# 13 - Time - Interpretation of Commodity Space A point is a...

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1 Interpretation of Commodity Space ± A point is a list of the amounts of the same good (“corn”) in two separate periods. ± Consumption opportunities with no trade or production 1 st period corn 2 nd period corn ω ω 1 st period corn 2 nd period corn 1 1+r Lending 1 st period corn Borrowing 1 st period corn Interpretation of Commodity Space If PV of endowment larger, budget set is larger. + = + = + = + 1 2 1 2 int 2 2 1 2 1 int 1 2 2 1 1 2 2 1 1 ω ) p p ( ω C ω ) p p ( ω C ω p ω p C p C p + + = + + = + = + = Endowment of Value d Capitalize ω r) (1 ω C Endowment of Value Present r) (1 ω ω C Factor tion Capitaliza r) (1 ) p p ( Factor Discount r) (1 1 ) p p ( 1 2 int 2 2 1 int 1 2 1 1 2 A Three Period Generalization ± Maximize the right-hand side of the budget constraint: p 1 C 1 + p 2 C 2 + p 3 C 3 = p 1 ω 1 + p 2 ω 2 + p 3 ω 3 maximize ω 1 + (p 2 /p 1 ) ω 2 + (p 3 /p 1 ) ω 3 ± Define p 2 /p 1 = 1 / (1+r 1,2 ) and p 3 /p 2 = 1 / (1+r 2,3 ) where r 1,2 and r 2,3 are the 1-year rates of interest between the adjacent years.

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13 - Time - Interpretation of Commodity Space A point is a...

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