Consider a country where in the formal banking sector the cost of money is 5% (business people can borrow from commercial banks at that rate). In remote rural areas, however, small farmers have no access to formal banks and can only borrow from local landlords at the higher interest rate of i = 20%. A small farmer can use borrowed funds (L) as working capital to pay for inputs and grow a crop. The size of the crop increases with the amount of working capital (size of the loan) according to the production function qSR = L0.5 where L is the size of the loan and q is the size of the crop in bushels.

1. In a diagram measuring loan size (L) along the horizontal axis and the size of the crop (q) along the vertical axis, draw the farmer's short run production function. Are we assuming diminishing marginal returns to working capital? Do you think this is a reasonable assumption?

Since the local landlord charges a net interest of 20%, the opportunity cost of borrowing money is (1+i) = 1+20% = 1.2 ((1+i) is the analog of the wage rate w we used in class). The farmer can sell its crop at the market price of p = 24 per bushel.

2. Write the expression for the farmer's Profit as a function of the money he borrows (L)