Transcript Urban and Regional Economics

Land Rent and Urban
Land-Use Patterns
Land Rent vs Land Value
– flow versus stock
Value = PV(Rents, i)
V = R/i
We define land price to be land rent to
keep everything in flow terms
Example of Present Value
Calculation
Let Rent = $1,000/month
i = .10 per year
Value = 12*1000/.1 = $120,000
Corn Law Controversy
and Ricardo
Great Economist
Great Contribution: Resolving Corn Law
Debate
– were import restrictions or land rents causing
high corn prices
Key Concept: land rent as residual input
Assumptions
Three types of land that very in their
fertility or productivity
Competitive market for corn and land
Rising marginal costs of corn production
Fixed supplies of land
Analysis: Figures 7-1 and 7-2
Low Quality
High Quality
$
MC
Pc
RENT
ATC
Ch
Corn
Cl
Land Rent and Accessibility
Fixed prices
Shipped to CBD for export
t dollars per ton per mile
Competitive markets
All land equally fertile
Case I: Fixed Input Ratio
TC = t Q u
– TC = total transport costs
– t = transport cost per ton per mile
– Q = total output
– u = distance from farm to CBD
profit = PQ -C - TC - R
Case I: Continued
Competition requires zero profit
Solve Profits for R
R = PQ - C - t Q u
or, R = a0 - a1 u
THIS IS A BID RENT FUNCTION
Spreadsheet: ch7fig74.xls
CASE I: fixed input ratio
Case II: flexible input ratio
Multiple Land Uses
Consider a case in which we have two
fixed producers
Who will locate closest to the city
– Producer with the steepest gradient
Land is allocated so that he firm with the
most expensive transport costs is closest
to the city
Market rent is the outer envelope
Graph Market Rent Function
CHAPTER 8
Household vs Firm Location
Choices
We now turn to household choices
Key decision is where to live
Key assumptions
– Works in CBD and commutes to work
– fixed transportation costs
– fixed income (wages and hours worked)
Key Result
Locational equilibrium occurs where the
marginal costs of moving farther away just
equal the marginal costs
dph/du h = - t
move away until the marginal savings in
housing costs just equal the marginal cost
of moving farther from the CBD
Household Choices
utility is a function of housing
services (h) and nonhousing (x)
u = u(x, h)
y - tu = px x(u) + phh(u)
y = income; tu = transportation costs; px
and ph are the prices of nonhousing
and housing; x(u) and h(u) are the
amounts of nonhousing and housing
goods and services consumed at
Review of Consumer Choice
Maximize utility subject to the budget
constraint
MRS = marginal rate of substitution
between x and h, which can be written as:
-dU/dx/dU/dh = dh/dx
slope of budget line:- px/ph
dh/dx = - px/ph
Application to Residential
Location Choice
What else can we change besides x and
h?
LOCATION
This implies a new equilibrium condition in
addition to the standard one
Namely, d ph/du h = -t
Implications of Locational
Equilibrium Condition
What is slope of housing price function:
NEGATIVE
What is the impact of an increase in t on
locational equilibrium: Move closer
What is the impact of an increase in h on
u: move farther away
What is the size of the gradient if h is
fixed: the gradient (slope) of the housing
price function is constant
Production of Housing
and Land Prices
Firms build housing for households
They produce housing with a production
function that depends upon L and K
The mix of land and K will change as land
prices change (substitution)
Land price function is negatively sloped
but with a decreasing slope (absolute
value)
that is, the gradient decreases with u
Next Class
Ch. 8 Continued
Do Problems 1-3 at end of Chapters 7 and
8