# 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.

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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 \$ Corn Pc ATC Ch Cl Low Quality High Quality RENT MC

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 = p x x(u) + p h h(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 location u.

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:- p x /p h dh/dx = - p x /p h

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 p h /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

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