Question

Housing Price and Land Bid-Rent Numbers
Consider a monocentric city where the cost of commuting is $40 per mile per month. A household located eight miles from the city center occupies a dwelling with 1,000 square feet at a monthly rent of $600. Nonland cost per dwelling is $250, and there are 10 houses per hectare.

a) The price of housing at a distance of eight miles is _____________ per square foot, computed as ......................

2. b) The bid rent for land at a distance of eight miles is ___________ per hectare, computed as ......................
3. c) Assume that the demand for housing is perfectly inelastic. The price of housing at a distance of five miles is ______________ per square foot, computed as ......................
4. d) Assume that housing firms do not engage in factor substitution. The bid rent for land at a distance of five miles is ______________ per hectare, computed as ..................
5. e) Suppose consumers engage in consumer substitution and firms engage in factor substitution. The bid rent for land at a distance of five miles would be [greater, less] than the number computed in part (d) because ...................

Answer 1

Answer: Cost of commuting is t = $40 per mile per month

A household located from the city center d = 8 miles

dwelling H = 1000 sq feet

Monthly rent R = $600

Nonland cost per dwelling = $250

Housing units per hectare = 10

a). The price of housing at a distance of eight miles is _____________ per square foot, computed as ......................

Price P(at 8 miles) = $600/1,000 = $0.60 per square foot

b). The bid rent for land at a distance of eight miles is ___________ per hectare, computed as ......................

The Bid Rent is R(8) = 10(600 - 250) = $3,500 per hectare

c). The demand for housing is perfectly inelastic. The price of housing at a distance of five miles is ______________ per square foot, computed as ......................

The slope of the housing price function is
p/d = - t/h = - 40/1,000 = -0.04.

P (5) = 0.60 + 5 * 0.04 = $0.80 per square foot.

d).  The bid rent for land at a distance of five miles is ______________ per hectare, computed as ..................

The total cost per unit is = $800 (0.80 x 1,000) per month

Non-land cost is $250 per month.

Therefore, bid rent is $550/unit/month ($800 - $250) or $5500 per hectare
(550 x 10).

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e). It will be greater than the number in part d, as the housing producers can produce the houses more cheaply and they can also substitute the non land inputs to land.