MACROECONOMIC VARIABLES
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The GDP
Nominal & Real GDP (and growth rate)
Inflation & measures
Pure inflation
Labor force
Unemployment importance
1. The GDP
Measure of aggregate output produced in an economy during a specified period. Useful tool to measure:
economic performance of a country, track its growth, or compare the sizes of 2 different economies
Computation of GDP depends on:
 Production level: value of all final goods and services produced (no intermediate goods) or value
added by firms in the economy
 Income level: sum of incomes produced by firms (labor + capital)
2. Nominal & Real GDP (and growth rate)
Nominal GDP: aggregate output produced in the economy, computed as the Quantity x Current year prices
Real GDP: aggregate output produced in the economy, computed as the Quantity x Constant prices
Differences: nominal GDP doesn’t account for inflation, becomes higher with inflation (goods & services are
more expensive due to increase in prices, not because the economy actually increases output and therefore
experiences GDP growth), real GDP accounts for inflation, it offers a more accurate measure of production and
its change (more accurate at representing wealth of an economy)
3. Inflation & measures
Inflation is the general increase in the price level of a country, the inflation rate describes the rate which price
level increases
 GDP deflator: ratio between nominal and real GDP in a given year (interested in calculating the rate
of change to look at how the inflation rate changed year to year)
 CPI – Consumer Price Index: Consumers are not interested in all the final goods and services
produced in an economy, but only about the average price of the goods they consume. CPI measures
are published monthly by national statistic offices, while the market basket is updated annually. The
market basket gives the relative cost of a hypothetical list of goods and services, it represents the
cost of purchasing a market basket one year from another
4. Pure inflation
If a higher inflation rate meant higher prices and wages – a situation called pure inflation – inflation would not
be highly relevant, because relative prices would not be affected and the purchasing power will remain the
same. In reality, pure inflation doesn’t exist: when inflation happens, not all wages and prices are raised
proportionately, thus producing negative effects on:
 Income distribution (some individuals loose PP)
 Distortions due to uncertainty
 Some prices of fixed by law
 Distortions in taxation
5. Labor force & unemployment rate
The labor force is the sum of employment and unemployment: L = N + U
 Employment is the number of people who currently have a job
 Unemployment is the number of people who do not have a job but have been actively looking for
one in the last 4 weeks
The employment rate is the ratio between the employed population over the working-age population (15-64
years old): e = N/pop15_64
The labor force participation rate measures the % of the working age population who is working or actively
looking for work (and therefore are part of the labor force): I = L/pop15_64
In the working-age population, we can find some individuals that by age could potentially work but are not
counted in the labor force: people with physical conditions, full-time students, people in jail, people that work in
the shadow market, discouraged
The unemployment rate is the ratio between the number of people who are unemployed and the number of
people in the labor force: u = U/L
6. Unemployment importance
The unemployment rate is a good indicator of how easy or difficult it is to find a job given the current state of
the economy. However, the problem of the unemployment rate is that it can over/underestimate the actual
value:
1. Underestimate: discouraged people, who would probably like to work, but after a long period of lack of
available jobs, have stopped applying for new positions, and therefore are not counted as part of the
unemployed population
2. Overestimate: those who were counted as unemployed during the surveys and perhaps might have found a
job the day after. Even if the market is healthy, it takes time to find the right job, meanwhile you count as
unemployed
THE GOODS MARKET RECAP
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3.
4.
5.
The short run
Composition of GDP
The demand for goods
The determination of equilibrium output
IS (Investment equals Saving) – market equilibrium
1. The short run
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Any year-to-year change (= fluctuation) in the economic activity is primarily attributed to changes in demand
Economists focus on the interaction between 3 variables: demand, production and income (chain reaction:
firms react to demand and adjust production, which will then affect income (ex. employe es), which will further
affect demand)
Demand determines output
2. The composition of GDP
C = Consumer spending – households
I = Investment spending – firms
G = Government spending – government, local government, state
X = Exports - IM = Imports
Inventory investment
3. The demand for goods
First of all, define total demand (Z) as the demand side of GDP: Z = C + I + G + X – IM
Since we are in a closed economy: Z = C + I + G
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Consumption is the largest component
Consumption is a function of disposable income: C = f (Yd) (with positive relationship, behavioural
equation)
We can rewrite it and be more precise with a linear relation: C = c0 + c1 Yd (c0: constant parameter:
level of income consumed regardless, c1: marginal propensity to consume: derivative of Yd, if Yd
increases, how much you will spend on goods & services)
Disposable income can be understood as income minus taxes: Yd = Y – T
We can expand the consumption function as: C = c0 + c1 (Y – T)
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We take investment as given (exogenous): I = I
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Government spending: T and G describe fiscal policy, taken as given
Replacing C and I, total demand is: Z = c0 + c1 (Y – T) + I + G
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Equilibrium in the goods market requires that production equals total demand: Y = Z
Replacing with Z: Y = c0 + c1 (Y – T) + I + G
In equilibrium, production (Y) equals demand, which depends on income (Y), which is equal to production
(indeed, GDP can be calculated both as production or income! Both are the same thing!)
Equilibrium output is determined by the condition that production is equal to demand
4. The determination of equilibrium output
Rewrite the equation by multiplying the brackets: Y = c0 + c1Y – c1T + I + G
By re-organizing and dividing both sides by (1 – c1): (1 – c1) Y = c0 + I + G + c1T
We get the formula for the equilibrium output in the goods market:
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The 1st part is the multiplier: c1 is between 0 and 1, so 1/1- c1 is a number greater than 1. It becomes larger when
c1 is closer to 1 (ex. c1 = 0.6, multiplier = 1/1 – 0.6 = 2.5, c1 = 0.8, multiplier = 1/1 – 0.8 = 5)
The 2nd part of the equation is autonomous spending = part of demand for goods that does not depend on
output. It is likely to be positive
We want to plot production as a function of income: because Y = Y, their relationship is the 45-degree line
(bisector).
We want to plot demand curve as ZZ = (c0 + G – c1T + I) + c1Y
Suppose autonomous spending increases: c0 increases, then the total demand curve shifts upwards. This will
affect firms, who will increase production. The total increase in production is larger than the initial increase in c0
due to the multiplier process: due to higher demand (Z) there is a higher production (higher Y, GDP), a higher
flow of income, which leads to more spending, so more demand, and more production, and more income…
Because c1 is less than 1, each increase in income and each increase in consumer spending is smaller than the
previous round. As a result, although GDP grows at each round, the increase diminishes from each round to the
next. At some point the economy converges to a new equilibrium (A’).
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Production depends on demand, which depends on income, which is equal to production. Higher demand
determines higher production in income, which in turn produces future increase in demand
5. IS (Investment equals Saving) – market equilibrium
So far, we have discussed equilibrium is determined by the equality between production and demand. Keynes
developed an alternative way that focuses instead on investment and saving
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Saving is the sum of private and public saving
Private saving is after-tax income that is not spent: S = Yd – C => S = Y – T – C
Public saving is the difference between taxes and government spending: T – G
In equilibrium: Y = Z => Y = C + I + G
Subtract T from both sides and move C to the left side: Y – T – C = I + G – T
The left end side is private saving, so: S = I + G – T
We can rearrange this formula as: I = S + (T – G) (IS relationship)
We have look at the equilibrium output with the production/demand relationship, does the IS approach lead us
to the same definition of equilibrium output?
I = S + (T – G) => I = Y – T – C + (T – G) => I = Y – C – G
I = Y – C0 – C1 (Y – T) – G => I = Y – C0 + C1Y – C1T – G => Y + C1Y = C0 – C1T + G + I =>
THE FINANCIAL SYSTEM
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The sound financial system
Demand for money
Supply for money
1. The sound financial system
A well-functioning financial system is critical in achieving long-run growth because it encourages greater savings
and investment spending.
There are 3 tasks for the financial system:
 Reduce transactions costs
 Reduce risk and uncertainty, also by diversifying the financial assets
 Providing liquidity
2. Demand for money
You may have a choice between 2 assets: bonds and money. Bonds pay a positive interest rate, but cannot be
used for transactions, money (currency & deposits) is used for transactions (fully liquid), but pays no interest.
The holding of money and bonds depends on: your level of transactions (nominal income) and the IR on bonds
The demand for money as a whole is the sum of all the individual demands for money by people and firms in
the economy.
Therefore, it depends overall on the level of transactions (roughly proportional to nominal income) in the
economy and a decreasing function of the interest rate: Md = $Y L(i)
 Md is decreasing in L: as IR increase, people put more wealth into bonds and reduce their demand for
money
 Md increases with nominal income
The Md function is downward sloping: a lower IR determines an increase in the demand for money, an increase
in nominal shifts the demand for money to the right
3. Money supply
Assume there is only one type of money (currency), supplied by the CB.
The CB decides: Ms = M
As in any market, equilibrium in the financial markets requires that Ms = Md => M = $Y L(i)
Of course, the equilibrium may change:
CBs can change the Ms with open market operations: by either selling (contractionary policy) or buying bonds
(expansionary policy), they control the Ms and the i.
But the equilibrium may also change due to Md specific factors, such as an increase in nominal income which
will determine a shift of the Md function
IS-LM RELATIONSHIP RECAP
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Goods market & IS
IS relation
Supply for money
IS-LM model is a diagram which denotes the relationship between Investment=Spending in the goods market and
Liquidity=Money supply in the financial market. The intersection between IS-LM denotes simultaneous equilibrium
in both markets
1. Goods market and IS
Equilibrium in the goods market: Y = Z Y = C (Y -T) + I + G
We use a more general assumption of consumption to simplify the function, without assuming that C is linear but
simply Yd = Y – T.
We drop the assumption that Investment spending is exogeneous, but instead it depends on income and
interest rate: I = I (Y, i)
 Investment spending increases when income increases (more durable goods invested upon)
 Higher i determines less investment spending because people would prefer to borrow at a lower i for
a durable good, and rather would prefer lending
The ZZ function changes and equilibrium goes to: Y = C (Y -T) + I (Y, i) + G
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Because we have not assumed our ZZ curve, and C and I, are linear, ZZ is going to be a general curve rather than
a line.
Demand increases output
 Multiplier effect: > output, > income, > consumption > demand
 New assumption: > output, > I, > demand
2. IS relation
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If i increases, I and ZZ drops and shifts down => Y drops
If i decreases, I and ZZ increase and shift up => Y increases
We can draw the same relationship in the space (Y, i) that is the IS curve. The IS relation describes how output
(Y) changes when i changes:
The IS curve models how output responds to changes in the interest rate. 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.
We have drawn the IS curve taking as given values T and G. What if something else other than i changes, such as
G or T?
 An increase in taxes, from T to T’. At a given i, disposable income decreases, consumption decreases,
demand decreases, and output decreases from Y to Y’.
FINANCIAL MARKETS AND LM
1. Financial markets equilibrium
We want to see how changes in income will affect changes in equilibrium in the money market (through LM
curve).
Ms = Md = $Y L(i)
Money demand depends on the nominal income, the level of transactions, and the interest rate. We prefer to
deal with real income, such that by dividing both sides for the price level P: M/P = Y L(i) is the LM relation
In equilibrium, real Ms = real Md
The CB aims at a given interest rate i, and it is ready to adjust the money supply to achieve it. In equilibrium, Ms
= M, an exogenous shock (increase level of transactions) increases income. To keep the money supply intact, the
interest rate should increase
But if the CB wants to keep i constant, they can increase money supply. So they adjust M to keep i constant.
Therefore, the LM relation can be represented as a linear horizontal curve. The central bank chooses a specific
interest rate, and adjusts the money supply to achieve it for any level of production.
Equilibrium in the goods market implies that an increase in the interest rate leads to a decrease in output (IS
curve). Equilibrium in financial markets is LM. Only at point A, which is on both curves, are both goods and
financial markets in equilibrium.
POLICY ANALYSIS IN IS-LM
1. Fiscal policy
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Fiscal consolidation: a reduction in the budget deficit achieved by increasing taxes, or by decreasing
government spending, or both
Fiscal expansion: increase in budget deficit achieved by decreasing taxes, or by increasing government
spending, or both
2. Monetary policy
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Monetary expansion: CB decreases i, achieved through an increase in Ms
Monetary contraction: CB increases i, achieved through a decrease in Ms
3. Fiscal policy effect
To look at the effects of changes in policies or exogenous variables, we ask whether it has effects in IS or LM
curve, what does it do to equilibrium output and equilibrium i
The fiscal contraction (lower deficit) will determine higher T, which will reduce Y at any level of i, such that the IS
curve shifts leftward. The LM curve, instead, does not shift. Therefore, there is only a leftward shift of the IS
curve, which means lower demand, and therefore lower level of output to Y’. Lower output will mean lower
income, and therefore lower money demand, the CB keeps its i target.
With increasing government spending, the IS curve shifts rightward, increasing aggregate demand and output.
4. Monetary expansion effect
A monetary expansion lowers the interest rate by increasing the Ms. The CB moves down i while increasing M, so
that, at any level of output, i is lower. Lower interest leads to lower output. In the IS relationship, lower interest
determines higher investment spending, hence output, hence investment…
5. Policy mix
The policy mix is a combination of monetary and fiscal policies, usually fiscal consolidation and monetary
expansion. In this case, an increase T and lower G will affect the IS curve, which will move to the left. If we want
to moderate the negative effect of the diverging policies, we could ask the CB to reduce the interest rate, which
would counterbalance in part the negative effect of the fiscal consolidation.
MEDIUM-RUN: THE LABOR MARKET RECAP
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The short-run assumption
The natural rate of unemployment
Wage determination
Model of wage determination
Goods prices determination
Equilibrium labor market
1. The short-run assumption
We assumed firms can vary the labor input (in order to meet demanded output) without affecting the price
level. This assumption only works in the short-run!
Indeed, an increase in production determines lower employment and higher unemployment. Higher
unemployment produces higher wages, which will make firms set higher prices. As a result, employees will ask
for higher wages: if firms accept, they will further increase prices and so on…
In the medium-run, we will see that workers have chances to negotiate nominal wages, and when those wages
change, firms likely adjust the prices of their products to maintain the same level of profits
2. The natural rate of unemployment
Some unemployment (frictional + structural) is natural in the first place. There are 3 kinds of unemployment:
 Frictional = takes time to find the right job
 Structural = excess supply of job searchers, even when the economy is at the peak of its business
cycle
 Cyclical = deviation from the natural rate, correlated with the business cycle
yh
3. Wage determination
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Often wages are set by collective bargaining (or employer wages setting, or individual bargaining) but also with
efficiency wage setting
Regardless of this, there are 2 factors at play in wage determination:
1. Labor market conditions: < unemployment rate => > wages
2. Employees are paid a wage that makes them to prefer being employed rather than unemployed, an
amount higher than their reservation wage
Both bargaining power and efficiency wages will depend on the nature of job and skills required, as well as the
labor market conditions
4. Model of wage determination
We assume the nominal wage depends on 3 factors: W = Pe x F (u,z)
WAGE-SETTING RELATION
1. Expected price: we care about real wages. Employees are interested in looking at the nominal
wage/amount of goods they can buy, firms the nominal wages they pay/price of goods they sell => P e
because wages are set in nominal terms and valid for a fixed time: employees bargain on their
current wage, based on the expectations they can on future price levels (ex. expected increase, ask
higher nominal wage, keeping real wage constant)
2. Unemployment: < unemployment rate => > wages
3. Other factors: unemployment benefits, employment protection programs, minimum wage which
mostly affect reservation wage but may also affect the bargaining power of workers
We can rewrite F (u,z) as 1 – αu+ z
W = Pe x F (u,z) => W = P x F (u,z)
W = Pe x (1 – αu + z) => W = P x (1 – αu + z)
Because we care mostly about the real wage rather than the nominal wage, we change the assumption: W/P =
P x F (u,z) REAL WAGE-SETTING RELATION
5. Goods prices determination
The prices firms set on their goods depend on their costs, which depends on the nature of the production
function: Y = AN
The relation between the inputs used in production and the quantity of output produced
If we consider that 1 employee produces 1 output, the relation becomes: Y = N
To increase 1 output, firms have to hire 1 additional worker: the cost of producing one additional output is
called the marginal cost (W): it is going to be the amount of additional wage paid (indeed, W!)
If the goods market was in perfect competition: W = P, but in reality firms charge prices higher than the
marginal cost by an amount called mark-up factor (m): P = (1+m) W PRICE SETTING RELATION
6. Equilibrium labor market
We want to get an expression of real wages, and so we will also assume that Pe = P
The WS relation: W/P = P x F (u,z)
The PS relation by expliciting W/P: W/P = 1/(1+m)
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The equilibrium requires that the real wage chosen in wage setting (employees) equals the real wage implied
by price setting (firms)
Price setting decisions determine the real wage paid by firms. Price setting relation can be seen as the amount of
real wage firms are willing to supply
MEDIUM-RUN: INFLATION AND UNEMPLOYMENT RECAP
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Phillips relationship
How to form inflation expectations πe
Phillips curve and the natural rate of unemployment
1. Phillips relationship
We do not assume anymore that workers can fully predict prices, so P is not equal to Pe
By combining the 2 relationships: P = Pe (1+m) F (u, z) => P = Pe (1+m) (1 – αu + z)
We get a relationship between current prices, expected prices, unemployment, mark-up and other factors who
push the wages up
Instead of price levels, now we want to focus on price changes year-to-year (inflation), such that we can rewrite
the relationship as the Phillips relationship: πt = πe + (m + z) – αut
 An increase in πe leads to an increase in π
 With constant πe, an increase in m or z leads to an increase in π
 With constant πe, an increase in u leads to a decrease in π
2. How to form inflation expectations πe
When forming expectations, people base on 2 main factors:
1. Fixed convictions => anchoring expectations
2. Inflation observed in the previous year => adaptive expectations
πe is actually based on both, and the weight of adaptive/anchoring expectations will be determined by the
following formula: πt = (1 – θ) π* + θ π t-1 where part of the society will have anchoring expectations, some
adaptive expectations
 θ = 0, expectations do not depend on past experience (πt = π* + (m + z) – αu)
 θ = 1, current inflation equal to the past (πt - πt-1 = (m + z) – αu)
1. Phillips curve and the natural rate of unemployment
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Our assumption was that un: WS = PS, assuming that P = Pe. However, as we have seen above, we now drop this
assumption
DYNAMIC DEFINITION: The natural rate of unemployment is the unemployment rate such that the realized rate
of inflation is equal to the expected rate of inflation at time of wage negotiations: π = πe
STATIC DEFINITION: The natural rate of unemployment is the unemployment rate such that the realized
price level is equal to the expected price level at time of wage negotiations
By imposing this condition, π = πe, we get that the Phillips relationship becomes 0 = (m + z) – αun
Which means that the natural rate of unemployment is equal to un = m + z / α
Can we make the Phillips relationship a function of un as well? Yes, by multiplying and dividing (m + z) by α, such
that we get πt – πe = – α (ut – un) or πt – πt-1 = – α (ut – un)
 If unemployment is at the natural rate, inflation will be equal to expected inflation
 If unemployment is below the natural rate, inflation will be higher than expected
 If unemployment is above the natural rate, inflation will be lower than expected
The unemployment rate which allows a constant rate of inflation (πt = πt-1) over time is called NAIRU
IS-LM-PC MODEL
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The previous models
Phillips curve in terms of output gap
Short to medium-run level of output
1. The previous models
Previously we developed the following equation from the IS curve: Y = C(Y – T) + I(Y, r + x) * G
Production (Y) depends on demand, which depends on consumption (which depends on disposable income: Y –
T), on investment (output, real rate + risk premium), on government spending, that is exogenous
We also developed the LM curve, which told us that the CB sets the real i rate to ensure equilibrium in financial
markets
We then lastly saw the relationship for the Phillips curve: πt – πt-1 = – α (ut – un)
When unemployment differs from the natural unemployment rate, then inflation will differ from its expected
value
2. Phillips curve in terms of output gap
Given that the aggregate demand equation is in terms of output, rather than unemployment, our first step is to
define the Phillips curve in terms of output.
The unemployment rate was defined as u = U/L => u = L – N/U => ut = 1 – N/L
By expressing the found function in terms of N N = L (1 – ut)
Recalling the production function Y = N, we find that Yt = N = L (1 – ut)
ut = 1 – Yt/L
When u = un (unemployment rate = natural unemployment rate)
 Natural employment is given by Nn = L (1 – un)
 Natural unemployment is given by un = 1 – Yn/L
 Natural output (= potential output) is given by Yn = L (1 – un)
The difference between output (Yt) and the natural output (Yn) is the output gap Yt – Yn = - L (ut – un)
 If unemployment is equal to the natural rate, output is equal to natural output
 If unemployment is above the natural rate, output is below natural output and output gap is negative
 If unemployment is below the natural rate, output is above natural output and output gap is positive
By replacing in the Phillips curve we get: πt – πe = α/L (Yt – Yn)
If expectations are anchored:
πt – π* = α/L (Yt – Yn)
 If output is higher than the natural output, the output gap is positive and inflation is higher than the
fixed expected rate π*
 If output is lower than the natural output, the output gap is negative and inflation is lower than the
fixed expected rate
If these deviations happen too frequently, people will stop trusting and shift to adaptive inflation expectations
(πe = πt-1), such that PC becomes πt – πt-1 = α/L (Yt – Yn)
 If output is higher than the natural output, the output gap is positive and inflation is higher than the
fixed expected rate
 If output is lower than the natural output, the output gap is negative and inflation is lower than the
fixed expected rate
3. Short to medium-run level of output
From the IS-LM curve we can explain the short-term equilibrium level of
output. Depending on whether this level of output is higher or lower
than the natural output, inflation will be lower/higher than expected.
The top part of the figure tells us that, associated with this interest rate r,
the level of output is given by Y. The bottom part of the figure tells us
that this level of output Y implies an inflation rate equal to π
When actual output corresponds to the natural output Yn, actual
inflation π corresponds to expected inflation πe. In this graph, Yn < Yt
such that inflation will be higher than expected, > 0
The CB sets the policy interest rate at r. From the IS, the short-run rate
corresponds to a level of output Y. If this level of output is higher than
the natural level, the inflation is higher than expected. Policy will react to
stop rising inflation (otherwise people will de anchor) and avoid adaptive
expectations. Equilibrium A only works in the short-run.
If the CB increases r, higher r will determine a decrease in output
(recession, because production lowers) and return to the natural level of
output Yn. In the end, price pressure is removed: lower level of output and
constant increase in inflation (which means in line with inflation
expectations). At point A’, the economy reaches the medium-run
equilibrium. The real interest rate at which output is at the natural level
and inflation constant is the natural interest rate rn or Wicksell interest
rate.
In the medium-run, the economy converges to the natural level of output
and stable inflation. If the CB wants to achieve a constant inflation, the
initial boom must be followed by a recession.
If the output remains above natural output and inflation above the target,
policy is likely to react. indeed, the CB wants to have inflation close to the
target, and inflation expectations could de anchor (and therefore wage
setters will expect inflation to equal past inflation). If the output gap
remains positive, inflation not only will be higher than the target but will start increasing.
The CB acts when the economy is in A. During the transition from A to A’, prices keep increasing more than
expected, but the gap gets smaller and smaller. Therefore, inflation is always higher than expectations, and
unless expectations are very negative, inflation will be positive and prices will increase.
In the medium-run, output returns to its natural level, and also unemployment returns to its natural level.
Real interest rate in A’ is rn. The nominal interest rate is i = r + πe, so in the medium run it will be i = rn + π*
4. Medium run equilibrium
With r = rn (Wicksellian real interest rate):
- Y = Yn
- u = un
- π = π*
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i = rn + π*
We will also have equilibrium between real Ms and real Md: M/P = Yn L(rn + π*)
This ratio is constant: in the medium run prices P must grow at the same rate as the nominal money stock M in
order for the ratio M/P to remain constant
 Inflation depends on the growth rate: π = gm
In the medium-run, real economic variables (output, unemployment, real rate of interest) are independent
of monetary policy
Indeed, what monetary policies can determine is the rate of inflation and the nominal interest rate.
5. Adjustment timing
The adjustment to the medium run equilibrium is more complex in reality.
- It is difficult for the CB to precisely estimate potential output Yn
- It takes time for the economy to respond
The economy adjusts slowly r: investment spending reacts but it takes time until the whole process is over.
Meanwhile, as long as output remains above potential, inflation will be higher than expected. A recession could
be needed to bring back inflation to the desired target.
6. Zero lower bound
Suppose an economy is in recession, where Yt < Yn. Inflation must be
lower than expected. CB should try to increase the level of output by
reducing the real interest rate.
Depending on how bad the economy is doing, rn could be negative. If i is
already too low, there is small room to act
If inflation is high, r will be brought to negative values.
However, if we have deflation, r will be positive: i = 0, r = i – π
Suppose we are in A and we cannot reduce r. In presence of continuous
deflation, people will start de-anchor expectations: in the PC, π will be
replaced by πt-1.
With expectations of further deflation (negative inflation) prices will
decline even further next year. Higher deflation means higher r, which
means lower output in the IS, which means worse output gap, which
means even more negative inflation…
THE OPEN ECONOMY RECAP
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Openness
Nominal ER
Real ER
Openness in financial markets
1. Openness
Until now, we have assumed closed economies, but in reality economies are open: nations’ economies are all
connected. This is why we can see similar trends in the main macroeconomic variables.
Additionally, we have seen that consumer decisions’ regard consuming or saving. In the open market, domestic
or foreign goods can be consumed. Consumption decisions will therefore affect the domestic output of the
country, therefore its GDP.
However, a crucial determinant of this choice is the real exchange rate: the comparison between the price of
domestic goods and foreign goods
2. Nominal ER
The nominal ER is the price of the domestic currency in terms of a foreign currency. We could consider Russia as
our domestic country, and therefore consider the ruble as the domestic currency: the ER will describe how many
dollars a ruble can buy. On the other hand, the ER from the point of view of American will tell how many rubles a
dollar can buy
 Appreciation of domestic currency: increase in D currency, increase in ER
 Depreciation of domestic currency: decrease in D currency, decrease in ER
3. Real ER
The real exchange rate is the price of domestic goods relative to foreign goods. It is essentially the ratio
between prices of the goods in the domestic country and in the foreign country, therefore we are comparing
prices of goods.
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However, we cannot compare prices because we cannot compare different currencies. We first need to convert
either of them in the other currency.
We convert domestic prices in terms of foreign prices
4. Openness in financial markets
In a closed economy, people choose between money or bonds. Openness of financial markets implies that
people can choose between holding between domestic or foreign assets.
Let’s say you want to decide whether on holding EU or UK bonds. EU is domestic.
 If you decide to hold German bonds, you get 1 + it payment next year
 If you decide to hold UK bonds, you first need to buy pounds. For every Euro, you get Et pounds and
you can buy Et bonds. Therefore, you will get Et (1 + i*t)
 The gain in Euro terms next year, is going to depend on the expected exchange rate next year between
Euros and Pounds (Et+1 e)
 Your gain in pounds is going to be Et (1 + i*t). Next year we want to convert pounds into euro with 1/E,
but next year you are going to have (Et+1 e), such that in the end we want to compute 1/(Et+1 e)
To decide whether to hold money, EU or UK bonds, you compare i with i*, but also consider whether the
domestic currency will appreciate or depreciate.
You will buy bonds in the country which has the largest expected rate of return, which for the domestic bonds
depends on (1 + i), for the foreign bonds depends on i*, current and expected Et.
To be indifferent between the two, bonds must provide you the same expected rate of return. Or, by using the
interest parity condition: the domestic interest rate must be equal to the foreign interest rate minus the
expected appreciation rate of the domestic currency.
 If you expect the Euro to appreciate, this is bad for your UK investment
 If you expect the Euro to depreciate, this is good for your UK investment (pound gains value and you
are interested only in what the pound does)
OPEN ECONOMY: GOODS MARKET
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The change in demand
Net exports and Marshall Lerner
Demand function
1. The change in demand
We have defined the demand function as: ZZ = C (Y – T) + I(Y, i) + G
Since we are now in an open economy: ZZ = C (Y – T) + I(Y, r) + G + X – IM
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Imports (in foreign currency): IM (Y, ε)
Positively related to income (increase in demand, also of foreign goods) and real ER (domestic goods
are more expensive)
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Exports: X (Y*, ε)
Positively related to foreign income (increase in foreign demand for domestic goods) and negatively
related to real ER (the more domestic goods are expensive, the lower the foreign demand)
Net exports NX is the difference between Exports – Imports (both by definition valued in domestic prices)
Now we need to convert imports (defined in foreign prices of goods) into the price of domestic goods. Since we
want to change the real ER, we will invert and use 1/ε: IMPORTS = IM (Y, ε) 1/ε
2. Net exports and Marshall Lerner
Net exports thus become: NX = X (Y*, ε) - IM (Y, ε) 1/ε
NX (Y*, Y, ε)
The Marshall Lerner condition guarantees us that higher ε leads to lower NX (IM increases enough to
counterback the decrease in X):
 Real appreciation leads to lower NX
 Real deprecation leads to high NX
Moreover, NX is a decreasing function of output: as Y increases, NX decreases
NX is a decreasing function of income Y* and output: as X increase, IM remain the same and NX decrease
3. Demand function
ZZ = C (Y – T) + I(Y, r) + G given that our economy is open, the demand for domestic goods needs to exclude the
demand for foreign goods (imports) and include the foreign demand for domestic goods (exports), so we will
sum the net exports: ZZ = C (Y – T) + I(Y, r) + G + NX (Y*, Y, ε)
In the short-run, prices are mostly fixed. Therefore, epsilon is likely to change only because of changes in E and
not in prices. We can therefore write our short-term assumption for demand as: ZZ = C (Y – T) + I(Y, r) + G + NX
(Y*, Y, E)
Since the beginning of the module, we have been interested in looking at GDP, that is domestic
output/production. We want to understand all the factors that increase or decrease the demand for domestic
production.
 In the closed economy, only nationals can change demand and produce goods.
 In the open economy, nationals can demand goods also from abroad and foreigner can purchase the
domestic goods too
To study the total demand for goods (new ZZ): we start from the old ZZ, and sum net export NX. As a result, the
slope is lower than before
The demand rises but not as much as in the closed economy (due to the fact that some domestic demand goes
into imports, which are not part of ZZ). The equilibrium point will be the point where old ZZ is equal to new ZZ:
where NX = 0.
When is the goods market in equilibrium? When the value of goods and services demanded is equal to the value
of goods and services produced. In equilibrium, Y’, the value of income (=output) determines a level of demand
equal to new ZZ (domestic and foreign buyers)
OPEN ECONOMY: FISCAL POLICY
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1. F
LONG-RUN: ECONOMIC GROWTH
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GDP and PPP
Growth and Malthusian trap
Model for economic growth
Returns to scale
Growth and output per worker
Steady state
1. GDP and PPP
To better understand the differences in GDP between countries and their growth we can look at the standards
of living. This is done with PPP adjustments (purchasing power parity)
The problem is: how do we compare output per person across countries? Most countries use different currencies,
thus, output in each country is expressed in terms of its own currency. A natural solution is to use the exchange
rates (E).
- Ex. Compare the output per person in rupees in India and in dollars in the US. We first compute the GDP
per person in rupees, then, we use the E to get the Indian GDP per person in terms of dollars, and
compare it to the GDP per person in dollars
However, only the E would not show us how costly is life in one country compared to another. Indeed, it is
possible that in one country you get more things that you would get in another. Therefore, we use the
Purchasing Power Parity exchange rate: the adjusted ER
Downsides: PPP E do not account for quality (across countries, goods have same type of quality), do not account
for public goods (quality of institutions)
2. Growth and Malthusian trap
Why was growth flat for hundreds of years? Our ancestors were trapped in poverty, Malthusian trap: unable to
increase the output per person.
- From the end of the Roman Empire to roughly year 1500, Europe was in the Malthusian trap with
stagnation (flatness) in output per person because most workers were in agriculture with little
technological progress. Between 1820 and 1950, growth was still positive but small. Sustained growth
was high since 1950.
 Malthus explained the poverty trap: any increase in output (income) was leading to a decrease in mortality,
leading to an increase in population until GDP per person was back to its initial level. Income, therefore, was
growing actually, but the increase lead just to a decrease in mortality, and income was divided between a
population that grew at the same rate!
The size of population was determining people’s living standards.
His analysis was right, but in reality productivity started growing faster than the size of population, such that
output per person increased. Indeed, innovation leads to productivity growth and the GDP per capita increased.
3. Model for economic growth
The starting point should be an aggregate production function, which relates every aggregate output to the
inputs in production:
Production (GDP) is an increasing function of: capital K, labor N, and the state of technology A: Y = F (K, N, A)
We will write it as: Y = F (K, AN)
Production is a function of capital, and labor multiplied by the state of technology. Productivity is directly related
with employment
Technology can affect the number of workers needed to produce an amount of output, such that AN can be
considered as the effective labor in the economy
4. Returns to scale
The economy shows constant returns to scale: for a given state of technology (A), an increase in workers and
capital in the economy by a same factor, its output will grow by the same factor: xY = F (xK, xAN)
But what happens if one inputs increases? We will have decreasing returns to inputs:
- Unitary increases in capital, given labor and technology, will lead to smaller increases in output
- Unitary increases in labor, given capital and technology, will lead to smaller increases in output
What happens if technology improves? Output increases, even with the same level of labor and capital as before.
The economy shows constant returns to scale: for a given state of technology (A), an increase in workers and
capital in the economy by a same factor, its output will grow by the same factor: xY = F (xK, xAN)
5. Growth and output per worker
Since we usually focus on GDP per capita, here we can focus on output per worker: Y/N = F (K/N, A)
Or we can focus on the output per effective worker: Y/AN = f (K/AN)
How can an economy increase output per workers? With A. If we reduce N, Y/N increases. By increasing K, Y/N
increases.
The easiest to increase is K/A, capital can be increased through savings and with them you can make higher
investment spending.
Can the increase in K/N sustain growth of Y/N forever, holding A constant? No, because when capital per worker
increases, output increase but at smaller and smaller rates (diminishing returns of capital). The only best way to
increase output per worker is to shift the curve through changes in technology.
Capital accumulation by itself cannot sustain output per worker growth. Due to the decreasing returns to capital,
higher output per worker will require higher and higher increases in the level of capital. However, at some stage,
the economy will be unable to save and invest enough to increase capital, so output per worker will stop growing.
This doesn’t mean saving rate is irrelevant: indeed, it will promote a higher level of growth in the long run, but at
a certain point growth will end.
6. Steady state
Output per effective worker
At a certain point, accumulation of capital will be less and less effective in boosting economic growth because of
the diminishing returns to capital. Moreover, you would have to save more and more and more…
As a result, in the long-run, the steady state would tell us that the capital per effective worker (K/AN) reaches a
constant level, and so does output per effective worker (Y/AN). They do not grow anymore!
If Y/AN is constant, output (Y) is growing at the same rate as effective labor (AN).
- If we call the growth rate of A ga and the growth rate of N gn: AN is growing in the long-run at a rate (ga +
gn) and also output growth gy = (ga + gn)
- The same reasoning applies to capital gk = (ga + gn)
 In the long-run, the growth rate of output will equal the growth rate of population + growth rate of
technological process.
It doesn’t depend on capital, therefore it doesn’t depend on the saving rate. Capital growth is not the key of
growth in the long-run because of the diminishing marginal returns.
Output per worker
In the long-run, output Y grows at rate (ga + gn), the number of workers grows at rate gn
Hence, output per worker (Y/N) grows at rate (ga + gn - gn)
When the economy is at its steady state, output per worker grows at the rate of technological progress.
 The growth of output per person is eventually (in the long-run) determined by its rate of technological
progress.
CAPITAL IMPORTANCE
1. Role of capital
To study the role of capital, we assume N (constant) and A (no technological progress) are fixed. This will lead us
to the question: could an economy where only capital increases sustain growth in time?
We need to relate investment I to capital K, which is a stock. Capital next year will be capital K, plus investment
done, minus the depreciation of capital at rate δ: K t+1 = Kt + It - δKt
As we want to study capital accumulation per worker, we divide by N
In equilibrium, investment spending must equal savings. Let’s assume public budgets are balanced, such that I =
S. We can easily assume that saving is proportional to income times saving rate: S = sY
Hence, in year t, investment It = sYt
- Investment increases if output (income) increases
- Investment increases if saving rate increases