Consider a monocentric city where the cost of commuting is $20 per mile per mont

Question

Consider a monocentric city where the cost of commuting is $20 per mile per month. A household located 5 miles from the city center lives in a 1,000 square foot house that costs it $500 per month. Non-land costs per house are $100 per month and there are 10 houses to the hectare.

1. What is the price per square foot of housing 5 miles from the center?

2. Suppose the demand for housing is perfectly inelastic. What is the price per square foot of housing 2 miles from the center?

3. Assume that housing developers do not engage in factor substitution. What is the residential bid rent for housing, per hectare, 2 miles from the center?

4. Now suppose housing demand was not perfectly inelastic (consumers do engage in consumer substitution), and housing developers did engage in factor substitution. Would the residential bid-rent 2 miles from the center be higher, lower, or the same than the amount you calculated in question 3? Why?

Explanation / Answer

1. $0.40 per sqaure foot

2.P(u) - Price per square foot of housing at location u Q - Square feet of housing K - Cost of non-land inputs per building R(u) - Price per acre of land at location u T - Acres of land

R(u)=(P(u)Q-K)/T

=0.1

3. Bid Rent for land can be determined by seeing how much revenue is “left over”. TR is $500 – non land costs is $100.  Thus Bid Rent is 500 - 100 = 400 per acre

4.Suppose consumers engage in consumer substitution and firms engage in factor substitution. The bid-rent for land at a distance of 2 miles would be [greater, less] than the number computed in part (d) because the price of housing would be higher (consumer substitution) and the land per dwelling would be lower (factor substitution). substituting non-land inputs for land as the price of land increases which means building progressively taller buildings as location approaches city center. The flexible firm (with factor substitution) is able to produce housing more cheaply than the inflexible firm since the #28: bidrent flexible firm uses less of the more expensive input at each location

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