Question

2. (10) Inefficiency and Homesteading         

This question illustrates Andersen and Hill's argument about the social cost of homesteading (ps. 120-1 in the book). The Homestead Act was introduced in 1862, and granted a quarter section (a quarter of a square mile or 160 acres) of land free to any household that would farm the land.

            The table below reports on the income a household would receive at the end of year t from working throughout the year in the nearest city, the corresponding number for working throughout the year on a homestead, and the market price of the quarter section at the beginning of the year. To simplify the arithmetic, assume that the discount rate is 0. Farming income is increasing over time due to cheaper rail transportation of crops to the city.

           

	1880	1881	1882	1883	1884
Urban income	10	10	10	10	10
Farming income	- 12	- 4.5	3	10.5	18
Homestead land value/ market price	-22	0	14.5	21.5	21

a) (3)   Land value equals the present value of the economic income from the property, and that the economic income from farming equals the accounting income from farming minus the opportunity cost of the farmer's time. Applying this principle, explain how the land values at the beginning of 1881 is derived from the given urban and farming incomes the land value at the beginning of 1882.

b) (2) What is the efficient year for the household to start homesteading?

c) (2)   What year would the household choose to start homesteading?

d) (3)   What is the efficiency loss from the requirement that the household start farming as soon as it acquires the homestead?

Answer 1

SOLUTION:

In this present case ,Urban income not relevent for thefollowing decission making, since there is no variance in Urbanincome, 10 for throughout the period 1 to 5. Therefor household canstart homestead based on Farming income.

a) Homestead land value in years 1 to 4 would be samevalue in year 5 ( ignore the time value of money, since discountrate is r=0)

b) Efficient year to start homesteading is Year 3(1882).Since in year 3 it starts earning positive Farmingincome.

c) Household will choose year 1883 to start homesteadingsince Farming income is more than Urban income in year1883.

d) Once household starts Farming, they will loose orsacrifice the Urban income. Hence efficiency loss will be the Urbanincome that is 10.