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14 - Time and Uncertainty

# 14 - Time and Uncertainty - Interpretation of Commodity...

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1 1 st period corn 2 nd period corn Interpretation of Commodity Space ω |slope| = 1+r ω * C I B S ± I i = B i + S i for every agent i. ± Two sources of investment financing: ± Own saving ± Borrowing from others. _ S = ω 1 -C 1 * Saving (Dis-saving if < 0) B = C 1 * - ω 1 * Borrowing (Lending if <0) I = ω 1 - ω 1 * Investment _ Definitions: Interpretation of Commodity Space ± What Can be Negative for an Individual? 1 st period corn 2 nd period corn i ω C * i ω * 1 i < 0 is possible: borrow to plant more than endowment C * 1 i < 0 is impossible i * i i ω - ω I = ω * i _ S = ω 1 1 * Saving (Dis-saving if < 0) B = C 1 * - ω 1 * Borrowing (Lending if <0) I = ω 1 - ω 1 * Investment _ Definitions: ± I i = B i + S i for every agent i.

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2 Maximizing Utility When Production and Trade are Possible: an Example = = = + = % 100 r C C U 100 ω ω 20 1 (40,20) ω 1/2 2 1/2 1 2 2 1 Givens: Example: Optimal Endowment = = + % 100 r 100 ω ω 20 1 2 2 1 Recall: Calculation ω * is on PPF so: 1/20 ( ω 1 * ) 2 + ω 2 * = 100 At ω * , |MRT| = 1+r so ω 1 * / 10 = 2 ⇒ω 1 * = 20 and ω 2 * = 80 Example: Optimal
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14 - Time and Uncertainty - Interpretation of Commodity...

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