Causes of Inflation: Quantity theory of money

inflation

ongoing process of persistently rising prices year on year

→ increase in average prices

price

rate at which money is exchanged for a good or a service

quantity theory of money

theory that links the inflation rate to the growth rate of money

M = money supply

V = velocity of money

P = price level (GDP deflator)

Y = real GDP

→ PY = nominal GDP = value of output

money velocity

number of times the average pound changes hands in a given time period

V = value of transactions/money supply

• eg 50 loaves of bread, £2 per loaf → value of transactions = 100

• V = 100/20 = 5

money demand function

M/P = real money balances = measures the purchasing power of the quantity of money

(M/P)^d = kY → money demand function

• k shows how much money people want to hold for every unit of income

money demand function & quantity equation

assume demand for real balances equals supply → (M/P)^d = M/P

kY = M/P → M1/k = PY

if V = 1/k then MV = PY

implications of money demand function & quantity equation

if demand for money for each unit of income is high → large k, then money changes hands infrequently (small V)

assumption of constant velocity: implication

if we assume velocity is constant then the quantity equation is interpreted as the quantity theory of money

→ change in M must cause a proportional change in nominal GDP

→ Y is determined by FoP and production function so nominal GDP (PY) only changes due to changes in price level (P)

→ therefore the P is proportional to M

how inflation is generated: growth version of quantity equation

growth version of quantity equation shows how the inflation rate (%P) depends on the growth rate of M, V, Y

money demand

depends inversely on the interest rate on other financial assets/market interest rate → opportunity cost of holding money

market rate = real interest rate when there is no inflation → rm = r

money demand in an inflationary world

Fischer equation

only consider anticipated change in money supply so consider economy being at the full employment output level

IS/LM curve

• LM plotted against rm and depends on real money supply

• IS depends on real interest rate r

• vertical gap between rm and r measures the inflation rate at income level y*

assume fixed output Y*: increase in M^s

an increase in M^s if prices are unchanged → LM shifts outward → pushes down the price of money = nominal interest rate

→ decrease in real interest rate

→ stimulated borrowing & spending → excess demand → price must increase until it matches the increase in M

→ pushes real money balances back to original real money → end of boom period

assume fixed output Y*: rising Y

excess supply → prices must fall → real money supply increases (M bar/P)

→ %ΔP = %ΔM - %ΔY

assume constant velocity so P falls by the same amount as the increase in Y

assume fixed output Y*: fall in k

k = propensity to hold money

k decreases due to contactless payments eg → real money demand falls

→ if price is constant then LM shifts outward

(M bar/P) = kYbar → (M bar/P)1/k = Y bar

yet no equilibrium until price increases to offset the tendency of fall in money demand that shifts LM

→ 𝛑 = %ΔP = %ΔM + %ΔV - %ΔY

inflation generated equation

• effects of inflation on velocity & real GDP are uncontrollable

• monetary authorities have trend growth rate in the money supply to control the trend rate of inflation precisely (1-1 relationship)

implications of growth theory of money for economies

→ implies that countries with high money growth rates should have higher inflation rates

→ across time the LR trend in a country’s inflation should be similar to the LR trend in the country’s money growth rate

how is inflation affected when the growth rate of money supply is increased?

assume %ΔM^s increases

→ LM0 shifts outward to LM1

constant inflation at 𝛑0: fall in rm and r → creates excess demand for goods

→ upward pressure on inflation → overshooting P → real money supply starts shrinking → shifts LM in opposite direction (inward)

how does the economy move from LM0 to LM1? (overshooting)

real money supply falls due to:

• higher money supply growth rate

• fall in money demand

→ extra effect on money demand occurs at the point in time at which the money supply growth rate increased if everything works instantaneously

how does a higher money supply growth rate cause a fall in money demand?

→ higher inflation & nominal interest rate

→ higher opportunity cost of holding money

→ people reduce demand for money

→ further induces additional excess demand for goods & services

→ raises price level

graph of overshooting

z = increase in the growth rate money supply eg covid

the price level and money supply

• when money supply growth rate rises, some is regarded as temporary and some as permanent

→ tendency for P to rise but in a steady fashion and at a higher rate than the growth rate of money supply = overshooting

how does this growth rate of M being temporary affect future inflation?

if people think the increase is temporary, they don’t raise their LR inflation expectations

→ nominal interest rate doesn’t increase → money demand only declines by a negligible amount

→ not much pressure on inflation rate: at z there is no overshooting effect as only force on inflation is growth rate of money supply itself

permanent?

the longer the new higher growth rate of M^s persists then more people will believe in permanency of the higher growth rate money supply

→ adjust inflation expectations to be higher in the long run

→ increases nominal interest rate → decreases real demand for money → inflation rises

outcome

→ new equilibrium as LM moves enough to raise rm above r by amount of new higher inflation

→ r and y unaffected

→ nominal interest rate is higher, inflation higher, money supply growth rate is higher

policy implications

• not possible for BoE to permanently lower interest rate by increasing money supply

• increase in growth rate of money supply produces a rise in the inflation rate and a rise in rm

  • initially possible to have a temporary fall in rm

social costs of inflation

• costs of expected inflation

• costs of unexpected inflation

expected: shoe leather cost

• real money balances reduced due to inflation tax

• nominal interest rate is high due to high inflation

• people want to hold just enough cash for their immediate consumption and deposit rest in back to earn interest

→ same monthly spending but lower average money holding → frequent trips to bank to withdraw smaller amounts of cash

expected: menu cost

• induces firms to change posted prices on menus more often

• eg stores regularly print and mail out new catalogues

• higher the inflation the more frequently firms must change prices and incur costs

expected: relative price distortions

• as a result of menu costs firms change prices infrequently so some prices do no keep up with inflation

• different firms change their prices at different times leading to relative price distortions that causes micro inefficiencies in allocation of resources

unexpected: tax treatment

• some taxes eg capital gains are not adjusted to account for inflation

• may accumulate wealth through nominal gain in stocks

• yet with high inflation there may be no real capital gain but will have to pay tax on the nominal gain

unexpected: general inconvenience

• inflation makes it harder to compare nominal values from different time periods

• complicates long term financial planning

• eg saving for uni education, retirement

unexpected: arbitrary redistribution of purchasing power

• many long term contracts (loans, fixed pensions) are not indexed but based on E𝛑

• if 𝛑 is different from E𝛑 then some gain at others’ expenses

• 𝛑>E𝛑 → purchasing power transferred from lenders to borrowers & vice versa

additional cost: increased uncertainty

high inflation is more variable and unpredictable

→ arbitrary redistributions of wealth are more likely which increases uncertainty, making risk-averse people worse off

benefits of inflation

• costs of inflation favour 0 inflation yet may not be optimal

• moderate inflation of 2-3% may be better as it helps adjust real wages without nominal cuts if there is a significant decrease in inflation

• non-0 inflation may facilitate labour market flexibility