# LectureI - AEB 6145 Agricultural Finance Professor Charles...

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AEB 6145 Agricultural Finance Professor Charles B. Moss 1 Lecture I: Robinson Crusoe Economy and Investment I. Setup A. Robinson Crusoe, a Ph.D. in Agricultural Economics and survivor of AEB 6145, is stranded on a desert island after a shipwreck. He knows that this group of islands is surveyed every three years and was surveyed last year. Thus, he must survive two years. B. He has 1. 100 lbs of potatoes 2. Sufficient tools and arable land to plant the potatoes such that they yield future consumption of ( 29 1 2 2 2 10000 yx =- where x is current consumption. 3. The production possibilities frontier for Robinson are thus [ ] [ ] 2 2 1000 0 ; 0,100 , 0,200 4 y x xy = + ∈∈ 4. Robinson’s preferences can be represented as ( 29 . 6 .4 , U x y = II. True Robinson Crusoe or economy choice of investment and consumption. A. Without trade, Robinson chooses x and y to ( 29 . 6 , 2 2 ma x, ..10000 4 y y s tx = ≥+ Thus, ( 29 ( 29 2 . 6 . 42 2 2 10000 4 . . 6 20 . . 40 2 1000 00 4 y L x U L x xx U Ly yy x l l l l  = + --   = -= = = --= Taking the ratio of the first two first-order conditions yields

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AEB 6145 Agricultural Finance Professor Charles B. Moss 2 ( 29 ( 29 22 . 6. 2 . 4. 2 34 2 8 3 U x x U y y yx xy l l = = = = Substituting this result into the third first-order condition yields 2 2 18 1000 00 43 5 1000 3 6000 77.460 xx x x x  - -=   = = Using the result from the ratio of the first two first-order conditions ( 29 ( 29 ( 29 ( 29 . 6 .4 2 8 126.492 3 , 77.4 6 126.49 2 94.248 . 6, .004712 2 U xy Uxy x l == To derive the Marginal Rate of Substitution between x and y ( 29 ( 29 ( 29 ( 29 . . 2 . . 3 2 77.460 .4082 3126.492 U U yy MRS UU x x = = = - =- = - B. Robinson Crusoe and the Natives 1. Assume that Robinson finds natives on the neighboring island who also consume potatoes among other things. Robinson decides that he can trade with these natives, but living with them may result in him becoming the meat in the native’s meat and potato diet. The natives decide that they will buy or sell potatoes at the rate of .925925 x /1 y . Put another way, they will give one lb of potatoes today for 1.08 lbs of potatoes tomorrow.
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LectureI - AEB 6145 Agricultural Finance Professor Charles...

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