EC3115: Money, Inflation and Welfare

The Fisher equation states that the nominal interest rate (R) is the sum of the real interest rate (r) and the expected rate of inflation (\(\pi^e\)). The relationship is expressed as \(R_t = r_t + \pi_{t+1}^e\). This holds because rational lenders require compensation for the expected loss of purchasing power due to inflation, in addition to the real return on their lending. Source: EC3115 - Ch 7 Money, inflation and welfare-1.pdf, p. 87; McCallum, p. 113.

The ex-ante real interest rate (\(r^A = R_t - \pi_{t+1}^e\)) is the real return expected at the time a loan is made. The ex-post real interest rate (\(r^P = R_t - \pi_{t+1}\)) is the actual real return realized after the fact. The distinction is necessary because the actual inflation rate (\(\pi_{t+1}\)) over the loan period is unknown when the nominal rate (\(R_t\)) is set. Decisions are based on the ex-ante rate, which incorporates expected inflation. Source: EC3115 - Ch 7 Money, inflation and welfare-1.pdf, p. 88.

Superneutrality is a stronger condition than neutrality. While neutrality means a one-time change in the money supply level affects only nominal variables, superneutrality means a change in the *rate of growth* of the money supply affects only nominal variables (like the inflation rate and nominal interest rate) but has no effect on *real* variables, including the real interest rate and real output. Source: EC3115 - Ch 7 Money, inflation and welfare-1.pdf, p. 88; McCallum, p. 121.

Monetary policy is not superneutral if a change in the rate of monetary growth (and thus inflation) affects real variables. The Mundell-Tobin effect is a key example. Higher anticipated inflation reduces the real return on money, causing individuals to reduce their real money balances. This fall in real wealth can lead to increased saving, which in turn lowers the real interest rate to restore goods market equilibrium. Since the real interest rate changes, money is not superneutral, even if it is neutral in a static sense. Source: EC3115 - Ch 7 Money, inflation and welfare-1.pdf, p. 89; McCallum, p. 121.

The Mundell-Tobin effect posits that higher expected inflation reduces the real value of money balances. This reduction in wealth induces households to save more to restore their wealth. The increase in saving (an outward shift of the IS curve in a standard model) leads to a lower equilibrium real interest rate, which stimulates real investment. Source: EC3115 - Ch 7 Money, inflation and welfare-1.pdf, p. 89; Mizen, p. 171.

Friedman's rule for the optimal quantity of money states that social welfare is maximized when the nominal interest rate is zero (R=0). This eliminates the opportunity cost of holding money, inducing people to hold real balances to the point of satiation (full liquidity). According to the Fisher equation (R = r + \(\pi\)), a zero nominal interest rate requires a rate of price deflation (a negative inflation rate) equal to the real rate of interest (\(\pi = -r\)). Source: EC3115 - Ch 7 Money, inflation and welfare-1.pdf, p. 91; McCallum, p. 130.

Anticipated inflation raises the nominal interest rate, which is the opportunity cost of holding money. To avoid this cost, individuals hold lower real balances and must make more frequent trips to the bank (wearing out their "shoe leather") to manage their cash. This time and effort represents a real resource cost to society, as it diverts resources from productive activities. This welfare loss is quantified by the area under the money demand curve. Source: EC3115 - Ch 7 Money, inflation and welfare-1.pdf, p. 91; McCallum, p. 125.

In consumer surplus analysis, the height of a demand curve at any quantity represents the marginal value or utility to the consumer of that unit. Therefore, the total area under the demand curve for real money balances up to a certain quantity represents the total utility or transaction-facilitating services that individuals receive from holding that amount of money. Source: EC3115 - Ch 7 Money, inflation and welfare-1.pdf, p. 91; McCallum, p. 125.

Seigniorage is the real revenue or purchasing power a government obtains by virtue of its monopoly power to create money. For fiat money, the cost of production is near zero, so the government can acquire real goods and services by printing money and spending it. This represents a transfer of real resources from the public (who hold the money) to the government. Source: EC3115 - Ch 7 Money, inflation and welfare-1.pdf, p. 91; Mizen, p. 177.

The inflation tax is the revenue the government obtains by creating money to finance its spending. This money creation leads to inflation, which erodes the real value of the public's existing money holdings. This loss of purchasing power is an implicit tax on holding money. The revenue from this tax is the rate of inflation (the tax rate) multiplied by the stock of real money balances (the tax base). Source: EC3115 - Ch 7 Money, inflation and welfare-1.pdf, p. 91; Mizen, p. 177.

Phillip Cagan, in his seminal 1956 study, provided the arbitrary but now standard definition of hyperinflation as beginning in the month when the price rise exceeds 50 percent and ending in the month before the monthly price rise drops below that amount and stays below it for at least a year. Source: Cagan, p. 25; Mizen, p. 172.

The Cagan model simplifies the money demand function for the extreme conditions of hyperinflation. It posits that changes in real income and real interest rates are dwarfed by the massive changes in inflation. Therefore, the primary variable determining the demand for real money balances is the expected rate of inflation, which represents the cost of holding money. The specific form is \(\ln(M/P) = -\alpha E - \gamma\). Source: Cagan, p. 35; Mizen, p. 174.

During hyperinflation, the cost of holding money (the expected rate of inflation) becomes extremely high. To avoid this "inflation tax," the public reduces their desired real money balances to a fraction of their initial value. This attempt to spend money as quickly as possible is known as the "flight from money" and corresponds to a massive increase in the velocity of circulation. Source: Mizen, p. 173; Cagan, p. 64.

In situations of political instability or weak institutions, enacting and administering complex tax programs can be difficult. Issuing money to finance expenditures is administratively very simple: "All that is required is to spend newly printed notes." This makes it an appealing, though ultimately dangerous, method for governments to raise revenue. Source: Mizen, p. 177; Dornbusch, p. 19.

The Olivera-Tanzi effect highlights that if there is a delay between when a tax liability is assessed and when it is actually paid, inflation will erode the real value of the tax revenue collected by the government. The higher the inflation rate, the greater the erosion, which can lead to a vicious cycle of larger deficits, more money creation, and even higher inflation. Source: Dornbusch, p. 20.

In a long-run steady-state equilibrium, real money balances (M/P) must be constant. For M/P to be constant, the numerator (M) and the denominator (P) must grow at the same rate. Therefore, if the money supply grows at a constant rate \(\mu\), the price level must also grow at the same rate, meaning the inflation rate equals the rate of money growth. Source: McCallum, p. 116.

The "shortage of money" is a shortage of *real* balances from the public's perspective, but it manifests as a demand for ever-increasing *nominal* balances. As prices explode, the amount of nominal currency required for even simple transactions becomes enormous. The public demands more and more nominal money to keep their real balances from vanishing, and the printing presses may struggle to keep up with this demand, even as they are the source of the problem. Source: Mizen, p. 173.

The IS curve represents goods market equilibrium, where investment and saving decisions depend on the *real* interest rate (r). The LM curve represents money market equilibrium, where money demand depends on the *nominal* interest rate (R). When plotting in (R, Y) space, the LM curve's position is given. The IS curve is given by \(R = r + \pi^e\). A rise in expected inflation (\(\pi^e\)) means that for any given real rate r, the corresponding nominal rate R is higher. This causes the IS curve to shift up (or right) by the amount of the increase in expected inflation. Source: EC3115 - Ch 7 Money, inflation and welfare-1.pdf, p. 89; McCallum, p. 116.

Total revenue from the inflation tax is the tax rate (\(\pi\)) times the tax base (real balances, M/P). Revenue is maximized when a percentage increase in the tax rate is exactly offset by the percentage decrease in the tax base. This occurs at the point where the elasticity of the tax base (M/P) with respect to the tax rate (\(\pi\)) is equal to -1. Source: Cagan, p. 81.

The adaptive expectations hypothesis, used by Cagan, posits that agents revise their expectations based on past forecast errors. This can be expressed as a geometrically weighted average of all past inflation rates, where more recent inflation rates are given more weight. The formula is \(E_t - E_{t-1} = \beta(C_{t-1} - E_{t-1})\). Source: Mizen, p. 174; Cagan, p. 37.

Hyperinflation is highly destructive. It undermines money's role as a store of value, unit of account, and medium of exchange. It leads to a massive and arbitrary redistribution of wealth (destroying the savings of those holding nominal assets), corrodes social institutions through corruption and fraud, and can lead to the collapse of the tax system and political stability. Source: Dornbusch, p. 15; EC3115 - Ch 7 Money, inflation and welfare-1.pdf, p. 93.

When the central bank increases the rate of monetary growth, the initial impact is an increase in real money balances (before prices have had time to adjust). This increase in liquidity shifts the LM curve to the right, causing a temporary fall in the nominal interest rate. This is the first step in the transmission mechanism described by Friedman. Source: Mizen, p. 170.

While other factors can contribute, the fundamental driver of all sustained high inflations is the need for the government to finance large budget deficits by printing money (seigniorage). When the government cannot raise revenue through taxes or borrowing, it turns to the printing press, leading to an excessive growth in the money supply that fuels inflation. Source: Dornbusch, p. 18; Mizen, p. 172.

This is a demonstration of the Fisher effect and superneutrality. In the long run, the real interest rate is determined by real factors (productivity and thrift). Therefore, a change in the money growth rate translates one-for-one into a change in the inflation rate. To keep the real interest rate constant, the nominal interest rate must rise by the full amount of the increase in inflation. Source: McCallum, p. 117; Mizen, p. 169.

Even if fully anticipated, inflation raises the nominal interest rate. Since money typically pays no interest, this increases the opportunity cost of holding real balances. Individuals and firms are induced to economize on their money holdings, which involves real costs (time and effort spent managing cash, more frequent financial transactions). These "shoe-leather" costs represent a real welfare loss to society, as resources are diverted from productive uses. Source: McCallum, p. 125; EC3115 - Ch 7 Money, inflation and welfare-1.pdf, p. 91.

The parameter \(\alpha\) measures the responsiveness of the logarithm of real money balances to a change in the level of expected inflation. This is known as a semi-elasticity. A higher \(\alpha\) means that demand for real balances is more sensitive to changes in expected inflation. Source: Cagan, p. 35.

As inflation accelerates, two effects worsen the government's fiscal position. First, the public reduces its real money holdings, eroding the base for the inflation tax. Second, the Olivera-Tanzi effect means the real value of conventional tax revenue falls. To finance the same level of real spending, the government must therefore print money at an even faster rate, leading to an explosive cycle. Source: Mizen, p. 178; Dornbusch, p. 20.

The price expectations effect is the final stage in Friedman's description of the transmission of monetary policy. After the initial liquidity and income effects, the sustained monetary expansion leads to inflation. As people come to expect this inflation, they demand a higher nominal interest rate to compensate for the loss of purchasing power, causing the nominal rate to rise, consistent with the Fisher effect. Source: Mizen, p. 170.

Rearranging the Fisher equation (\(R = r + \pi^e\)), we can solve for the expected inflation rate: \(\pi^e = R - r\). Plugging in the given values, we get \(\pi^e = 10\% - 3\% = 7\%\). Source: EC3115 - Ch 7 Money, inflation and welfare-1.pdf, p. 87.

The core assumption of the classical model's supply side is that the nominal wage adjusts promptly to equate labor supply and demand. This ensures the labor market always clears at the full-employment level of employment (n*), which in turn determines the full-employment level of output (y*) via the production function. This results in a vertical aggregate supply curve. Source: McCallum, p. 89.

The welfare cost of anticipated inflation is the deadweight loss resulting from individuals holding less-than-optimal real money balances. This loss is represented by the area of a trapezoid under the money demand curve, bounded by the nominal interest rates before and after the inflation. This area represents the lost consumer surplus (utility from money's services) that is not captured by anyone as revenue. Source: McCallum, p. 126; EC3115 - Ch 7 Money, inflation and welfare-1.pdf, p. 92.

This describes the unstable side of the inflation tax Laffer curve. As the government increases the inflation rate, people reduce their real money holdings (the tax base). Past a certain point, the erosion of the tax base is so severe that it outweighs the increase in the tax rate, causing total revenue to fall. To maintain its required revenue, the government must then increase the inflation rate even more, leading to an explosive, self-reinforcing spiral. Source: Mizen, p. 178; Cagan, p. 80.

A key stylized fact of hyperinflations is the "flight from money." As the cost of holding money skyrockets, the public's demand for real balances collapses. Cagan's data for Germany shows this dramatically, with real money balances shrinking to only 3% of their starting level, indicating a massive increase in the velocity of money. Source: Mizen, p. 173; Cagan, p. 26.

Since persistent budget deficits financed by money creation are the ultimate cause of hyperinflation, a credible and drastic fiscal reform is the essential anchor for any successful stabilization program. The government must convince the public that it will no longer rely on the printing press to finance its expenditures. This is often accompanied by a currency reform and a commitment to a new monetary rule. Source: Dornbusch, p. 25; Cagan, p. 89.

Financial liberalization and dollarization provide the public with alternatives to holding the domestic, non-interest-bearing monetary base. This reduces the demand for domestic money, shrinking the tax base for the inflation tax. To finance the same real deficit, the government must then rely on a higher rate of inflation. Thus, financial adaptation and innovation intensify the inflationary process. Source: Dornbusch, p. 21.

Using the Fisher equation, \(R = r + \pi^e\). With a real rate of 2% and an expected inflation rate of -3%, the nominal rate is \(R = 2\% + (-3\%) = -1\%\). A negative nominal rate is possible and implies that holding nominal bonds yields a negative return, but one that is still better than holding cash, which loses value at 3%. Source: EC3115 - Ch 7 Money, inflation and welfare-1.pdf, p. 87.

The resources (time, effort, technology) used to economize on money holdings are a deadweight loss because they are diverted from other productive or leisure activities without creating any new goods or services for society. It is a net loss of welfare, represented by the area C+E in the welfare cost diagram. Source: EC3115 - Ch 7 Money, inflation and welfare-1.pdf, p. 92.

In classical and neoclassical models, the real interest rate is the price that equilibrates the supply of saving (determined by household preferences for present vs. future consumption, or thrift) and the demand for investment (determined by the productivity of capital). It is therefore determined by fundamental 'real' factors in the economy, not by monetary variables. Source: Mizen, p. 165; McCallum, p. 115.

When contracts become shorter, wages and prices are adjusted more frequently to past inflation. This creates greater inertia and makes the current inflation rate more sensitive to the past inflation rate. A shock (like a devaluation) that raises inflation will be passed through into wages and prices much more quickly, leading to a faster and more volatile inflationary spiral. Source: Dornbusch, p. 23.

This is the property of monetary neutrality in the classical model. Because the model dichotomizes, with real variables (output, employment, real interest rate) determined independently of the monetary side, a change in the level of the money supply only affects nominal variables. To keep real money balances (M/P) constant at the new equilibrium, the price level (P) and nominal wages (W) must rise in exact proportion to the money supply (M). Source: McCallum, p. 95.

The inflation tax is an implicit tax on holding money. The tax rate is the rate at which money loses its value, which is the rate of inflation (\(\pi\)). The tax base is the real quantity of money on which the tax is levied (M/P). Therefore, the real revenue is \(\pi \times (M/P)\). Source: Mizen, p. 177; Cagan, p. 78.

The term \(\alpha\beta\) is the "reaction index." If it is less than one, the dynamic process is stable. This means that after a shock to the money supply, the price level will eventually converge to a new equilibrium path determined by the money supply process. If \(\alpha\beta > 1\), the system is unstable, and a shock can cause prices to become self-generating and explosive, independent of the money supply. Source: Cagan, p. 65, 69.

The Classical model assumes fully flexible wages and prices, which means the labor market always clears at the full-employment level, resulting in a vertical aggregate supply curve at potential output \(y^*\). The Keynesian model assumes that nominal wages are "sticky" or predetermined. With a fixed nominal wage, a higher price level reduces the real wage (W/P), inducing firms to hire more labor and produce more output, resulting in an upward-sloping aggregate supply curve. Source: McCallum, p. 89, 99.

The nominal interest rate R is the opportunity cost of holding money. When R increases, the demand for real money balances (M/P) decreases. Since velocity (V) is the ratio of nominal income (PY) to nominal money (M), we have \(V = PY/M = Y/(M/P)\). If M/P decreases, V must increase. Intuitively, when it's more costly to hold money, people spend it faster. Source: Mizen, p. 154, 165.

The Fisher effect, or Fisher hypothesis, states that in the long run, the real interest rate is determined by real factors and is independent of monetary variables. Therefore, the nominal interest rate must fully adjust to changes in the expected rate of inflation to keep the real rate constant. A one percentage point increase in expected inflation will lead to a one percentage point increase in the nominal interest rate. Source: Mizen, p. 169.

When people begin to anticipate inflation, the nominal interest rate rises. This increases the opportunity cost of holding money, causing them to reduce their desired real money balances. This reduction in M/P is achieved through a one-time jump in the price level (or a temporary period where prices rise faster than money). This is equivalent to a permanent increase in the velocity of money. The overall price increase reflects both this velocity adjustment and the new, higher rate of money creation. Source: Mizen, p. 169, 172.

The Classical model assumes fully flexible wages and prices, which means the labor market always clears at the full-employment level, resulting in a vertical aggregate supply curve at potential output \(y^*\). The Keynesian model assumes that nominal wages are "sticky" or predetermined. With a fixed nominal wage, a higher price level reduces the real wage (W/P), inducing firms to hire more labor and produce more output, resulting in an upward-sloping aggregate supply curve. Source: McCallum, p. 89, 99.

This is the standard Laffer curve argument. If the tax rate (inflation) is in the elastic region of the demand curve for the tax base (real balances), it means the government has gone "over the top" of the Laffer curve. A further increase in the inflation rate would cause real balances to fall by a more-than-proportionate amount, leading to a decrease in total real revenue. To increase revenue, the government would need to lower the inflation rate. Source: Cagan, p. 81.

Friedman's crucial first point in his 1956 restatement was to reframe the quantity theory not as a mechanical theory of the price level, but as a theory of the demand for money. He argued it is a stable function of a limited number of variables. The stability of this demand function is the key proposition that allows changes in the money supply to have predictable effects on nominal income. Source: Mizen, p. 153.

In Cagan's model, the term \(\alpha\beta\) is the 'reaction index', where \(\alpha\) is the semi-elasticity of money demand and \(\beta\) is the coefficient of expectation adjustment. If \(\alpha\beta < 1\), the model implies a stable dynamic equilibrium. This means that after a shock, the price level will not explode but will converge back to a stable path determined by the underlying money supply process. Source: Cagan, p. 65.