L1: Capital Market, Consumption and Investments 1

Capital Market, Consumption and Investment (L1)

• Consumption and investment without capital market• Consumption and investment with capital market• Fisher separation theorem• Breaking down the separation : transaction costs• Breaking down the separation: agency problem• Application of Fisher Separation theorem: capital budgeting

and shareholder value maximization

– Materials from Chapters 1&2, CWS

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Consumption PlaneHow individuals make choices among consumption bundles

C0

C1

Indifference curve: time preference of consumption in a consumption

The slope of the tangent line MRS

U

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Investment Schedule and Production Opportunity Set

A

B

X

C0

C1Marginal rate of return

Total Investments

X

B

A

ri

I0

y0

y1

Investment schedule and production opportunity set are equivalent

The slope for the tangent line of production opportunity set in B is –(1+r i) = marginal rate of transformation (MRT)

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Equilibrium in a Robinson Crusoe World

MRS=MRT = -(1+ri)

C0

C1

Individual 2

Individual 1

Individual 1 consumes more than individual 2 in period 0

No capital market, thus there is no exchange.

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Optimal Consumption in the Presence of Capital Market

r

CC

r

yyWtosubject

CCEUCC

11

),(max

*1*

01

00

21, 21

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Capital Market Line

A

W0

U1

U2

B

W1

With capital market, an agent can move from A to B, reaching a higher utility.

On the capital market line, one’s wealth does not change. But consumption differs.

The slope of the capital market line is –(1+r).

C0

C1

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Slope of Capital Market Line

r

CCW

1

*1*

00

We have: *00

*1 )1()1( CrrWC

And since W0(1+r)=W1. We thus have: *

01*1 )1( CrWC

W1 is the intercept; -(1+r) is the slope of the capital market line. Under what condition, the slope would increase?

What Constitutes Consumptions?

GDP= C + I + G + NX– C = consumption– I = investment– G = government purchases of goods and services– NX = net exports of goods and services

http://research.stlouisfed.org/fred2/categories/18

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Consumption

• Spending by domestic households on final goods and services, accounting for about 2/2 of GDP in the United States, including:– Consumer durables– Nondurable goods– services

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Investment

• Includes both spending for new capital goods, called fixed investment, and increases in firms’ inventory holdings, called inventory investment.

• Fixed investment includes:– business fixed investment– residential investment

L1: Capital Market, Consumption and Investments 10

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Joint effect of capital market and production/investment

• See figure 1.8• Two steps of the decision process related to

production opportunity and capital market exchange opportunity:– Choose the optimal production decision by taking on

projects until the marginal rate of return on investment equals the objective market rate -- investment

– Choose the optimal consumption pattern by borrowing or lending along the capital market line equate your subjective time preference with the market rate of return -- consumption

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Fisher Separation Theorem• Given perfect and complete markets, the production decision is governed

solely by an objective market criterion without regard to individuals’ subjective preferences that enter into their consumption decisions.

• See figure 1.9• In equilibrium, the marginal rate of substitution for all investors is equal to

the market rate of interest, and this in turn is equal to the marginal rate of transformation for productive investment.

• MRSi=MRSj=-(1+r)=MRT• That is, the marginal return on investment (MRT, marginal rate of

transformation) equals market-determined opportunity cost of capital (r)• Irving Fisher's theory of capital and investment was introduced in his

Nature of Capital and Income (1906) and Rate of Interest (1907), although it has its clearest and most famous exposition in his Theory of Interest (1930).

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Fisher Separation Theorem

C0

C1

Individual 1

Individual 2

P1

P0 W0

W1

Individuals choose their respectful consumptions, where their consumptions can be delivered by productive investments (P0, P1).

This is what we mean by separation: a separation of investment and consumption.

Implications

• All the consumption decisions are made along the capital market line.

• The slope of the capital market line is –(1+r), where r is the interest rate, not stock return.

• This is the case of consumption choices under certainty.

• What is missing here?

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Perfect Market

• Necessary conditions– Markets are frictionless

– Perfect competition in securities markets

– Markets are informationally efficient; that is, information is costless, and it is received simultaneously by all individuals

– All individuals are rational expected utility maximizers

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Complete Market

• When the number of unique linearly independent securities is equal to the total number of alternative future states of nature. The market is said to be complete.– Page 77, CWS– Details will be provided in the lectures related

Arrow-Debreu assets.

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Role of Capital Market – Reducing Transaction Costs

• Trading is costly – thus the market is not perfect• Having marketplaces helps to reduce transaction costs

– page 12, CWS.• Thus financial market has its role only when

– Trading costs are non-trival• Demsetz (1968); Kyle (1985); Glosten and Milgrom (1985);

Grossman and Miller (1988)

– Information asymmetry• Akerlof (1970); Spence (1973); Myers and Majluf (1984)

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Breakdown of the Separation: Transaction Costs

• See figure 1.12• Lending rate is lower than borrowing rate• Then the optimal consumption decision depends on

individuals’ subjective utility functions

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Breakdown of the Separation: Agency Problem

• Given Fisher separation theorem, the investment decision and consumption decision can be separated.

• In other words, shareholders can delegate managers to perform the investment function

• This separation leads to separation of ownership and control.

• Monitoring costs and compensation issue arise, which lead to the large literature on corporate governance and corporate finance.– Berle and Means (1932) and Jensen and Meckling (1976)

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Value to Shareholders• Present value of shareholders’ wealth can be

expressed as:

• Note: the above expression involves both capital gains and dividends (see page 20) – all go to shareholders

• Economic definition versus accounting definition of profit

10 )1(t

ts

t

k

DivS

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Capital Budgeting Techniques

• Maximizing shareholders’ wealth is equivalent to maximizing the discounted cash provided by investment projects.

• Decision rules: payback period, …• What’s the point?

– Utility function collapses to the value function– Given the Fisher separation theorem, maximizing

shareholders’ wealth will lead to a social optimal at the presence of the capital.

• In reality, firms have the option to undo their decisions– Thus the decision rule could be altered.

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Exercises

• CWS, 1.5&1.6

• What is meant by “separation” in the Fisher’s separation theorem?