Macroeconomics – A European perspective
Chapter 2: A Tour of the Book
GDP (gross domestic product) is the measure of aggregate output, which we can look at from the
production side (aggregate production) or the income side (aggregate income)
Aggregate production and aggregate income are always equal
Three definitions of GDP
o GDP equals the value of the final goods and services produced in the economy during a given period (production side)
o GDP is the sum of value added in the economy during a given period (production side) o GDP is the sum of incomes in the economy during a given period (income side)
Nominal GDP (€Y): sum of the quantities of final goods produced multiplied by their current prices
Real GDP (Y): Sum of the production of final goods multiplied by constant prices
Level of real GDP depends on the base year, but the rate of change from year to year remains the same
GDP growth rate:
GDP deflator inflation: measure of the increase in the price level of the goods produced in the economy
during a given year: growth rate of nominal GDP – growth rate of real GDP =
Inflation: sustained rise in the price level > 1
Deflation: sustained decline in the price level < 1
Two price indexes:
o GDP deflator: ration of nominal to real GDP: o Consumer price index: average price of goods consumed in the economy
(set equal to 100 in the base period)
Rate of change in the GDP deflator = rate of inflation:
Employment (N): number of people who have a job
Unemployment (U): number of people who do not have a job but are looking for one
Labour force:
Unemployment rate:
Participation rate = labour force/population of working age
Determining factors for the level of aggregate output: o Short run (a few years): demand
o Medium run (a decade): supply factors: capital stock, level of technology, labour force o Long run (a few decades or more): education system, saving rate, role of the government
Chapter 3: The Goods Market
Consumption (C): purchase of goods and services by consumers
o Consumption function: ,
Consumption depends on disposable income (YD), the income that remains after consumers
have received transfers from the government and paid their taxes o
= marginal propensity to consume: effect, that an additional euro of disposable income has on consumption (must be positive, but less than 1)
= autonomous consumption: what people would consume if their disposable income
were equal to zero (the intercept of the consumption function) (income – taxes)
o
Investment (I): purchase of capital goods: sum of non-residential investment (purchase by firms of new
machines) and residential investment (purchase by people of new houses) o Exogenous variable (taken as given): ̅
Government spending (G): purchases of goods and services by the governments
o G and T are given as exogenous variables
Imports (IM): purchases of foreign goods and services by domestic consumers, firms and the
government must be subtracted
Exports (X): purchases of domestic goods and services by foreigners must be added
Net exports = trade balance: difference between exports and imports (X – IM) o : trade balance
o : trade surplus o : trade deficit
Inventory Investment: difference between production and sales (equals zero in this model)
Total demand for goods (Z):
Assumptions in the short run:
o Closed economy no imports or exports
̅
o Firms are willing to supply any amount of the good at a given price – thus output is determined by demand production equals demand, no inventory investment
equilibrium in the goods market:
̅ ̅ ̅
̅
o ̅ = part that does not depend on output: autonomous spending (positive when G = T)
o
> 1 since is between 0 and 1, the closer is to 1, the larger the multiplier
Any effect on autonomous spending will change output by more than its direct effect
Increase in G (= an increase in autonomous demand) leads to an increase in Y:
Increase in T leads to a decrease in Y, whether it’s larger or less than -1 depends:
Increase in G financed by an increase in T keeps the budget balanced: Output increases by the same amount, “balanced budget multiplier”
First round:
o Increase in demand equals €1 billion (A – B) o Equal increase in production (A – B)
o Equal increase in income (B – C)
Second round:
o Increase in demand equals €1 billion times the propensity to consume = (C – D) o Equal increase in production (C – D)
o Increase in income (D – E)
Third round:
o Increase in demand equals billion billion
Total increase in production after rounds: ∑
multiplier!
Increase in (autonomous) demand increase in production increase in income
Result: increase in output that is larger than the initial shift in demand, by a factor equal to the
multiplier
In response to an increase in consumer spending, firms increase their production successively
Saving: sum of private and public saving = Investment
o Private saving (S): o Public saving: : budget surplus : budget deficit o ̅ ̅ ̅
IS relation: investments = saving (sum of private and public saving)
what firms want to invest = what people and the government want to save o
is the marginal propensity to save, which states how much of an additional unit of income people save
o In equilibrium: ̅
̅
o Paradox of saving: People want to save more, but since ̅ stay constant and
̅ , private saving does not change and a reduction in is compensated by a reduction in ̅
Chapter 4: The Financial Markets
Income: money earned from working or received in interest and dividends
flow variable, expressed in units of time (e.g. monthly income)
Saving: part of after-tax income that is not spent, flow variable
Financial wealth: value of all financial assets minus all financial liabilities, stock variable
(value of wealth at a given moment in time)
Investment: purchase of new capital goods (e.g. machines, buildings) financial investment
Money: can be used for transactions, pays no interest, two types: currency and checkable deposits
Bonds: pay a positive interest rate ( ) but cannot be used for transactions
Wealth = money demand + bond demand Bond demand = Wealth – money demand
Increase in wealth Increase in bond demand, no effect on money demand (depends on and )
Increase in income Increase in money demand, decrease in bond demand, since wealth does not
change right away when people earn more income and is therefore considered as constant
Proportions of money and bonds depend on two variables:
o Level of transactions (enough money on hand to avoid having to sell bonds constantly) o Interest rate on bonds
Money demand: amount of money people want to hold:
money demand is equal to nominal income multiplied by a function of the interest rate ( ) o Demand for money increases in proportion to nominal income/level of transactions o Demand for money decreases if the interest rate increases
curve is downward sloping (the lower the interest rate, the higher the demand for money)
Equilibrium on the money market must imply also an equilibrium on the bond market
Money supply is independent of the interest rate
In equilibrium, money supply must be equal to money demand : : LM relation
1. An increase in nominal income leads to an increase in the interest rate
(higher income leads to an increased demand for money that exceeds the supply, so an increased interest rate is needed to decrease the amount of money people want to hold)
Interest rate on bonds: value of the bond in one year (e.g. 100) in comparison to today:
Price of a one-year bond today:
the higher the interest rate, the lower the price today, if prices of bonds increase interest rates decrease
Balance sheet of the central bank: Assets are bonds, liabilities are money/currency held by the public
By changing the supply of money, the central bank can affect the interest rate open market operation
Open market operations: if the central bank wants to increase the amount of money in the economy, it
buys bonds, if it wants to decrease the amount of money, it sells bonds
o Expansionary open market operation: central bank buys bonds, more bonds and money supply (demand for bonds goes up price for bonds increases interest rate on bonds decreases) o Contractionary open market operation: central bank sells bonds, less bonds and money supply
(demand for bonds goes down price for bonds decreases interest rate on bonds increases)
Financial intermediaries: institutions which receive funds from people/firms (=liabilities) and use these
funds to buy financial assets (bonds/stocks) or to make loads to other people/firms (=assets) banks
o = proportion of the money people hold in currency; the rest in bonds
o = number of deposit accounts; = amount people want to hold in deposits
o = reserve ration, the amount of reserves banks hold per euro of deposit accounts
o Demand for central bank money:
Higher interest rate: demand for currency and demand for deposit accounts by people go down lower demand for central bank money
Determination of the interest rate: supply of central bank
money = demand for central bank money:
Overall supply of money is equal to central bank money (=monetary base) multiplied by a term
money multiplier (constant!)
Other ways to think about the interest rate:
o Equality of overall supply of money to central bank money times the money multiplier
o equality of the supply and demand for bank reserves (Interbank market: market for bank reserves)
Chapter 5: The IS – LM Model
Investment is in fact not constant, but depends on the level of sales and the interest rate:
o increase sales/production increase investment; increase interest rate decrease investment
New IS relation:
Equilibrium in the goods market: demand for goods must be equal to the output
Demand for goods is an increasing function (not linear!) of output, since an increase in output leads to
an increase in disposable income/consumption and to an increase in investment
Demand curve is flatter than the 45°line, since an increase in output leads to a less than one-for-one increase in demand
1. An increase in the interest rate decreases the demand for goods at any level of output, leading to a decrease in the equilibrium level of output
2. Equilibrium in the goods market implies that an increase in the interest rate leads to a decrease in output. The IS curve is therefore downward sloping
Higher interest rate is associated with a lower level of
output
IS curve gives the equilibrium level of output as a
function of the interest rate
Increase of taxes (at a given interest rate):
disposable income decreases decrease in consumption decrease in the demand for goods decrease output IS curves shifts to the left, lower output, constant
Any factor that decreases the demand for goods/output (for a given interest rate), causes the IS curve to shift to the left (e.g. decrease in government spending, decrease in consumer confidence), any factor that increases the demand for goods/ output causes the IS curve to shift to the right (e.g. decrease tax)
Real income: nominal income divided by the price level (P):
Assumption: price level is fixed in the short run (but not in the medium run!)
Short run: increase in the interest rate decrease in output, increase in unemployment
Equilibrium condition: real money supply (money stock in terms of goods)= real money demand
1. Increase in income (at a given interest rate) increase in money demand increase interest rate (since the money supply is fixed, the interest rate must go up until the two opposite effect – the increase in income that leads people to want to hold more money and the increase in the interest rate that leads people to want to hold less money – cancel each other to reach a new equilibrium)
2. Increase in income increase in the interest rate LM curve upward sloping
General: the higher the level of output, the higher the demand for money, the higher the interest rate
Changes of money supply shift the LM curve: o money supply increases interest rate
decreases LM curve shifts down o money supply decreases interest rate
increases LM curve shift up
LM relation as an interest rate rule:
1. Depending on whether and by how much the central bank increases the money supply in
response to a shift in money demand coming from changes in income, the interest rate may remain constant, increase a little or increase a lot
2. The LM curve shows whether and by how much the central bank allows the interest rate to increase in response to increases in income
IS relation: increase in the interest rate leads to a
decrease in output downward sloping
LM relation: increase in output leads to an increase in
the interest rate upward sloping
Any point on both curves corresponds to an equilibrium
in the goods market/in the financial market
Only at point A are both markets in equilibrium
Fiscal expansion: increase in the deficit (e.g. by increase
in government spending, decrease in taxes)
increase output, interest rate; IS curve shifts to the right
Fiscal contraction/consolidation: decrease in the deficit
Example: increase in taxes
o IS curve: people have less disposable income, decrease in consumption, output and interest rate shift to the left
o LM curve: nothing, taxes do not appear in the LM relation
New equilibrium at a lower interest rate, since the decrease in output/income reduces the demand for money and therefore the interest rate decreases as well
two contradictory effects on investment: lower output means lower sales and lower investment, but a lower interest rate also leads to higher investment, question is which effect dominates
Monetary expansion: increase in money supply one-for-one increase in real money (since P fixed) o IS curve: M does not appear in the IS relation, IS curve doesn’t shift
o LM curve: increase in money supply, output decrease interest rate LM curve shifts down economy moves along the IS curve, output increases (lower interest rate leads to an increase in investment and, in turn, to an increase in demand and output)
Monetary expansion is more investment-friendly than a fiscal expansion
Monetary contraction: decrease in money supply, output increase interest rate LM curve shifts up
(Monetary-fiscal) policy mix: combination of fiscal and monetary policy
Liquidity trap:
1. As the interest rate decreases, people want to hold more money, demand for money increases
(increase in the money supply still leads to a decrease in the interest rate)
2. When the interest rate is equal to zero and once people have enough money for transaction
purposes, they become indifferent between holding money and bonds
demand for money becomes horizontal, willingness to hold even more money since = 0 further increases in the money supply have no effect on the interest rate
once the interest rate is equal to zero, expansionary monetary policy becomes powerless
IS relation: supply of goods = demand for goods interest rate affects the output moves left/right
LM relation: supply of money = demand for money, output affects the interest rate moves up/down
For low levels of output, the LM curve is a flat segment, with an interest rate equal to zero.
For higher levels of output, it is upward sloping: an increase in income leads to an increase in the interest rate.
Dynamics: time is needed for output to adjust to changes in fiscal and monetary policy
(e.g. consumers take time to adjust their consumption after a change in disposable income, firms take time to adjust investment after a change in their sales/the interest rate)
If the interest rate is zero, further increases in the money supply have no effect on the interest rate.
1. Increased money supply LM curve shifts from LM to LM’ higher output
2. Increases money supply LM curve shifts from LM’ to LM’’ equilibrium remains at point B, output remains equal to Y’ (liquidity trap, people hold additional money)
Chapter 6: The IS-LM Model in an Open Economy
Now: Open economy – three dimensions:
1. Openness in goods markets (choice between domestic and foreign goods, but: tariffs and quotas) 2. Openness in financial markets (choice between domestic and foreign assets, but: capital controls) 3. Openness in factor markets (choice where to locate production, where to work)
Appreciation of the domestic currency: increase in the price of the domestic currency in terms of a
foreign currency (increase in the exchange rate )
Depreciation of the domestic currency: decrease in the price of the domestic currency in terms of a
foreign currency (decrease in the exchange rate )
Revaluations and devaluations: increases/decreases in the exchange rate, when countries operate
under fixed exchange rates
Real exchange rate: price of domestic goods in terms of foreign goods (relative price)
if exchange rate increases by 10%, this means that domestic goods are 10% more expensive than foreign goods
Nominal exchange rate ( ):
1. Price of the domestic currency in terms of the foreign currency (0,77€ = 1$) 2. Price of the foreign currency in terms of the domestic currency (1,3$ = 1€)
From nominal to real exchange rates: multiplying the domestic price level by the nominal exchange rate
and dividing it by the foreign price level: = real exchange rate index number, uninformative 1. P = domestic price level (GDP deflator of the home country), P*= foreign price level (GDP deflator) 2. E = nominal exchange rate
If inflation rates were exactly equal, would be constant and and would move together
Real appreciation: increase in the relative price of domestic goods in terms of foreign goods
increase in the real exchange rate
Real depreciation: decrease in the relative price of domestic goods in terms of foreign goods
decrease in the real exchange rate
Multilateral real exchange rate: weighted average of bilateral real exchange rates, with the weight for
each foreign country equal to its share in trade
Openness in financial markets: most of the transactions are associated with purchases and sales of financial assets, not with trade
Due to the openness in financial markets, a country can run trade surpluses and trade deficits
Balance of payments (summary of a country’s transactions with the rest of the world):
1. Current account: payments to and from the rest of the world: exports, imports, investment income, foreign aid = net transfers received (negative amount reflects a net donor of foreign aid) Sum = current account balance (current account surplus/current account deficit)
2. Capital account: country that runs a current account deficit must finance it through positive net capital flows, it must run a capital account surplus; the capital account thus describes how this was achieved capital account balance/net capital flows = increase in foreign holdings of domestic assets – increase of domestic holdings of foreign assets capital account surplus/ deficit current account balance and capital account balance should be equal, but mostly they aren’t
GDP (gross domestic product): value added domestically (within the country)
GNP (gross national product): value added by domestically owned factors of production
from GDP to GNP by adding factor payments received from the rest of the world and subtracting factor payments paid to the rest of the world GNP = GDP + net factor payments
Choice between domestic interest-paying assets and foreign interest-paying assets
Assumption: investors only hold the asset with the
highest expected rate of return, if both bonds are to be held, they must have the same expected rate of return: (
)
( = expected nominal exchange rate)
(Uncovered) interest parity relation:
(
)
Expected rate of appreciation of the domestic currency = Approximation: domestic interest rate = foreign interest rate – expected rate of appreciation of the domestic currency (arbitrage by investors)
lower interest rate can be compensated by an appreciation of the currency higher than the difference between the two interest rates
If the expected exchange rates remain fairly constant, the expected depreciation will be equal to zero and therefore the interest rates move together if
IS Relation in an Open Economy
Domestic demand for goods ≠ demand for domestic goods, since part of domestic demand falls on foreign
and part of foreign demand falls on domestic goods
Demand for domestic goods:
domestic demand for goods minus imports divided through the real exchange rate (value of imports in terms of domestic goods) plus exports (in units of domestic goods)
Imports: higher domestic income + higher real exchange
rate higher imports: deterioration of the trade balance
Exports: higher foreign income + lower real exchange
rate higher exports:
Marshall-Lerner-condition: quantity of imports increases
and exports decreases with the real exchange rate 1. Domestic demand for goods is an increasing function of
income (output). Subtraction of imports leads to AA, the domestic demand for domestic goods. The distance between DD and AA equals the value of imports. AA is flatter than DD, as income increases the domestic demand for domestic goods increases less than total domestic demand
2. Demand for domestic goods (ZZ) is obtained by adding the exports to AA. The distance between ZZ and AA equals exports. Exports do not depend on domestic income distance between ZZ and AA is constant 3. Trade balance (net exports=NX) is a decreasing function
of output: as output increases, imports increase and exports are unaffected, so net exports decrease.
New equilibrium in the goods market:
LM Relation in an Open Economy
Equilibrium is still , since foreign residents won’t hold
foreign currency, but rather foreign bonds
Domestic vs. foreign bonds: in equilibrium, both domestic and
foreign bonds must have the same expected rate of return, otherwise investors would only hold one or the other:
( ) ̅ o Increase in increase in (appreciation)
o Increase in decrease in (depreciation) o Increase in ̅ increase in (appreciation)
If ̅ : to compensate investors for the expected
depreciation of the domestic currency
If ̅ : to compensate investors for the expected depreciation of the foreign currency (appreciation domestic currency)
If ̅
Relations in the open economy:
̅
Two effects of an increase in the interest rate on output ( steeper IS curve)
1. Direct effect on investment: higher interest rate decrease in investment decrease in output 2. Indirect effect through the exchange rate: increase in the domestic interest rate increase in the
exchange rate (an appreciation) domestic goods are more expensive relative to foreign goods decrease in net exports decrease in the demand for domestic goods decrease in output The goods market is in equilibrium when
domestic output is equal to the demand for domestic goods (Y=Z). At the equilibrium level of output, the trade balance may show a deficit or a surplus (before: ).
In the short run: prices are assumed to be constant, so real exchange rate = nominal exchange rate could be replaced by
IS curve: downward sloping: an increase in the interest rate leads to lower output
LM curve: upward sloping: given the real money stock , an increase in output leads to an increase in
the demand for money and to an increase in the equilibrium interest rate
Chapter 7: The Labour Market
Labor force: sum of those either working or looking for work
Participation rate: ration of the labour force to the population in working age non-participation rate
Unemployment rate: ration of the unemployed to the labour force
Given unemployment rate reflects two different realities:
o Active labour market: many separations and hires, thus with many workers entering and exiting unemployment (average duration of unemployment is low)
o Sclerotic labour market: few separations, few hires and a stagnant unemployment pool (average duration of unemployment is high)
Two types of separations:
o Quits: workers leaving their job for a better alternative o Layoffs: effect of changes in employment level across firms
Discouraged workers: not actively looking for a job, but would take one if they found one
Non-employment rate: ratio of working age population minus employment to population
Average duration of unemployment equals the inverse of the proportion of unemployed leaving unemployment each month
Unemployment rate: flows x duration
(flows of workers becoming unemployed each month x average time they stay unemployed)
Wage determination:
Collective bargaining: bargaining between firms and unions
(Individual) bargaining power: the higher the skills needed for a job, thus the more costly it is for the
firm to replace the worker (nature of the job), and the easier it is for the worker to find another job (labour market conditions), the more bargaining power he has
Implication of a low unemployment rate (high unemployment rate vice versa):
o More difficult for firms to find acceptable replacement workers o Easier for workers to find other jobs
stronger bargaining position the lower the unemployment rate, the higher the wages
Reservation wage: wage that would make workers indifferent between working or being unemployed
workers are typically paid a wage that exceeds their reservation wage
Reasons for the firms to pay more than the reservation wage:
o They want the workers to stay for some time(lower turnover rate)
o They want their workers to feel good about their jobs, since that promotes good work and leads to higher productivity efficiency wage theories (labour productivity is related to the wage) Wage depends on nature of the job and labour-market conditions
Wage determination:
o = expected price level: workers and firms don’t care about the nominal, but the real wages: workers: nominal wages they receive (W) relative to the price of the goods they buy (P)
firms: nominal wages they pay (W) relative to the price of the goods they sell (P)
An increase in the expected price level leads to a proportional increase in the nominal wage o = unemployment rate: increase in the unemployment leads to a decrease in the nominal wage o = other factors that may have an impact such as unemployment benefits (replacement rate*,
duration of benefits), the level of employment protection (the higher the protection, the more expensive are lay-offs) or the presence of a minimum wage set by the law
An increase in leads to an increase in nominal wage (per definition)
* Replacement rate: fraction of the last wage which the social security administration provides to a person if he or she no longer works
Price determination
Production function (relation between inputs and outputs): (for A=1: )
= output, = employment, = labour productivity (output per worker, constant)
Price setting: is the mark-up of the price over the cost and depends on the degree
of competition in the market. If goods markets were perfectly competitive, would equal zero and the price ( ) would equal the marginal cost ( )
Natural Rate of Unemployment
Wage-setting relation:
Negative relation between the expected real wage and the unemployment rate: the higher the unemployment rate, the lower the expected real wage (as a result of weaker bargaining position)
Price-setting relation:
price-setting decisions determine the real wage paid by firms (constant!): an increase in the mark-up leads firms to increase their prices, so even if the nominal wage remains the same, the real wage decreases since less goods can be purchased for the same money higher mark-up lower real wage
Equilibrium labour market: real wage expected by wage setting = effective real wage paid by firms
equal, when expected price level = effective price level
resulting equilibrium unemployment rate : natural rate of unemployment 1. Increase in unemployment benefits:
Prospect of unemployment less painful, increase in the reservation wage
Increase in the nominal wage desired by wage setters for a given expected price level
Upward shift of the wage-setting relation (WS to WS’)
At the initial equilibrium rate of unemployment, the expected real wage is higher than the effective real wage
Higher unemployment rate is needed to bring the expected real wage back to what firms are willing to pay
2. Less stringent enforcement of anti-trust legislation
Firms collude more easily, increased market power
Increase their mark-up ( )
Decrease in the effective real wage firms pay
Downward shift of the price-setting relation (PS to PS’)
At the initial equilibrium rate of unemployment, wage setters still expect the real wage they were getting before, increased equilibrium rate of unemployment to force workers to accept a lower real wage
Relation unemployment, employment, labour force:
Natural level of employment:
Natural level of output: level of production when employment = natural level of employment
(
)
Natural level of output is such that, at the associated rate of unemployment, the real wage expected in wage setting (left side) = effective real wage implied by price setting (right side)
In the medium run, unemployment tends to return to the natural rate and output to the natural level
Chapter 8: The AS-AD Model
Assumption: constant money stock, no nominal money growth (no inflation) AS-AD model describes movements in output and the price level
Aggregate supply relation: effects of output on the price level, derived from equilibrium in labour market:
(wage determination), (price determination) (for A=1)
( ) AS relation
Increase in output ( ) leads to an increase in the price level ( ):
Increase in output increase in employment decrease in the unemployment rate increase in the nominal wage increase in the prices increase in the price level
Increase in the expected price level ( ) leads to a proportional increase in actual price level ( )
Higher expected price level higher nominal wage increase in costs increase in the prices set by firms higher actual price level
AS-curve :
Upward sloping: increase in output
increase in price level
At point A: when output is equal to the natural level of output, the price level is exactly equal to the expected price level
When output is above (below) the natural level of output, the price level is higher (lower) than expected higher expected price level lower real wage reduced labour supply lower employment ( ) leads to lower output, since
Increase in the expected price level: upward shift of the AS-curve (Output remains on the same level!)
increase in the expected price level increase in wages increase in prices higher price level
Decrease in the expected price level: downward shift of the AS-curve (Output remains on the same level!)
Aggregate demand relation: effect of the price level on output, derived from the equilibrium conditions
in the goods and financial markets:
o Goods market equilibrium: (output = demand goods: IS relation) o Financial market equilibrium: (supply = demand for money: LM relation)
At the intersection of the IS curve and the LM curve (A) both goods market and financial markets are in
equilibrium
Increase of the price level from P to P’
Decrease of the real money stock (at a given level of output)
Increase in the interest rate , decrease investment Decrease of demand and thus output
upward shift of the LM curve along the IS curve
Negative relation between output and price level is drawn as the downward-sloping AD curve: increase in the price level leads to a decrease in output
Any variable (other than ) that shifts either the IS curve or the LM curve also shifts the aggregate demand relation
Example: increase in government spending (G)
at a given price level level of output increases AD curve shifts right
Example: decrease in the nominal money stock (M) at
a given price level decrease of output AD curve shifts to the left
Composition of the As and the AD relation
o AS relation: ( ) o AD relation: ( )
Given: , determination of the equilibrium values of output and price level
(first characterisation of equilibrium in the short run, since is given there)
Equilibrium in the short run:
AS curve drawn for a given value of (shift), upward sloping (the higher the level of output, the higher the price level; in B: )
AD curve drawn for given values of (shift) downward sloping (the higher the price level, the lower the level of output)
Equilibrium of goods, financial and labour market in A
In the short run, there is no reason why output should equal the natural level of output, so
From the short run to the medium run:
In the short run, price level higher than the expected price level. So wage setters are likely to make the next decision based on a higher expeced price level
( )
Higher expected price level higher nominal wage
higher price level lower demand and output.
upward shift of the AS curve
As long as equilibrium output exceed the natural level of output, the AS curve shifts upwards
Ends, when equilibrium output = natural level of output price level = expected price level
(same procedure for )
In the medium run, output returns to the natural
level of output
The Effects of a Monetary Expansion (shift AD)
Given price level: increase in nominal money = increase in the real money stock ( ) decrease in the interest rate
increase in output
AD curve shifts to the right
In the short run: new equilibrium at point A’
In the medium run: adjustment of price level
expectations AS curve shifts up until output reaches its natural level (price level equals the expected price level) equilibrium at A’’
Proportional increase in prices = proportional increase in the nominal money stock
( ( ): fixed, so and must increase in the same proportion)
Background: increase in nominal money downward shift of the LM curve decreasing interest rate,
increasing output over time, price level increases, shifting the LM curve back to the natural level of output (if the price level did not increase, the shift in the LM curve would be larger)
In the short run, monetary expansion leads to an increase in output, a decrease in the interest rate and an increase in the price level. In the medium run, the increase in nominal money is reflected in a
proportional increase in the price level, no effect on output or the interest rate
A Reduction in the Budget Deficit (shift AD)
Budget deficit, government decreases its spending from G to G’ (fiscal contraction), taxes unchanged
Output initially at natural level, decrease in G reduces the demand for goods and output, AD curve shifts to the left
In the short run: new equilibrium at A’, output below the
natural level of output
In the medium run: decrease in the price level, increase in
the real money stock, decrease in the interest rate, downward shift of the AS curve until output returns to the natural level of output
Price level and the interest rate are lower , investment higher than before
Background: reduction of the budget deficit IS curve shifts to the left decrease in output price
level declines real money stock increases downward shift of the LM curve (lower output + interest rate)
As long as output remains below the natural level of output, price level continues to decline further increase in money stock LM curve shifts down until output reaches its natural level, but the interest rate is lower than before increase in investment
( unchanged, so investment must be higher by an amount exactly equal to the decrease in
In the short run: decreases, increases or decreases, in the medium run: unchanged, increases
An Increase in the Price of Oil (shift AS)
AS relation: ( )
Short run: increase in the price of oil
increase in the mark-up increase in the price level lower real wage PS (price setting) curve moves downwards contraction of demand and output
Medium run: increase in the price of oil
decrease in the real wage paid by firms increase in the natural rate of
unemployment decrease in the natural level of output
Increase in the price of oil leads in the short run to a decrease in output and an increase in the price level. Over time, output decreases further and price level increases further.
Increase in the price of oil
New AS curve goes through point B, output equals the lower natural level of output
Economy moves along the AD curve from A to A’, output decreases from to
At A’, price is higher than the expected price level
Price expectations increase, AS curve shifts further upwards
Process stops when the AS curve intersects with the AD curve at the new (lower) natural level of output
Chapter 9: The Natural Rate of Unemployment and the Phillips Curve
First step: AS relation:
Function F captures the effect of the unemployment rate ( ) and other factors ( ) on wage: :
the higher the unemployment rate, the lower the wage, the higher , the higher the wage
)
Inflation rate: ; expected inflation rate: : Relation between inflation, expected inflation and unemployment rate
o Increase in Increase in
(derived from the fact that a higher expected price level leads to an increase in the price level) o Increase in Increase in
o Increase in Decrease in (lower nominal wage lower price level decrease inflation)
(Original) Phillips curve: if the expected inflation = zero, the equation becomes:
negative relation between unemployment and inflation
Wage-price spiral: low unemployment higher nominal wage increase in prices increase of the
price level workers ask for higher nominal wages further increase in prices further increase in price level etc… steady inflation
Relation between unemployment and inflation vanished for two reasons:
o Increase in oil prices increase in prices (mark-up) increase in inflation
o Change in the way expectations were formed due to a change in the behavior of inflation: inflation became positive and persistent, leading wage setters to expect positive inflation rather than zero
o Expectations are formed according to:
parameter : effect of last year’s inflation rate on this year’s expected inflation rate the higher , the higher the significance of last year’s inflation, the higher
increased over the time, till , which means people expected this year’s inflation rate to be the same as last year’s inflation rate
o For : original Phillips curve
o For : inflation depends on last year’s inflation rate o For : unemployment influences change in inflation rate
high unemployment decreasing inflation; low unemployment increasing inflation (Modified) Phillips curve
Natural rate of unemployment: unemployment rate such that the actual inflation rate = expected
inflation rate, so
The higher the mark-up ( ) and the highter the factors that affect wage setting ( ) the higher the natural rate of unemployment
( ) higher to decrease inflation! (assuming is approximated by )
Change in the inflation rate depends on the difference between the actual and the natural
unemployment rates:
o Actual unemployment rate > natural unemployment rate inflation rate decreases o Actual unemployment rate < natural unemployment rate inflation rate increases
If unemployment return to the natural rate, output must return to its natural level; AD relation becomes ( ) If are constant, the real money stock must also be constant, so rate of inflation = rate of money growth ( ): in the medium run, inflation determined by money growth
Labour market rigidities such as unemployment insurance, employment protection, minimum wages
affect wage setting and are responsible for the high natural rate of unemployment in Europe
Another factor that supports the high natural rates of unemployment in some European countries:
price-setting behavior of firms (the level of mark-up): the higher the degree of competition (the lower
the product market regulations), the more elastic the demand, the lower the mark-up, the higher real wages and the lower natural rates of unemployment
Two measures to decrease inflation: 1. Unemployment above the natural rate
2. Increase in the unemployment rate not necessary, if wage setters expect an inflation rate as high as the actual inflation rate, so credibility of monetary policy is the point
Wage indexation: nominal wages move one-for-one with variations in the actual price level
When wage indexation is widespread, small changes in unemployment can lead to very large changes in inflation
At very low or negative rates of inflation, the Phillips curve appears to become weaker
Inflation, Money Growth and the Real Rate of Interest
Three relations in the economy:
o Relation between output growth and the change in unemployment (Okun’s law) o Relation between unemployment, inflation and expected inflation (Phillips curve) o Relation between output growth, money growth and inflation (AD relation)
Before: change in the unemployment rate equals the negative of the growth rate of output
(e.g.: if output growth 4% a year, unemployment rate should decline by 4%)
Okun’s law differs in two ways:
o Annual output growth has to be a least 3% to prevent the unemployment rate from rising (because of labour force growth and labour productivity growth)
Normal growth rate: output growth must be equal to the sum of labour force growth and labour productivity growth (=output per worker) to maintain a constant unemployment rate o Output growth 1% above normal leads only to a 0,4% reduction in unemployment rate, since
employment responds less than one-for-one to movements in output (labour hoarding) and an increase in the employment rate does not lead to a one-for-one decrease in the un employment rate since labour force participation increases as well
Okun’s law in general: ̅ - change in unemployment – output growth
o ̅ : normal growth rate
o : effect of output growth above normal on the change in the unemployment rate Output growth above normal leads to a decrease in the unemployment rate
Phillips curve (AS relation): change in inflation – unemployment
Since expected inflation is well approximated by last year’s inflation:
: effect of unemployment on the change in inflation
AD relation: ( ) Simplification: ( ) output – money growth, inflation
o Assumption: linear relation between real money balances and output: ( ) Demand for goods/output is proportional to the real money stock
o Required: relation between growth rates:
growth rate of output; : growth rate of nominal money; : growth rate of price level
o Expansionary monetary policy (high nominal money growth) high output growth
Contractionary monetary policy (low nominal money growth) low/negative output growth
Nominal interest rate ( ): the interest rate in terms of units of national currency
Real interest rate ( ): the interest rate in terms of a basket of goods
How much consumption we must give up next year to consume more today
From nominal interest rate to real interest rate by taking into account the expected inflation
1 plus the real interest rate = ratio of 1 plus the nominal interest rate divided by 1
plus the expected rate of inflation
Approximation: (if and are <20%) :
When expected inflation equals 0, nominal and real interest rates are equal
Because expected inflation is typically positive, real interest rate is lower than nominal interest rate For a given nominal interest rate: higher expected rate of inflation lower real interest rate Real interest rate can be negative when inflation > nominal interest rate ( can’t be negative!)
Nominal and real interest rates in the IS-LM model
o IS relation: in deciding how much investment to undertake, firms care about the real interest rate:
o LM relation: when people decide whether to hold money or bonds, they take into account the opportunity cost of holding money which is the nominal interest rate:
Effects of monetary policy on output depend on how movements in the nominal interest rate translate into movements in the real interest rate
Effects of money growth:
Medium run
Assumption: central bank maintains a constant growth rate of nominal money, ̅
Unemployment rate constant, so Okun’s law: ̅
̅ ̅ (output growth = normal rate of growth, ̅ )
Inflation: since nominal money growth and output growth are constant, AD relation becomes: ̅ ̅ ̅ ̅
Inflation = nominal money growth – normal output growth adjusted nominal money growth (output growth must equal real money growth, difference between nominal and real growth is inflation)
Unemployment: in the Phillips curve:
In the medium run, unemployment rate = natural rate of unemployment
In the medium run, output return to the natural level of output; for given values of G and T, the interest rate must be such that: natural real interest rate
, since in the medium run, inflation = money growth ( )
Increase in money growth leads to an equal increase in the nominal interest rate
In the medium run, money growth does not affect the real interest rate, but inflation and nominal interest rate one-for-one, thus increases in inflation are reflected in a higher nominal interest rate Fisher effect
Short run
Central bank decreases the nominal money growth:
o AD relation: lower nominal money growth lower real money growth lower output growth o Okun’s law: output growth below normal increase in unemployment
o Phillips curve: unemployment above the natural rate decrease in inflation tighter monetary policy leads to lower output growth and lower inflation
In the short run, monetary tightening leads to a slowdown in growth and a temporary increase in
unemployment. In the medium run, output growth returns to normal and the unemployment rate returns to the natural rate. Money growth and inflation are permanently lower, so the temporary increase in
unemployment buys a permanent decrease in inflation.
Short run: real and nominal interest rate go down
Medium run: low interest rates higher demand higher
output higher inflation decrease in the real money stock increase in (real) interest rates back to initial value (nominal interest rate converges to a higher value, equal to the real interest rate plus the higher rate of nominal money growth)
Higher money growth Short run Medium run
Nominal interest rate Lower Higher Real interest rate Lower No effect
IS-LM model: in the IS relation: ; LM relation: o IS curve: downward sloping: for a given expected rate of inflation, , a decrease in the nominal
interest rate leads to an equal decrease in the real interest rate, leading to an increase in spending and output
o LM curve: upward sloping: given the money stock, an increase in output, which leads to an increase in the demand for money, requires an increase in the nominal interest rate
Economy initially at the natural rate of output ( , increase of the rate of growth of money o Short run: increase in nominal money will not be matched by an equal increase in the price level
increase in the real money stock ( )
o LM curve shifts down: for a given level of output, increase in the real money stock leads to a decrease in the nominal interest rate
o IS curve doesn’t shift in the short run, since people don’t revise their expectations straight away o New equilibrium at point B: higher output, lower nominal and thus real interest rate (given )
Disinflation (decrease in inflation) can only be obtained if the unemployment rate exceeds the natural rate (Phillips curve relation: )
whether high unemployment for a few years or smaller increases in unemployment spread over many years turns out the same (point years of excess unemployment required to decrease inflation the same) central bank can only choose the distribution of unemployment over time, not the point-years
Sacrifice ratio = ratio is constant
How quickly disinflation is realized influences the reduction of output growth: to realize a disinflation within one year, the unemployment rate must by high above the natural rate for one year and the output growth reduces even by a higher percentage (since according to Okun’s law, relation between unemployment and output is not one-for-one) traditional approach
Sargent-Lucas approach: Phillips curve assumes that wage setters would keep expecting inflation in the
future to be the same as it was in the past (since ), but why shouldn’t wage setters take policy
changes directly into account?
By returning to the previous equation ( , inflation can also be reduced by people reducing their expectations, without any change in the unemployment rate
Nominal rigidities and contracts (Fisher-Taylor approach):
o many wages and prices are set in nominal terms for some time and are not readjusted when there is a policy change
o Staggering of wage decisions: wage contracts are not all signed at the same time, which imposes strong limits on how fast disinflation could proceed without triggering high unemployment decrease in nominal money growth leads to an unproportional decrease in inflation real money stock decreases recession, increase in the unemployment rate slow, but credible disinflation!
Policy makers face a trade-off between unemployment and inflation: to permanently lower inflation, higher unemployment for some time is required. With credible policies (changing the expectations), the trade-off could be more favorable.
Chapter 11: The Facts of Growth
Growth: steady increase in aggregate output over time ( fluctuations in the short and medium run)
Problems when calculating output per person: variations in exchange rates, price differences
Solution: construction of the numbers for GDP by using a common set of prices for all countries:
measures of purchasing power across time or across countries: purchasing power parity (PPP) numbers
Malthusian trap: increase in output (due to technological change etc.) decrease in mortality
increase in population output per person stays constant
Aggregate production function: relation between aggregate output and the inputs in production
Inputs: capital and labour How much capital is produced for given K, N?
State of technology: determines how much output can be produced for given quantities of K, N
the higher the state of technology, the higher
Constant returns to scale: if the scale of operation is doubled (if the quantities of capital and labour are
doubled), output will double as well ; general:
Decreasing returns to capital: increases in capital lead to smaller and smaller increases in output
Decreasing returns to labour: increases in labour lead to smaller and smaller increases in output
( ) ( )
Amount of output per worker depends on the amount of capital per worker
Sources of growth:
o Increases in capital per worker: movements along the production function
o Improvements in the state of technology : upward shifts of the production function Growth comes from capital accumulation and technological progress, but since capital accumulation by itself cannot sustain growth, technological progress is the key to growth
Three reason for different per capita income in Europe compared to the US: lower ratio of workers to the working age population (L/N), fewer hours (hours/L), lower hourly productivity per worker (Y/hours)
Chapter 12: Saving, Capital Accumulation and Output
Saving rate: ratio of saving to GDP affects the level of output and the standard of living, but not the
economy’s growth rate over long periods
Two relations:
o Amount of capital determines the amount of output being produced
o Amount of output determines the amount of saving and thus the amount of accumulated capital
Capital stock and output: aggregate production function under constant returns to scale: ( )
Output per worker increasing function of capital per worker, but decreasing returns to capital
Simplification: ( ) ( )
Assumptions:
o Size of population, participation rate, labour force, unemployment rate, employment constant o No technological progress, so the production function does not change
Easier to focus on how capital accumulation affects growth
New production function with time indexes: ( ) higher capital per worker higher output/N
Output and investment: Assumption: public saving
Private saving proportional to income, so ( = saving rate; ) The higher the output, the higher the saving and thus the investment
Investment and capital accumulation: evolution of the capital stock:
o : capital stock at the beginning of year t+1
o : rate of depreciation of the capital stock, so is the proportion that remains intact capital stock at the beginning of the year equals the proportion of the previous capital stock still intact plus the new capital stock, thus investment during the year t
Relation from output to capital accumulation:
change in the capital stock equals saving per worker minus depreciation
Bringing together the two relations from the production and saving side: ( ) change in capital per worker depends on investment per worker and depreciation per worker given the capital per worker, output per worker is then given by the equation: ( )
Output per worker increases with capital
per worker, but because of decreasing returns to capital, the effect is smaller the higher the level of capital per worker
Investment per worker has the same shape
but is lower by a factor s (saving rate)
Depreciation per worker increases in
proportion to capital per worker: straight line with slope
Change in capital per worker: difference
between investment and depreciation per worker
At , output per worker and capital
When capital per worker is low, investment exceeds depreciation and capital and output increase When capital per worker is high, investment is less than depreciation and capital and output decrease
Steady state: state in which output per worker and capital per worker are no longer changing, so change
in capital per worker is zero: ( ) ( ) ( )
capital per worker is such that amount of saving per worker = depreciation of the capital per worker
Steady-state capital per worker: steady-state value of output per worker: ( )
Saving rate has no effect on the long-run
growth rate of output per worker, which is
equal to zero since eventually, the economy converges to a constant level of output per worker (and capital per worker)
only with capital accumulation, impossible to sustain a constant positive growth rate forever
Saving rate determines the level of output
per worker in the long run
higher saving rate
higher output per worker in the long run
An increase in the saving rate leads to a period of higher growth until output reaches its new, higher steady-state level
Governments can affect the saving rate by increasing public saving (budget surplus) or use taxes to affect private saving (e.g. tax breaks)
Higher saving: decrease in consumption initially, but increase in consumption in the long run
Golden-rule level of capital: level of capital at which
steady-state consumption is highest: For : higher saving rate higher capital, output and consumption per worker
For : higher saving rate higher values of capital and output per worker, but lower values of
consumption per worker because the increase in output is offset by the increase in depreciation
Cobb-Douglas production function: √ √ √ production function: ( ) √ √
Steady state: amount of capital per worker constant, so √ ( )
Steady-state output per worker: √ √( ) (ratio of saving rate to the depreciation rate) Increase in the saving rate leads to an increase in the steady-state level of output
It takes a long time for output to adjust to its new, higher level after an increase in the saving rate. An increase in the saving rate thus leads to a long period of higher growth
Modification of the production function to include human capital: ( )
Effect of an increase in starting from a low level is strong, becomes smaller with increasing (to measure use of relative wages as weights since they reflect relative marginal products)
Output per worker depends on the level of physical and human capital per worker. Both forms of
capital can be accumulated, one through investment, the other through education and training. Increasing either the saving rate and/or fraction of output spent on education and training can lead to much higher levels of output per worker in the long run, but not to a permanently higher growth rate
Models of endogenous growth: models that generate steady growth even without technological
progress (growth depends on variables such as saving rate and rate of spending on education)
Chapter 13: Technological Progress and Growth
Technological progress = variable that tells us how much output can be produced from given amounts of
capital and labour at any time production function: = Amount of effective labour in the economy: technological progress reduces the number of workers needed/increases the output for a given number of workers (Harrod-neutral technological p.)
Output per effective worker: division by : ( ) ( )
Output per effective worker is a function of capital per effective worker; increases in lead to increases in , but at a decreasing rate (decreasing returns to capital)
Investment = private saving: ( )
Since increases over time, an increase in the capital stock, , proportional to the increase in the number of effective workers is needed in order to maintain the same ratio of capital to effective workers
Growth rate of effective labour ( ) = (rate of technological progress + population growth)
Investment needed to maintain a given level of capital per effective worker:
o : needed to keep the capital stock constant
o : to ensure that the capital stock increases at the same rate as effective labour
Level of investment per effective worker (required investment):
Capital per effective worker: : o Output per effective worker: AB o Investment per effective worker: AC o Investment required to maintain the level
of capital per effective worker: AD Actual investment > investment required increases
economy moves to the right until investment per effective worker is sufficient to maintain the existing level of capital per effective worker and remain constant steady state of the economy
If constant, and must grow at the same rate as :
balanced growth path (output, capital and effective labour are all growing in balance = at the same rate)
In steady state, output per effective worker and capital per effective worker are constant, put another way grow at the same rate as effective labour, thus at a rate equal to the growth rate of the number of workers (population growth) plus the rate of technological process
rate of output growth is independent of the saving rate
The effects of the saving rate:
Increase in the saving rate
investment relation shifts up
increase the steady-state level of output and capital per effective worker:
Economy initially on the balanced growth path AA: output is growing at rate – the slope of AA
Increase in the saving rate at time t makes output grow faster for some period of time
Output ends up at a new higher level, growth rate returns back to
(same rate, higher growth path)
Technological progress depends on:
1. Fertility of research & development (how spending on R&D translates into new ideas and products) 2. Appropriability of the results of R&D (extent to which firms benefit from the results of their R&D)
Governments must balance between the desire to protect future discoveries and provide incentives for
firms to do R&D with the desire to make existing discoveries available to potential users without restrictions
Two sources of (fast) growth:
1. High rate of technological progress ( )
Output per worker should be growing at a rate equal to the rate of technological progress 2. Adjustment of capital per effective worker to a higher level, period of higher growth
growth rate of output per worker that exceeds the rate of technological progress
Institutions are a fundamental cause of economic growth in the long run and of divergence in economic