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IH1_Asset_RQ

# IH1_Asset_RQ - Review Questions Asset pricing(deterministic...

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Review Questions: Asset pricing (deterministic) Prof. Lutz Hendricks. August 6, 2009 1 Deterministic Fruit Tree Prices of identical, in²nitely lived households. Each receives an endowment of e t in each period. In addition, each household owns one tree at the beginning of time (date 1) which yields d t units of the consumption good in each period. Goods cannot be stored, but trees live forever. Trees can be bought or sold at a price of p t , which is of course endogenous. The number of trees in the economy cannot be altered; it is always 1 per household. Hence, the household solves max X 1 t =1 t u ( c t ) subject to p t k t +1 = k t ( d t + p t ) + e t c t with k 1 = 1 . In the budget constraint, the household receives as income the endowment e t and capital income proportional to the number of trees owned ( k t ) . This is spent on consumption ct and the purchase of new trees ( k t +1 ) . (a) State the household problem as a Dynamic Program. (b) State the conditions that de²ne a solution to the household problem. (c) De²ne a competitive equilibrium. (d) Assume that e t and d t are constant over time. Derive the steady state price of a tree ( p ) and the steady state rate of return of holding a tree. 1.1 Answer: Deterministic Fruit Tree Prices (a) Bellman equation V ( k ) = max u ( e + k ( d + p ) pk 0 ) + ( k 0 ) (b) A solution consists of sequences ( c t ;k t ) that satisfy the budget constraint and the Euler equation u 0 ( c ) = &u 0 ( c 0 )( d 0 + p 0 ) =p (c) A CE consists of sequences ( c t ;k t ;p t ) that satisfy the 2 household optimality conditions and

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IH1_Asset_RQ - Review Questions Asset pricing(deterministic...

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