Dr Andros Gregoriou Lecture 5, Money Demand 2 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).
With real money demand, leaving all relative prices, output, and the nominal interest rate the same and depreciating the domestic currency in proportion to the fall in real money demand. The long-run level of real balances is (M/P2), a level where the interest rate in the long-run equals its initial value. The dynamics of adjustment to a.
A real interest rate is adjusted to remove the effects of inflation and gives the real rate of a bond or loan. A nominal interest rate refers to the interest rate before taking inflation into.

Real Vs Nominal Money Demand
Real Vs Nominal Money Demand Definition
Real Vs Nominal Interest Rates

In some sectors, particularly mining, models are often built using real cashflows, i.e. without any projected inflation. This makes sense when a mining company is looking at an investment in a developing country, where inflation might be quite high, so modelling without the impact of inflation shows the project’s true value.

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 magnitude of the volatility of money demand has crucial implications for the optimal way in which a. Jan 15, 2019 Growth in real output (i.e., real GDP) will increase the demand for money and will increase the nominal interest rate if the money supply is held constant. On the other hand, if the supply of money increases in tandem with the demand for money, the Fed can help to stabilize nominal interest rates and related quantities (including inflation).

However, there are some very significant tax and finance issues to be aware of when using a real model, which can quite materially alter the results - here at JPA Financial Modelling we see these all too often. The easiest of these to demonstrate with a very simple example is the value of carried forward tax losses.

Take a ten year project which makes a $100 loss in the first year, breaks even in each subsequent year and finally makes a $200 profit in the final year, using real 2017 dollars. Discounting the cashflows at a real WACC of 5% gives an NPV of 9.13:

Now let’s add 2.5% inflation to the project, and as we’re discounting nominal cashflows we’ll increase our real WACC of 5% to 7.625% (=(1.05 * 1.025)-1)

The difference of 3.81 between the real and nominal NPVs is of course because the tax department (in most countries) won’t let you inflate your tax losses, so the $100 tax loss generated in 2017 will still only be worth $100 in 2026 in nominal terms, so in real terms it’s worth much less.

A similar issue arises with tax depreciation – if you buy an asset for $100 in 2017 that’s written off straight-line for tax over 10 years then you’ll get a tax expense of $10 each year. However if you don’t deflate that $10 each year in a real model then you’ll understate the tax liability.

So should you model in real? Ideally not if you have tax or debt calculations in your model, but if you must then you've got a few options, including:

Only model the cashflows as far as EBITDA in real and then switch to nominal for the rest of the model; or
Model in real throughout but have separate workings for tax losses, tax depreciation, deferred taxes, debt finance, franking credits, etc - trust me, this is really hard; or
Model everything in nominal and then convert to real.

Finally, a justification sometimes given for modelling in real is that the inflation rate is too uncertain. But is it any more uncertain than the other inputs in your model? And even though it's uncertain, you still need it to deflate your tax and debt finance calculations which are inherently nominal, otherwise you're mixing real and nominal cashflows, which is a bit like comparing a Ford Model T with a Tesla Model 3.

Thanks for reading - please let me know in the comments below if you have a different way of correctly modelling in real terms.

Learning Objectives

Explain the meaning of the equation of exchange, MV = PY, and tell why it must hold true.
Discuss the usefulness of the quantity theory of money in explaining the behavior of nominal GDP and inflation in the long run.
Discuss why the quantity theory of money is less useful in analyzing the short run.

So far we have focused on how monetary policy affects real GDP and the price level in the short run. That is, we have examined how it can be used—however imprecisely—to close recessionary or inflationary gaps and to stabilize the price level. In this section, we will explore the relationship between money and the economy in the context of an equation that relates the money supply directly to nominal GDP. As we shall see, it also identifies circumstances in which changes in the price level are directly related to changes in the money supply.

The Equation of Exchange

We can relate the money supply to the aggregate economy by using the equation of exchange:

Equation 11.1

The equation of exchange shows that the money supply M times its velocity V equals nominal GDP. Velocity is the number of times the money supply is spent to obtain the goods and services that make up GDP during a particular time period.

To see that nominal GDP is the price level multiplied by real GDP, recall from an earlier chapter that the implicit price deflator P equals nominal GDP divided by real GDP:

Equation 11.2

[latex]P = frac{Nominal ; GDP}{Real ; GDP}[/latex]

Multiplying both sides by real GDP, we have

Equation 11.3

[latex]Nominal ; GDP = P times real ; GDP[/latex]

Letting Y equal real GDP, we can rewrite the equation of exchange as

Equation 11.4

We shall use the equation of exchange to see how it represents spending in a hypothetical economy that consists of 50 people, each of whom has a car. Each person has $10 in cash and no other money. The money supply of this economy is thus $500. Now suppose that the sole economic activity in this economy is car washing. Each person in the economy washes one other person’s car once a month, and the price of a car wash is $10. In one month, then, a total of 50 car washes are produced at a price of $10 each. During that month, the money supply is spent once.

Applying the equation of exchange to this economy, we have a money supply M of $500 and a velocity V of 1. Because the only good or service produced is car washing, we can measure real GDP as the number of car washes. Thus Y equals 50 car washes. The price level P is the price of a car wash: $10. The equation of exchange for a period of 1 month is

[latex]$ 500 times 1 = $ 10 times 50[/latex]

Now suppose that in the second month everyone washes someone else’s car again. Over the full two-month period, the money supply has been spent twice—the velocity over a period of two months is 2. The total output in the economy is $1,000—100 car washes have been produced over a two-month period at a price of $10 each. Inserting these values into the equation of exchange, we have

[latex]$ 500 times 2 = $ 10 times 100[/latex]

Suppose this process continues for one more month. For the three-month period, the money supply of $500 has been spent three times, for a velocity of 3. We have

[latex]$ 500 times 3 = $ 10 times 150[/latex]

The essential thing to note about the equation of exchange is that it always holds. That should come as no surprise. The left side, MV, gives the money supply times the number of times that money is spent on goods and services during a period. It thus measures total spending. The right side is nominal GDP. But that is a measure of total spending on goods and services as well. Nominal GDP is the value of all final goods and services produced during a particular period. Those goods and services are either sold or added to inventory. If they are sold, then they must be part of total spending. If they are added to inventory, then some firm must have either purchased them or paid for their production; they thus represent a portion of total spending. In effect, the equation of exc

Real Vs Nominal Money Demand