
Pland
8 9 10 11
1 2
(
1
2
3
4
5 6 7
Land Units
6
Tangency Conditions
• Slope of indifference curve = slope of budget constraint
• Slope of indifference curve = MRS = - MUland / MUbundle
• Slope of budget constraint = -Pland / Pbundle
• Therefore,
MRS  
MU land
P
  land
MU bundle
Pbundle
MU land MU bundle

Pland
Pbundle
Consumer Equilibrium
• Point where utility is maximized subject to the
budget constraint occurs at
MUland
Pland
=
MUbundle
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.
Individual Demand Curve
Bundle of goods
3 4 5 6 7 8
Original Price = $20 / unit
Consumption bundle
2.5 bundle units and
5 units land
1 2
What if price decreases to $15?
What happens to budget constraint?
1
2
3
4
5 6 7
Land units
8 9 10 11
7
Bundle of goods
3 4 5 6 7 8 9 10 11
Land Price Decreases
New x-intercept
New equilibrium
Same Why
1 2
= 2.75 bundle and 6 land
Why an increase in bundle
and increase in land?
1
2
3
4
5 6 7
Land Units
8 9 10 11 12 13 14
Land Price Increases
Bundle of goods
3 4 5 6 7 8 9 10 11
New y-intercept same
Why?
New equilibrium
1 2
= 3.125 bundle and 1.5 land
Why an decrease in land
and increase in bundle?
1
2
3
4
5 6 7
Land Units
8 9 10 11 12 13 14
Individual Demand Curve - Land
Demand Schedule
Price
Quantity
Pincrease
1.5
Po
5
Pdecrease
6
8
Market Demand Curve - Land
+
=
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
• Population one of the most important factors in
determining demand for land
• Trends
Price
• Changing characteristics
• Future outlook
P3
• Density
S
P2
Increasing population leads to
1) increasing price and
2) increasing land use
assuming no change in supply curve
P1
D
L1 L2 L3
Land Quantity
9
World Population
Source: http://one-simple-idea.com/Environment1.htm
World Population
Year
Population
1 AD
200 million
Change
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
World Population Distribution
http://en.wikipedia.org/wiki/File:World_population_distribution.svg
10
World Population by Country
http://www.nationsonline.org/oneworld/world_population.htm
Urban Areas >= million
inhabitants in 2006
http://en.wikipedia.org/wiki/World_population
World Population Density
(people/km2)
•
http://www.worldometers.info/world-population/#region
11
http://www.census.gov/population/international/data/idb/worldgrgraph.php
World Population Growth Is Almost Entirely
Concentrated in the World's Poorer Countries.
World Population (in Billions): 1950-2050
Source: United Nations Population Division, World Population Prospects, The 2008 Revision.
© 2009 Population Reference Bureau. All rights reserved. www.prb.org
12
Population Density Projections
•
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
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
13
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
14
U.S. Population
http://www.census.gov/popest/data/maps/11maps.html
U.S. Population
15
U.S. Population
U.S. Population
Components of Population Change
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
http://www.census.gov/popclock/embed.php?component=counter
10 Most Populous States
Population, Pop. per sq. mi.,
2013
2013
California
38,332,521
246.1
Texas
26,448,193
101.2
New York
19,651,127
417.0
Florida
19,552,860
364.6
Illinois
12,882,135
232.0
Pennsylvania
12,773,801
285.5
Ohio
11,570,808
283.2
Georgia
9,992,167
173.7
Michigan
9,895,622
175.0
North Carolina 9,848,060
202.0
State
2030 Poplation
46,444,861
33,317,744
28,685,769
19,477,429
13,432,892
12,768,184
12,227,739
10,712,397
12,017,838
10,694,172
http://www.census.gov/popclock/#populous-counties
16
Fastest Growing Cities 2010- 2011
Percent
Increase
New Orleans
4.9
Round Rock,
2.
4.8
Texas
3.
Austin, Texas
3.8
4.
Plano, Texas
3.8
5.
McKinney, Texas
3.8
6.
Frisco, Texas
3.8
7.
Denton, Texas
3.4
8.
Denver
3.3
9.
Cary, N.C.
3.2
10. Raleigh, N.C.
3.1
11. Alexandria, Va.
3.1
12. Tampa, Fla.
3.1
13. McAllen, Texas
3.0
14. Carrollton, Texas
3.0
15. Atlanta
3.0
http://www.census.gov/newsroom/releases/archives/population/cb12-117.html
1.
2011 Total
Population
360,740
104,664
820,611
269,776
136,067
121,387
117,187
619,968
139,633
416,468
144,301
346,037
133,742
122,640
432,427
Fastest Growing States 2010- 2011
The 10 Fastest Growing States from April
1, 2010, to July 1, 2011
The 10 States with the Largest Numeric
Increase from April 1, 2010, to July 1, 2011
Percent
change
1.
District of Columbia
2.70
2.
Texas
3.
Utah
4.
Numeric
change
1.
Texas
529,000
2.10
2.
California
438,000
1.93
3.
Florida
256,000
Alaska
1.76
4.
Georgia
128,000
5.
Colorado
1.74
5.
North Carolina
121,000
6.
North Dakota
1.69
6.
Washington
105,000
7.
Washington
1.57
7.
Virginia
96,000
8.
Arizona
1.42
8.
Arizona
90,000
9.
Florida
1.36
9.
Colorado
88,000
10.
Georgia
1.32
10.
New York
87,000
http://www.census.gov/newsroom/releases/archives/population/cb11-215.html
U.S. Population Movement
http://www.census.gov/dataviz/visualizations/051
17
U.S. Population Projections
Table 1. Projections of the Population and Components of Change for the United States: 2015 to 2060
Year
Population
2015
2020
2025
2030
2035
2040
2045
2050
321,363
333,896
346,407
358,471
369,662
380,016
389,934
399,803
Numeric Percent Natural
change change increase
2,471
2,521
2,478
2,364
2,159
2,022
1,969
1,985
0.77
0.76
0.72
0.66
0.59
0.53
0.51
0.50
1,677
1,612
1,453
1,225
1,002
848
778
781
Vital events
Births
Deaths
4,290
4,380
4,413
4,433
4,505
4,612
4,729
4,820
Net
international
migration1
2,613
2,768
2,959
3,208
3,503
3,765
3,951
4,038
794
909
1,024
1,139
1,156
1,174
1,191
1,204
thousands
http://www.census.gov/population/projections/data/national/2012/summarytables.html
50.0
Interim Projections: Percent Change in Population by Region of
the United States, 2000 to 2030
45.8
42.9
45.0
40.0
35.0
30.0
29.2
25.0
20.0
15.0
10.0
7.6
9.5
5.0
0.0
United States
Northeast
Midwest
South
West
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/
18
Texas Population Projections
Growth
rates vary
by year
and area
http://txsdc.utsa.edu/
Changing Demographics
Aging Population
19
Changing Race Make-up
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?
20
Changing Income and Utility Max
Bundle of goods
Increase in budget
constraint move
equilibrium
Increase in income
increase budget
constraint
Land Units
Changing Income
Land Price
Increase in demand
D new
D original
Land Units
World GDP – Increase - Projected
21
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
22