Question

Potato Farming on Homogeneous Land 1 Suppose there is a landowner in a small isolated village that posssses 1,000 acres of fertile land that is ideal for growing potatoes. To grow potatoes, the landowner needs to employ labor (he is too lazy to work himself). Assume that potatoes are sold at a per pound price of P 1, and that the costs associated to labor employed is C(n) 2n where n is the number of worker employed; hence the wage payed to each worker is equal to 2. The quantity of potatoes (in pounds) produced on his land is given by: (n) 50n2 (f) Would the village be better off if the land was under open access and the villagers did not have to purchase the food from the landowner (think in terms of quantities of potatoes, and in terms of total rent)? Find the number of people that would be working on the land under open accesS n , and the amount of potatoes produced on the land if it was under open access (QOA). [0.5 point]

Answer 1

F)

Under open access equilibrium, Average Revenue (AR) = wage

As TR = P* Q = 50n - n^{​​​​​​2}

Thus AR = TR/n = 50-n

at equilibrium, 50-n = 2

n* = 48.answer

now Q* = 50*48-48² = 96 answer