Inflation

Value of money

1/P (the value of $1 in goods); inflation raises P and lowers the value of money

Velocity formula (transactions)

V = T / M (T = value of all transactions, M = money supply)

Velocity formula (GDP)

V = (P × Y) / M

Quantity equation

M*V=P*Y

Money demand function

(M/P)^d=L(r+Eπ,Y)

Quantity theory of money

Theory linking inflation to money growth; assumes V is constant and exogenous

Quantity equation in growth rates

ΔM/M + ΔV/V = ΔP/P + ΔY/Y

Quantity theory assumption about ΔV/V

ΔV/V = 0 (V is constant)

Inflation rate (π)

π = ΔP/P

Quantity theory inflation equation

π=ΔM/M−ΔY/Y

Money growth beyond real output growth

Leads to inflation

Evidence for the quantity theory

Higher money growth countries have higher inflation; long-run trends in U.S. inflation and money growth match

Seigniorage

The "revenue" the government raises by printing money

Real interest rate (r)

Interest rate adjusted for inflation: r = i − π

Fisher equation

i = r + π

Fisher effect

An increase in inflation causes an equal increase in the nominal interest rate (one-for-one)

Expected inflation (Eπ)

The inflation rate people expect; actual π isn't known until after it occurs

Ex ante real interest rate

i-Eπ

Ex post real interest rate

i − π

How money demand depends on i and Y

Negatively on i; positively on Y

Long-run money market equilibrium

M/P = L(r + Eπ, Y)

What determines M in the long run?

Exogenous (the Fed)

What determines Y in the long run?

Production function: Y = F(K, L)

What determines P in the long run?

Adjusts so that M/P = L(i, Y)

Shoeleather cost

Costs and inconveniences of reducing money balances to avoid the inflation tax (more trips to the bank)

Menu costs

The costs of changing prices (e.g., printing new menus or catalogs)

Relative price distortions

Firms change prices at different times, so relative prices get out of line, causing inefficient resource allocation

Unfair tax treatment (inflation)

Some taxes (e.g., capital gains) aren't adjusted for inflation, so you pay tax on a nominal gain that isn't a real gain

General inconvenience of inflation

Harder to compare nominal values over time, complicating long-range planning

Five costs of expected inflation

Shoeleather, menu costs, relative price distortions, unfair tax treatment, general inconvenience

Cost of unexpected inflation

Arbitrary redistribution of purchasing power

Hyperinflation

Inflation above 50% per month

Cause of hyperinflation

Excessive money supply growth (printing money)

Neutrality of money

Changes in the money supply do not affect real variables (approximately true in the long run)