# Lecture 4 The Micro-foundations of the Demand for Money.

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Lecture 4 The Micro-foundations of the Demand for Money

Keynes Demand for Money Sound micro-foundations on the demand for money based on risk and return Extension of risk-return analysis to a multi- asset framework

The Keynesian Demand for Money Demand for money = demand for active balances + demand for idle balances The Motives approach - 3 motives 1) Transactions 2) Precautionary 3) Speculative

Regressive Expectations Agents expectations of interest rate adjustment depended on their subjective evaluation of the normal rate of interest. The normal rate varies between individuals If the normal rate is above the current rate, the interest rate is expected to rise If the normal rate is below the current rate, the interest rate is expected to fall

All or Nothing Theory

Expectations of capital gain or loss So g > 0 if r > r e g < 0 if r < r e But this evaluation is for one agent only and will differ for different agents

R M TotalMTMT R* Idle balances

MdMd R M

The breakdown in liquidity preference The special case is when all expectations merge between agents If all agents have the same expectation then the speculative demand for money breaks down

The Liquidity Trap MdMd

Criticism No portfolio diversification - all or nothing model Psychological basis for the expectation of the rate of interest is not explained - inelastic expectations Only a short-run argument. If the rate of interest is constant for any length of time, then agents would revise their normal rate.

Tobin Model Assumptions.Agents choose between two assets, Money (M) with zero yield and bonds (consols) (V) with known coupon B per period..No borrowing.No transactions costs.Each agent has a quadratic utility function in return R.Wealth W = M + V

Tobin continued Let = share of money in wealth, let = share of bonds in wealth and g = capital gain Return on the portfolio is R

Tobin preliminaries W=M+V; = M/W and = V/W + = 1 Capital gain = g R = (r + g) 0< <1 g = E(g) = 0 g ~ N(0, 2 g ) R = E(R) = E[ (r+g)] = r

-+ 0

Mathematical preliminaries

The Opportunity Set

R R 0 P P = 1

Risk averter - plunger R R U0U0 U1U1

Risk averter - diversifier U0U0 U1U1 R R

Risk lover U1U1 U0U0 R R

Risk lover - always at maximum risk position U0U0 U1U1 R R

Plunger - all or nothing U0U0 U1U1 R R

Diversifier U1U1 U0U0 R R

Quadratic utility function U = aR + bR 2 a > 0, b < 0 It can be shown that all that is relevant to the agents choice is the first and second moments of the distribution of returns dU/dR = a + 2bR > 0 (positive marginal utility) d 2 U/dR 2 = 2b < 0 (risk aversion)

Implications

First 2 moments

Conclusion While Keynes is based on ad-hoc theories of psychology, Tobins theory is based on explicit optimising behaviour Wealth effect may outweigh substitution effect Analysis based on first 2 moments only Assumes cash is riskless

More ? Money is dominated by income certain riskless assets Better at explaining the diversified portfolio between income certain bonds and risky bonds Capital risk may not be the motivation for holding safe assets Not robust to state of nature

Multi - asset application The model can be extended to dealing with money and a composite bundle of risky assets 2 stage process Stage 1 - identify the combination of assets that is superior in risk and return - efficient set Stage 2 - allocate wealth between money and composite

B C A 0 U0U0