Question

Housing Prices and Land Prices

A household located x = 10 km from the city center occupies a pays an annual rent of $9,000 for a standard dwelling. The annual non-land cost per dwelling is $5,000, and there are 8 dwellings per hectare. The annual interest rate is 5 percent.

1. At x = 10, the willingness to pay for land is $[____] per hectare per year and the market value (purchase price) of land is $[____] per hectare.

2. Suppose we shift attention to x = 11. How would the calculations change? For what variables would we use (i) a larger value, (ii) a smaller value, or (iii) the same value?

Answer 1

Answer:

a) At x=10, annual rent - non land cost per dwelling = 9000-5000 = $4000.

Per hectare annual rent = 9000*8 = $72,000

Per hectare non land cost = 5000*8 = $40,000

A person would be ready to pay the differential amount of revenue and cost per hectare per year.

So, the willingness to pay for land is $32,000 (72000-40000) per hectare per year.

Assuming the land would earn $32,000 every year, we can calculate the market value by taking into account the interest rate and calculating present value. Present value of $32,000 per year perpetuity earning at r=5%

PV = Earnings per year / r = 32000/0.05 = $640,000

So, land is valued at $640,000 per hectare.

b) If we increase distance from city center, we would take both annual rent per dwelling and non land cost per dwelling to be a smaller amount because emperically as distance from city increases, prices get lower. We would also expect a lower valuation of the land. But the annual interest rate and number of dwellings per hectare would be the same.