Lecture7_467 - Monetary Macroeconomics Lecture 7 Capital and Financial Intermediation Dr Pınar Ye¸ sin December 9 2005 University of Zurich 1

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Unformatted text preview: Monetary Macroeconomics Lecture 7: Capital and Financial Intermediation Dr. Pınar Ye¸ sin December 9, 2005 University of Zurich 1 Including Other Assets in Our OLG Model Fiat money is not the only asset available in the real world for saving. Now we will ana- lyze how the presence of other assets affect the demand for money. 2 What is Capital? Capital is an asset that can be used for pro- duction, e.g. machinery, seeds, etc. We generally denote the production function with F ( K,L ) where K is capital, and L is labor. One usually assumes that each period capital depreciates at rate δ , such that 0 ≤ δ ≤ 1. So next period one still has (1- δ ) K capital left after receiving the output F ( K,L ). 3 The Model Consider our OLG model with 2 period lived agents. There is one country, and no fiat money! The young have y units of endowment and the old have no endowment. The initial old have k units of capital that can be used for production of the consump- tion good. Assume that when k units are invested in the production technology then f ( k ) units of the consumption good are pro- duced next period. We assume that capital depreciates completely after one period. Thus δ = 1. Consider stationary allocations. 4 Generation t ’s budget constraints: when young: c 1 + k ≤ y . when old: c 2 ≤ f ( k ). Hence the lifetime budget constraint is: c 2 ≤ f ( y- c 1 ) So his problem is max u ( c 1 ,c 2 ) s.t. c 2 ≤ f ( y- c 1 ) 5 The Lagrangian is L = u ( c 1 ,c 2 ) + λ [ f ( y- c 1 )- c 2 ] ∂ L ∂c 1 = ∂u ( c 1 ,c 2 ) ∂c 1 + λ [ f ( y- c 1 )(- 1)] = 0 ∂ L ∂c 2 = ∂u ( c 1 ,c 2 ) ∂c 2 + λ (- 1) = 0 ∂ L ∂λ = f ( y- c 1 )- c 2 = 0 So marginal utility of c 1 = λ marginal product marginal utility of c 2 = λ Thus- MRS = MP 6 At the solution ( c * 1 ,c * 2 ), the marginal rate of substitution between the two period con- sumptions is equal to the marginal product of capital. Note that there is nothing special about the OLG model here. Agents are not trading with each other. 7 Properties of the Production Function In general f ( k ) > 0 and f 00 ( k ) < 0, so that we have diminishing marginal product of cap- ital. That is the added output from an extra unit of capital gets smaller as capital increases. 8 A Model of Private Debt Here we will find conditions so that more than one asset can exist in the economy. Consider an OLG model with 2-period lived consumers. There is no fiat money in the economy. Assume first that there is no capital either....
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This note was uploaded on 06/16/2008 for the course ECON 131 taught by Professor Fasd during the Spring '08 term at Boston Conservatory.

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Lecture7_467 - Monetary Macroeconomics Lecture 7 Capital and Financial Intermediation Dr Pınar Ye¸ sin December 9 2005 University of Zurich 1

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