Question

consider a developer that has 96,000 square ft of vacant land ready for building houses in a neighborhood that is desirable because of its superior schools. There are two types of households: lower income (L) and higher-income (H). Each type L household is willing to pay $250,000 to live in the neighborhood, and each H is willing to pay $500,000. The preferred lot size is 6,000 square feet for type L, and 16,000 square feet for type H.

a. What is the willingness to pay per square feet for each household type?

b. If there are no restrictions on lot sizes, to which type of household will the developer want to sell the vacant land?

c. Suppose the existing neighbors are considering whether to set a minimum lot size with the goal of excluding the lower-income households. How big would the minimum lot size have to be for the willingness to pay per square feet for type L to be the same as the willingness to pay per square feet for type H? Show your work.

Can anyone help to solve these questions, a to c? on (a), I got 31.25 for type H and 41.67 for type L. Are these correct? If not, I would like to see how to answer it.

Answer 1

Answer a

Preferred Size for L Household is 6000 sqft with willingness to pay $250000. Hence Willingness to pay per sq ft for L Household is 250000/6000 = $41.67

Preferred Size for H Household is 16000 sqft with willingness to pay $500000. Hence Willingness to pay per sq ft for H household is 500000/16000 = $31.25

Hence you have calculated it correctly.

Answer b

Since L type Household is paying more per Sqft Developer would sell all lots to L Household

Answer c

We need to calculate that L Household is willing to pay how much for lot with respect to H Household, hence it will be given by, L Household Willingness to pay/ H Household willingness to pay = 250000/500000 = 0.5. Hence L household willingness to pay is half of H Household willingness to pay. Hence the L Household should get half of lot size H Household is getting to make the Willingness to pay per sq ft equal for H & L Households i.e 16000 * 0.5 = 8000 sq ft

Hence the lot size shall be 8000 sq ft.