solpr6ec70204

# solpr6ec70204 - Solutions to Problem Set 6 Econ 702 Spring...

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Unformatted text preview: Solutions to Problem Set 6 Econ 702, Spring 2004 Prepared by Ahu Gemici March 20, 2004 Problem 1 (ADE in a stochastic RA-NGM) In the beginning of the semester, we defined certain objects in the deterministic AD environment, i.e. the com- modity space, consumption possibility set, production possibility set, etc. Then we wrote the growth model in the AD language with the purpose of applying the welfare theorems to the growth model. Now we want to do the same for the stochastic growth model. 1. Define the consumption possibility set, X , for the stochastic growth model. 2. Define the production possibility set, Y , for the stochastic growth model. Solution: Remark 1 Note that before, in the deterministic case, we only had 3 commodi- ties for each period. Now we have 3 commodities for each date event ( h t ). Also note that now the constraints need to hold for all periods and all histories. X , Consumption Possibility Set: X = { x ∈ L : ∃{ c t ( h t ) , k t +1 ( h t ) } ∞ t =0 ≥ such that (1) c t ( h t ) + k t +1 ( h t ) = x 1 t ( h t ) + (1- δ ) k t ( h t- 1 ) ∀ t, ∀ h t x 2 t ( h t ) ∈ [- k t ( h t ) , 0] ∀ t, ∀ h t x 3 t ( h t ) ∈ [- 1 , 0] ∀ t, ∀ h t k , z given } Y , Production Possibility Set: Y t = { ( y 1 t ( h t ) , y 2 t ( h t ) , y 3 t ( h t )) : y 1 t ( h t ) ≤ f (- y 2 t ( h t ) ,- y 3 t ( h t )) ∀ t, ∀ h t y 1 t ( h t ) ≥ ∀ t, ∀ h t y 2 t ( h t ) , y 3 t ( h t ) ≤ ∀ t, ∀ h t } 1 Problem 2 Consider an economy with two periods. There are two states ofConsider an economy with two periods....
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solpr6ec70204 - Solutions to Problem Set 6 Econ 702 Spring...

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