Question

TSR Silding! 5. Consider a farmer who must sale an extensive pasture of 100 acres (the "Owner"). The pasture is currently covered by cedars and it is impossible to be sure of the productivity. The soil of the pasture is likely poor quality and can only support 10 cows, making it worth $50,000. But there is a 20 percent chance that it is high quality, meaning it can support 40 cows with a value of $200,000 a. After the pasture is purchased the Buyer can determine the productivity of the soil by clearing cedars, which he must do to use it in any event. 1. At what price will the owner sell the land? ii. Describe the returns to the owner and the buyer under each state of nature, and the expected returns. Also describe the expected returns to society. HINT: USE A TABLE iii. Should Courts enforce the contract if it turns out the land is high productivity? b. Suppose that there is a technology available to the Buyer for $25000 which can determine the productivity of the soil before buying. i. At what price will the owner sell the land? ii. Describe the returns to the owner and the buyer under each state of nature, and the expected returns. Also describe the expected returns to society. HINT: USE A TABLE ili. Should Courts enforce the contract if it turns out the land is high productivity? c. Now suppose that if the buyer discovers the value of the land by soil testing, he can build greenhouses for growing organic vegetables, making the land worth $300,000 1. How does this affect the expected returns to society? ii. Should Courts enforce the contract if it turns out the land is high productivity?

Answer 1

a)

i)

Given,

Value of low productivity soil = $50000

Chance of low productivity soil = 80%

Value of high productivity soil = $200000

Chance of high productivity soil = 20%

Hence, the value of soil = 0.8* 50000 + 0.2*200000 = 80000

Thus, the seller should sell the soil at $80000

ii)

Now,

the return of seller in low productivity soil condition = (80000 - 50000) / 50000 =  60%

the return of seller in high productivity soil condition = (80000 - 200000) / 200000 = -60%

Hence expected return for seller = 0.8*60% + 0.2*(-60%) = 36%

similarly for buyer

return in low productivity = (50000-80000) / 80000 = -37.5%

return in high productivity = (200000 - 80000) / 80000 = 150%

Thus,

expected return = 0.8*(-37.5%) + 0.2* (150%) =0%

iii)

The court should not enforce a contract after it is found that the soil is of high productivity.

b)

Since selller doesn't have any such device which can help it in finding what type of soil is there. Thus, he should sell at $80000 only.

For the r, he should purchase the soil at $80000 if he found it is of low productivity. so he will incur a loss of only $25000 as he won't purchase a low productivity soil. whereas, in earlier case his profit loss was -$30000