{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

lecture7_467 - Monetary Macroeconomics Lecture 7 Capital...

Info icon This preview shows pages 1–11. Sign up to view the full content.

View Full Document Right Arrow Icon
Monetary Macroeconomics Lecture 7: Capital and Financial Intermediation Dr. Pınar Ye¸ sin December 9, 2005 University of Zurich 1
Image of page 1

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
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
Image of page 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
Image of page 3

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
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 0 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
Image of page 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
Image of page 5

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
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 0 ( 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
Image of page 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
Image of page 7

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Properties of the Production Function In general f 0 ( 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
Image of page 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. There is one type of consumption good that everybody likes to consume when young and when old. 9
Image of page 9

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
There are two types of people: borrowers and lenders. Borrowers have no endowment when young and y units of the consumption good when old.
Image of page 10
Image of page 11
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern