Question

Consider a simple economy that has a fixed amount of land, and where the only use of land is for housing. It is assumed that housing units can be produced at constant marginal cost, and that these units can be stacked (by building upward). A given parcel could therefore support all the units of housing demanded in the community. Assume there are 10 parcels of land, each owned by a different individual.

a) What is the marginal productivity of land in the production of housing? Assuming there is competition in the supply of housing (among the owners of land), what is the competitive renatl payment to land?

b) If one person owned all the parcels, what is the rental payment to land?

c) In the case of several owners and competition in the supply of housing units, would a parcel of land sell for a positive price? Carefully explain your reasoning.

Answer 1

a) What is the marginal productivity of land in the production of housing? Assuming there is competition in the supply of housing (among the owners of land), what is the competitive renatl payment to land?

Marginal productivity of land in the production of housing units is the change in output of housing production resulting from employing one or more units of the parcel of land. Each 10 units of the parcel of land provides an additional marginal productivity of housing by one unit each in the long run.

There is a fixed stock of land L to be used for residential purpose. Assume the supply of housing is H. the production function for housing is given by P= H (K, L), where k represents physical unit of capital.

From the function P=H (K, L), increase in supply of housing H, will increase the rental payment P by the same unit given that K and L are held constant.

c) In the case of several owners and competition in the supply of housing units, would a parcel of land sell for a positive price? Carefully explain your reasoning.

Assume that the demand for housing and land are at a given income level and price in the market such that the capital to land ratio employed in production of housing is low compared to the cost of each parcel of land then each parcel of land will sell at a higher price in the market. This indicate a positive higher prices.