Md=kPy Money demand (Md) is assumed to be a proportion (k) of nominal income, the price level (P) multiplied by the level of real income (y). Since the primary objective of money demand is expenditure it seems logical that money demand is a function of expenditure (price. income). Mar 22, 2021 Unlike centralized currency, which is government controlled, cryptocurrency is decentralized. Its value is controlled by the network based on supply and demand. The real interest rate is fixed in the goods market at r=0.05 per year. Suppose that the nominal money supply is growing at a rate of 10% per year and; Question: Suppose that the real money demand function is:, where Y is real output, re is the real interest rate, and is the expected rate of inflation. Real output is constant over time at Y. The real demand for money is defined as the nominal amount of money demanded divided by the price level. For a given money supply the locus of income-interest rate pairs at which money demand equals money supply is known as the LM curve. The real demand for money is defined as the nominal amount of money demanded divided by the price level. For a given money supply the locus of income-interest rate pairs at which money demand equals money supply is known as the LM curve.

The Keynes’ Theory of Demand for Money!

Keynes treated money also as a store of value because it is an asset in which an individual can store his (her) wealth.

To Keynes an individual’s total wealth consisted of money and bonds.

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Keynes used the term ‘bonds’ to refer to all risky assets other than money.

So money holding was the only alternative to holding bonds. And the only determinant of an individual’s portfolio choice was the interest rate on bonds.

This would affect an individual’s decision to divide his portfolio into money and bonds. To Keynes, it costs money to hold money and the rate of interest is the opportunity cost of holding money. At high rates of interest an individual loses a large sum by holding money or by not holding bonds.

Capital gain/loss:

Another factor affecting an individual’s portfolio choice was expected change in the rates of interest which would give rise to capital gain or loss. According to Keynes when the interest rate was high relative to its normal level people would expect it to fall in near future. A fall in the rate of interest would imply a Capital gain on bonds. According to Keynes at a high rate of interest there would be low demand for money as a store of value (wealth).

There are two reasons for this:

(i) At high rate of interest the opportunity cost of money holding (in terms of forgone interest) is high.

(ii) At a high rate of interest future capital gain on bonds is likely due to a fall in the rate of interest in future. It is because there is an inverse relation between the rate of interest and the price of old bonds. Thus if the present rate of interest is high, people will expect it to fall in near future, in which case they will expect to make capital gain.

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Since the demand for money would fall at high rates of interest, and increase at low rates of interest, there is an inverse relation between the asset (speculative) demand for money and the rate of interest.

Keynes also considered transactions and precautionary demand for money whose primary determinant was income. Such demand would increase proportionately with increase in income.

So Keynes’ demand function for money can be expressed as

M_d = L(Y, i) … (3)

where Y is income and i is nominal interest rate and L stands for liquidity preference.

Policy Conclusions:

Thus, in Keynes’ view, the demand for money is a function of both income and interest rate, though in the classical theory, it was a function of income alone. This point is important in explaining the differences in policy conclusions between the classical and Keynesian models.

Real Money Demand Function

1. Determination of nominal income by the supply of money:

If the demand for money is exactly proportional to income, as in equations (1) and (2), then nominal income (PY) is completely determined by the supply of money. Since M= M_d= kPY, if k is assumed to remain fixed in equation (1) an increase in money supply (M) in equilibrium would result-in a proportional increase in PY. So we get

ΔM = kΔPY

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or, 1/K ΔM = Δ PY … (4)

Thus equation (4) makes it abundantly clear that PY can change only when M changes, k remaining fixed. This means that changes in fiscal policy or autonomous changes in investment demand have no role in determining the equilibrium value of income. This is indeed the classical case of vertical LM curve, in which if M is fixed the level of income is automatically fixed. And any shift of the IS curve will only affect the rate of interest.

2. Role of fiscal policy change in income determination:

In Keynes’ money demand function, income is not proportional to the supply of money. This means that income changes can occur due to changes in fiscal policy and autonomous shifts in investment demand. In this case the LM curve will be upward sloping and any shift of the IS curve will change the equilibrium value of income. Of course, slopes of the IS and LM curves will determine the relative importance of monetary factors and other determinants of income (that shift the IS curve).

The Monetarists’ View:

The monetarists believe that the LM curve is quite steep, although not vertical. This largely, if not entirely, explains why money exerts a dominant influence on nominal income.

The Regressive Expectations Model:

According to Keynes the demand for money refers to the desire to hold money as an alternative to purchasing an income-earning asset like a bond. All theories of demand for money give a different answer to the basic question: If bonds earn interest and money does not why should a person hold money? The first theory to answer these questions known as the Keynesian theory of demand for money is based on a model called the regressive expectations model.

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This essentially says that people hold money when they expect bond prices to fall, that is, interest rates to rise, and, thus, expect that they would incur a loss if they were to hold bonds. ‘Bonds’ here represent the whole range of risky assets that exist in reality. Since people’s estimates of whether the interest rate is likely to rise or fall — and by how much — vary widely, at any given interest rate there will be some people expecting it to rise and, thus, they would be holding money.

According to the regressive expectations model a bond holder has an expected return on the bond from two sources, the bond’s yield — the interest, payment he receives — and a potential capital gain — an increase in the price of the bond from the time he buys it to the time he sells it. The bond’s yield i is normally expressed as a percentage yield equal to Y divided by the face value of the bond. Thus

i = Y/P_b …(5)

Since the yield Y is fixed percentage of the bond’s face value, the market price of a bond is given by the ratio of yield to market rate:

P_b = Y/I …(6)

The expected percentage capital gain is the percentage increase in price from the purchase price P_b to the expected sale price P^e_b. From this we can derive the percentage capital gain, g = (P^e_b – P_b)/P_b. From equations (5) and (6), with a fixed Y on the bond, we can get an expected price P^e_b, corresponding to an expected interest rate, i_e = Y/P^e_b. Thus, in terms of expected and current interest rates, the capital gain can be expressed as

This is the expression for expected capital gain in terms of current and expected interest rates.

The total percentage return (earning) on a bond — denoted by e — is the sum of the market rate of interest at the time of purchase plus capital gains, e = i + g. Now if we substitute for g from equation (7), we get an expression for the total percentage return as the sum of interest yield and capital gains:

Now, with an expected return on bonds given by e, and with a zero return on money, the asset-holder can be expected to put his liquid wealth into bonds, if he expects the return e to be positive. If the return on bonds is expected to be negative, he will put all his liquid wealth into money.

In Keynes’ regressive expectations model, each person

What Is Real Money Demand