UNIVERSITY OF TORONTO
Joseph L. Rotman School of Management
PROBLEM SET #1
1. Suppose you own a farm that, if run efficiently, can produce corn according to the following “transformation” formula:
W1 = 400 I0
where I0 is the number of bushels of corn planted in date 0, and W1 is the number of bushels turned over to you in date 1, net after all payments to labor and other hired inputs.
Your utility function of consumption at date 0 and consumption at date 1 is: U (C0 , C1 ) = minimum(C0 , C1 )
(a) If 50,000 bushels of corn are planted, what will be the net output of corn at date 1? (b) If you set a target for output of 100,000 bushels, what is the minimum number of bushels that must be planted?
(c) Suppose capital markets do not exist, and you can neither borrow, lend, or store any corn at the beginning of date 0. If you have 22,500 bushels of corn at date 0, what will your production plan be? Your consumption plan? What will be the average rate of return on investment of corn? What will be the rate of return on the marginal investment?
(d) If 22,500 bushels are planted, what will be the average rate of return on the investment? What will be the rate of return on the marginal investment? (e) If a capital market exists, and the rate of interest is 33 31 %, what will be your optimal investment?
(f) If you have no corn at date 0, a capital market exists (33 13 % rate of interest), and you invest optimally, what is your equity in the venture? What will be your optimal consumption plan? Outline your sources and uses of funds for date 0 and date 1. (g) Will you loan your farm for a period for 23,100 bushels of corn? Why? If you have no corn at date 0, and you decide to loan the farm, what will be your consumption plan?
2. Your life span is two periods. You are endowed with $500 today. You √have a production
technology which can transform an investment of $I today into $40 I next year. Also, you can borrow at 33 31 % per annum and lend at...
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