A farmer sets aside corn this year to use as seed. He finds that his next harvest q1 is related to the year's input of q0 in the following way: q1 = 2q0 - 0.001q0^2

Seed is the only resource that's scarce to him. He now has 1000 bushes and his utility function depends on the quantity of corns he consumes this year and next U = c0c1 where c0 is consumption this year and c1 is consumption next year. Answer the following questions, assume complete divisibility of land and corn. a. If there is no capital market how much should he consume this year and how much next year to maximize utility? What is his rate of time preference at the equilibrium point? What is the marginal rate of transformation of present into future corn at this point? b. If he can borrow or lend any amount at 5% per annum, how much corn should be devoted to next year's production? How much should he consume in each year?