Economics essay

ECON 1110 Intermediate Macroeconomics

James R. Maloy

Spring 2019

Lecture Notes for Topic 3: Classical Macroeconomics (II)

Readings: Froyen Ch. 4

This section discusses the determination of prices in the classical model. The roles of money and the classical quantity theory of money are discussed. The classical aggregate demand curve is derived and equilibrium prices and output are determined by the intersection of aggregate demand and aggregate supply. The determination of interest rates and the role of interest rates in stabilisation are analysed, as well as the role of government policy.

I. The Quantity Theory of Money

There are two main versions of the classical quantity theory of money—Fisher’s quantity theory and the Cambridge quantity theory. Both models are similar and draw basically the same conclusions, but the techniques and analysis are a bit different.

One of the oldest economic theories still in use today, the quantity theory of money traces its origins to theorists who were trying to determine the effects of an increase in the gold supply. At that time, most of the world was on a gold standard, so the quantity of gold in the nation determined the quantity of money. When new gold supplies were discovered (i.e. in the New World) it increased the quantity of money in the economy. Under mercantilist theory, the increase in gold would make the country more affluent, but theorists such as David Hume and some of his contemporaries disagreed. They developed a theory which is familiar today—the idea that increases the money supply only cause inflation. The quantity theory shows a relationship between the quantity of money (the independent variable) and the price level (the dependent variable). Hume wrote that in the long run the absolute size of the money stock was insignificant because the price level would eventually adjust to match it. This idea became known as the neutrality of money, as mentioned in the last topic. If the money stock were to double, for example, prices would eventually double and employment would be at the normal level. The classical economists argued that monetary policy would only cause inflation in the long run, although there was some room for short-run non-neutrality due to lags in the adjustment process. Therefore, early quantity theorists suggested that in the short run it may be possible to experience an increase in output as a result of an increase in the money supply, but this would be a transitory effect. Hume even suggested that output could be continually increased, but at the cost of ever-increasing inflation.

Fisher’s Quantity Theory

Fisher greatly advanced the quantity theory by coupling it with the equation of exchange .

MV = PY

M is the money supply, V is the velocity of money, P is the price level, and Y is the real level of output. PY is of course nominal output. Velocity measures the turnover rate of money (money being currency and demand deposits) in the economy, i.e. how many times on average a pound coin changed hands in a year. For example, if nominal output PY was $100 and the money supply M was $20, it means that each dollar was used an average of 5 times.

The equation of exchange is true by definition, but Fisher and other quantity theorists went further by attempting to explain the determination of each component. The equilibrium level of output Y is determined exogenously by the factors considered in the previous chapter; a change in the money supply is not a factor that affects equilibrium output. Velocity is dependent on the paying habits of society. An increase in credit transactions, for example, would increase velocity, since things could be bought immediately without needing up-front payment. Shorter pay periods yield smaller paychecks, which would cause a decrease in the amount of money held at any given time and therefore increase velocity. These factors, however, are assumed to be relatively stable in the short run and would therefore generate constant velocity. It is important to note that many classical economists did not believe that velocity was necessarily stable; they only believed that in equilibrium, velocity (like output) was independent of the money supply, and could therefore be treated as an exogenously-given constant. In other words, a change in the money supply would not affect equilibrium velocity. Therefore, for simplicity, we will treat velocity as a constant. In summary, the changes in the money supply do not affect equilibrium values of V and Y.

The equation of exchange can be used to determine the price level. Holding Y and V constant, an increase in the money supply must be met by an equal increase in the price level for the identity to hold, ceteris paribus. Fisher wrote in his work The Purchasing Power of Money that doubling the quantity of money will initially decrease velocity by fifty percent, and the person will be left with “double the amount of money and deposits which his convenience had taught him to keep on hand…and there cannot be surplus money and deposits without a desire to spend it, and there cannot be a desire to spend it without a rise in prices.” P will therefore double and V will return to its original level. In other words, an increase in the money supply increases demand for goods, but does not increase the productive capacity of the economy to produce more goods—it is demand without production to match it; prices simply increase. Thus Fisher’s quantity theory of money (sometimes called the transactions quantity theory): the quantity of money determines the price level. Note that in the short run, before prices double, there may be some non-neutrality of money, and velocity and output can be affected. Thus we have an important conclusion: although the economy can move away from full employment output, any change in output is only temporary and the economy, through natural behaviour in the "perfect system," will correct itself. Laissez-faire should be maintained because firstly, any fluctuation in output will correct itself without government interference and secondly, any attempts to use monetary policy to artificially increase output will only cause inflation.

The Cambridge Quantity Theory

The Cambridge approach is named for two famous classical economists from Cambridge University, A.C. Pigou and Alfred Marshall. They arrived at the same conclusion as Fisher, but unlike the Fisher version, which said that by definition changes in the money supply generate changes in prices, the Cambridge economists developed a model of money demand to analyse how people decide how much money to hold, and therefore how changes in the money supply will affect their optimum money holdings. They thus generated an economic rationale for the link between money and prices.

The Cambridge economists argued that people would hold money for transactions or for unexpected expenses. But, holding wealth in the form of money would entail an opportunity cost, namely the foregone interest that could be obtained from holding bonds. There is therefore an optimum level between the desire to hold money for transactions or emergencies and the desire to not hold money and hold interest-bearing bonds instead. Interestingly they veer towards the foundation of Keynes’ monetary theory—their model treats money as an asset rather than just a means of transactions, but they do not explore the full implications. Marshall and Pigou theorized that the demand for money (MD) would be a proportion, k, of nominal income (PY):

MD = kPY

Since in equilibrium money demand must be equal to money supply (M), we have:

M = MD = kPY

Marshall and Pigou also expected k and Y to be fixed exogenously, thus generating another model that shows that changes in the money supply generate identical changes in the price level. Indeed, if k = 1/V, the Fisher and Cambridge equations are identical.

Therefore, both versions generate the same results, but the Cambridge approach generates a more economics-oriented argument by deriving the quantity theory as a money demand theory, not just a mathematical identity.

II. The Classical Aggregate Demand Curve

The quantity theory is an implicit theory of aggregate demand, and can be used to build the aggregate demand (AD) curve. Using the equation of exchange:

MV = PY (or M = kPY)

the AD curve is derived by plotting different combinations of P and Y for a fixed money supply (M). For example, if V is a constant 2.0 and M = 600, we know that PY = 1200. Supposing P=2.0 and Y = 600 gives us one point on the AD curve. Now suppose P = 3.0 and Y = 400. We have another point on the AD curve. Continuing with different combinations of P and Y that generate a product of 1200, we find a downward sloping AD curve: the aggregate quantity demanded increases as the price level decreases for a given quantity of money. This should make sense: if you have 50 pounds in your pocket, you will demand more goods the cheaper the goods are!

We note that an increase in the money supply (holding V constant) will generate an equal change on the other side of the equation. Therefore, we can plot a new AD curve with different combinations of P and Y for the new quantity of money. An increase (decrease) in the money supply shifts the AD curve to the right (left). Any point on the AD curve is a point of equilibrium in the money market—where money supply equals money demand. That is,

M = MD = kPY

Furthermore, any point on the AD curve is a point where P and Y are at levels where their product PY corresponds to the quantity of money M. If MV does not equal PY, we are at a point off the AD curve for money supply M. In summary, for any point on the AD curve for quantity of money M, it must be that M = MD and MV = PY.

Aggregate Demand and Supply in the Classical System

Combining the classical AD and AS curves gives equilibrium in the output (or product) market. The vertical AS curve shows that output is independent of the price level. Changes in the money supply generate shifts in the AD curve, which in turn generate changes in the price level. Therefore, only the real factors from the last topic determine the equilbrium level of output; changes in these variables shift AS and affect prices and output. The quantity of money determines the AD curve, which in turn determines the price level. Note that a change in the money supply leads to a change in prices but not output via the quantity theory.

III. The Classical Theory of the Interest Rate—The Loanable Funds Theory

In the classical model, the interest rate played a critical role in maintaining the stability of aggregate commodity demand. The classical model argued that any change in any component of aggregate demand—consumption, investment, and government spending—would be matched by a counterbalancing change in one of the other components, and the interest rate was the mechanism that ensured this result.

The equilibrium interest rate is determined by the amounts of borrowing and saving (saving = lending). All transactions were assumed to be in the form of bonds. If a firm wished to borrow money, it would issue a bond. The saver would then buy the bond, giving the firm money in exchange for it. The bond would bear an interest rate (r), as determined by the interaction of demand for bonds (lending) and supply of bonds (borrowing).

The demand for bonds is called supply of loanable funds in classical terminology. Likewise, the supply of bonds by borrowers is termed demand for loanable funds. The supply of loanable funds is expected to be a positive function of the interest rates. Recall that individuals can either consume or save their income. At higher interest rates, the opportunity cost of consumption increases and people are more willing to forego current consumption to take advantage of higher interest rates. Therefore, the supply of loanable funds curve is upward sloping.

The demand for loanable funds is the level of investment by businesses plus the amount of government borrowing, i.e. the government budget deficit (g-t). The amount of investment undertaken is expected to increase as the interest rate decreases. This is because firms invest up to the point where the interest rate equals the expected return of the project (i.e. MC=MR), and as interest rates decline, more projects become profitable and investment increases. Therefore, the demand for loanable funds for investment is a downward sloping function of the interest rate. The level of the government deficit (g-t) is assumed to be independent of the interest rate, so the total demand for loanable funds curve is shifted to the right by the amount of g-t.

Equilibrium is where the supply and demand of loanable funds curves intersect. At that intersection, the equilibrium interest rate is set, and demand and supply of loanable funds intersect, i.e. s = i + (g-t). (Recall that this is the same identity as the relationship derived in Topic I: I + G = S + T).

Why does the interest rate ensure that desired commodities demand (C+I+G) remains at a constant level? Assume that G is constant. Suppose that there is an increase in autonomous investment. The firms need money for the new investment, so the demand for loanable funds curve shifts right. At the new equilibrium, the interest rate has increased and the quantity of funds loaned out has increased. Therefore, more investment has taken place and people save a greater quantity of money to take advantage of the higher interest rates. We see that the increase in investment is exactly equal to the increase in savings. But recalling that people either consume or save their income, the increase in savings must yield an equal decrease in consumption. Therefore, investment and consumption have changed by equal and opposite amounts, and the net change in C + I + G is zero! Therefore, the interest rate in the classical model works to smooth out and eliminate any changes in desired demand.

IV. Government Policy in the Classical Model

Note that monetary and fiscal policy are known as demand management. The goal of these policies is to alter aggregate demand. We know that output in the classical model is determined by aggregate supply, not aggregate demand, so even if these policies succeed in shifting AD, output will be unchanged. However, it will also be shown that fiscal policy is generally ineffective even in adjusting AD, since only changes in the money supply shift AD.

Monetary Policy

We have seen that money is neutral in the classical model. Only real factors determine the level of aggregate supply and output. A change in the money supply only changes aggregate demand and the price level. Therefore, monetary policy does not cause real changes; it only affects inflation and prices. The quantity theorists argued that any short run non-neutrality of money that caused a recession and potential use of a monetary expansion was so short-term that it was not worth the long run cost of higher inflation.

It should be noted that money can be considered insignificant in the sense that it does not determine long-run output. However, money is significant in its use as a medium of exchange, and stable money is a requirement for stable prices. As John Stuart Mill wrote,

There cannot be intrinsically a more insignificant thing, in the economy of a society, than money; except in the character of a contrivance for sparing time and labour. It is a machine for doing quickly and commodiously, what would be done, though less quickly and commodiously, without it; and like many other kinds of machinery, it only exerts a distinct and independent influence of its own when it gets out of order.

Fiscal Policy

There are two types of fiscal policy—changes in government spending and changes in taxes. Assuming that taxes remain unchanged, the effects of a change in G can be analysed. An increase in government spending (fiscal expansion) will alter the government budget deficit g-t. Therefore, the government will have to finance this increase in the deficit by borrowing, thus shifting the demand for loanable funds curve to the right. What happens is similar to the case of an increase in investment. At the original level of interest, there is excess demand for loanable funds, so the interest rate increases. As the interest rate increases, some investment projects cease to be profitable, so investment declines. The increase in the interest rate causes savings to increase and consumption to decrease. Therefore, the increase in government spending is completely offset by the decreases in consumption and investment, and the sum of C + I + G is unchanged. The government spending crowds out private expenditures, and the fiscal policy is ineffective. Recalling that we constructed the AD and AS curves without mention of government, it is evident that a bond-financed increase in government expenditures will have no impact on prices or output. If, alternatively, the government finances the increased spending through the printing of more money, it is obvious that the increase in the money supply will only increase the price level.

Tax Policy

Suppose the government chooses to expand the economy by a tax cut. On the demand side, a tax-cut could stimulate consumer demand. However, if the government sells bonds to finance the tax cut, the interest rate will adjust to ensure that the level of AD remains unchanged. The increased demand for loanable funds (g-t becomes larger) will increase the interest rate and cause saving to increase, thus partially eroding the initial increase in consumption stimulated by the tax cut. The higher interest rates would also cause investment to decline. The same crowding out effect as before would occur, with C + I + G unchanged. Likewise, paying for the cut by printing new money will just increase the price level. Therefore, tax policy is ineffective in changing AD.

However, if the tax cut is not lump sum, but a decrease in marginal tax rates, the change can have important impacts on supply decisions. A decrease in marginal income tax rates, for example, will make people more willing to work for a given real wage, since the worker gets to keep a larger percentage of his earnings. The labour supply curve will increase, generating an increase in the equilibrium quantity of labour and thus aggregate supply. Therefore, changes in marginal tax rates can have real effects on the economy. However, this affect is typically considered detrimental, as it simply distorts the market---note that employment (and thus output) are the highest when there is no income tax, and changes in the policy cause fluctuations, rather than cure them. Classical economists therefore viewed taxes as having either no effect or a detrimental effect, based on the case. Taxes were simply ways to pay for necessary government expenditure rather than a tool to manage the economy. In any case, there was no need for tax policy to stimulate the economy in the Keynesian sense due to self-correction. In the classical era there typically was no such thing as an income tax, or where it existed the rate was very low. Therefore, classical economists usually did not pay much attention to this type of situation---it is with hindsight that we can apply their theory to income taxes. Modern supply-side economics theories centre around this classical concept.

� The first known mention of the quantity theory is actually in the writings of Copernicus in the 1520s, although the development of the theory happened much later as a response to New World gold entering Europe.

� Fisher's version actually looked at total transactions T such that MV=PT, not just transactions related to current production Y. If the proportion of transactions related to current production is stable, then replacing T with Y works—if not, it is a problematic assumption. Interestingly he also distinguished financial transactions, an idea which has been largely lost. See Fisher (1911)