1

Determinants of the Level of Real Interest Rates

Societal PreferencesSocietal Preferences» The more present oriented are societal

preferences, the higher the market r– Shifts borrowing curve out

Societal Endowments» The more present oriented are societal

endowments the lower the market r

ECON 422:Fisher 48© R.W.Parks/E. Zivot

endowments, the lower the market r– Shifts lending curve out

Productive Opportunities [see later]

II. Intertemporal Production (Real Investment) and

Exchange: OutlineExchange: Outline

A. Individual optimaB. The Fisher Separation TheoremC. Market equilibrium

ECON 422:Fisher 49© R.W.Parks/E. Zivot

C. Market equilibrium

2

An Intertemporal Production Function Shows the Relationship Between Inputs Today and

Outputs in the Future

IOutputOutput

Q0

Q1F(I)

Note: slope of F(I) is called the marginal

ECON 422:Fisher 50© R.W.Parks/E. Zivot

0 Io I1 Input

grate of transformation(MRT)

From Production Function to Fisher Diagram

Reverse the production function aroundReverse the production function around the vertical axisDrag the origin to the endowment point of the Fisher diagram

ECON 422:Fisher 51© R.W.Parks/E. Zivot

3

Production Function to Fisher Diagram

OutputOutput

Production Function Reversed

Inputs

Output

C1

0 0Inputs

ECON 422:Fisher 52© R.W.Parks/E. Zivot

0 Co

Endowment point

Consumer-Investor Optimum with No Borrowing or Lending

ECON 422:Fisher 53© R.W.Parks/E. Zivot

4

Optimal Real Investment with Borrowing and Lending Opportunities

ECON 422:Fisher 54© R.W.Parks/E. Zivot

Optimal Real Investment with Borrowing and Lending Opportunities

ECON 422:Fisher 55© R.W.Parks/E. Zivot

5

Optimal consumption and investment

ECON 422:Fisher 56© R.W.Parks/E. Zivot

The Fisher Separation Theorem

The consumer - investor’s two-fold problem ofThe consumer - investor s two-fold problem of determining the optimal level of investment and the optimal consumption stream can be separated into two steps:» First choose the investment level that

maximizes wealth. This choice does not

ECON 422:Fisher 57© R.W.Parks/E. Zivot

maximizes wealth. This choice does notdepend on preferences.

» Next determine the optimum consumption stream, based on the maximized wealth.

6

The Fisher Separation Theorem (continued)

The choice of optimal investment can beThe choice of optimal investment can be separated from the choice of optimal consumption. i.e it does not depend on investor preferences.A necessary condition for utility maximization is wealth maximization.

ECON 422:Fisher 58© R.W.Parks/E. Zivot

is wealth maximization.Note: The separation result depends on the existence of a perfect capital market. Investors can borrow or lend at the market rate r.

Optimal Investment and NPV

Optimal investment maximizes currentOptimal investment maximizes current wealthEquivalently, optimal investment maximizes Net Present Value (NPV)» NPV = PV of investment cash flows – initial

ECON 422:Fisher 59© R.W.Parks/E. Zivot

investment cost

7

Example: Fisher Separation

ECON 422:Fisher 60© R.W.Parks/E. Zivot

Example: Fisher Separation

ECON 422:Fisher 61© R.W.Parks/E. Zivot

8

Determinants of the Level of Real Interest Rates Revisited

Societal Preferences» The more present oriented are societal preferences, the» The more present oriented are societal preferences, the

higher the market r– Shifts Borrowing curve out

Societal Endowments» The more present oriented are societal endowments, the

lower the market rS f

ECON 422:Fisher 62© R.W.Parks/E. Zivot

– Shifts lending curve outProductive Opportunities» The more productive are the opportunities for converting

present into future resources through real investment (i.e. production), the higher the market r.