Core Macroeconomic Models: IS-LM-PC, Phillips Curve, and Key Laws
The natural rate of unemployment is a function of the firm’s markup and non-labour related cost, 𝑚, the labour market characteristics, 𝑧, and the strength of the effect of unemployment on wages, alpha–> un=(m+z)/alpha Y EXPLICAMOS EL CAMBIO
Potential output,Yn, is a function of the natural employment level, Nn, which depends on the natural rate of unemployment: Yn=Nn=L(1-un)Y EXPLICAMOS EL CAMBIO
b) Analyse the policy’s short-run effects. SOLUTION: Initially, the economy is in equilibrium in all markets: goods and financial markets. Inflation is equal to the target inflation set by the central bank. In both graphs of the IS-LM-PC, the initial equilibrium is represented at point 0, with output Y0 being equal to potential output 𝑌n , 𝚤̅ is the policy interest rate set by the centraal bank, and the difference between inflation and target inflation is equal to 0. Y AHORA EXPLICAMOS EL CAMBIO PRIMERO
C) Explain the transition to the medium run. LO EXPLICAS// d) Compare the medium run equilibrium to the 0
initial equilibrium. Comparing the final medium run equilibrium with the initial equilibrium: • Output is (the same and equal to potential output.) • The interest rate is (lower.) • Consumption has (decreased, as disposable income is lower because taxes are higher.) • Investment is (higher because the interest rate is lower.)
Fiscal expansion: ↑G->IS–> (↑ y,i, pi)/Fiscal contraction: ↑ T->IS<-
monetary expansion(↓ i o ↑ M)/pi>pi e–>LM↓ / monetary contraction( ↑ i o↓ M)-/pi<pi e->LM↑
↑pi e–>↑ PC / ↑ m–>↑ PC / ↓ pi e–>↓ PC / ↓ m–>↓ PC
GDP=C(Y(+)-T(-))+I(Y(+), i(-))+G(G palito exogenous)+(X(YF(+), e rara(-))-(IM(Y(+), e rara(ambigua)))
OUTPUT GAP=diff bet actual output(Y) and its ntural level of output(Yn)->which is the level of production when the economy is using its resources fully and unemp is at its natural rate.–> Y-Yn=-L(u-un)/ if u=un->y=yn->outp gap=0 economy producing at its potential.//if u>un->y<yn->otpg- economy below potential(slack)/al reves economy overheating output above sustainable levels.
The Marshall–Lerner condition explains how a change in the real exchange rate affects a country’s net exports (NX).A real depreciation (a decrease in ε, meaning domestic goods become cheaper for foreigners) will increase net exports, if the sum of the absolute values of the price elasticities of exports and imports is greater than one. // The Marshall–Lerner condition states that a real depreciation of the domestic currency will increase net exports if the combined responsiveness (elasticities) of exports and imports to price changes is greater than one. This means that the positive quantity effects from cheaper exports and lower imports outweigh the negative price effects. Therefore, real appreciation reduces net exports.
Okun’s Law, first identified by economist Arthur Okun, describes an empirical relationship between economic growth and unemployment: when output (GDP) grows rapidly, unemployment tends to decrease. Because the population and labor force increase over time, employment must also grow just to keep the unemployment rate constant. Therefore, if the economy grows below its potential, unemployment rises; if it grows faster, unemployment falls.
The original Phillips Curve, developed by A.W. Phillips, showed an inverse relationship between unemployment and inflation, based on data from the UK between 1861 and 1957, later confirmed by Samuelson and Solow for the US. With expected inflation close to zero (πᵗᵉ = 0), the model πᵗ =(m + z)− αuᵗ suggests that lower unemployment can be achieved only at the cost of higher inflation. In other words, policymakers faced a trade-off: reducing unemployment required accepting faster price increases.
The modified Phillips Curve emerged around 1970, when the original relationship between inflation and unemployment broke down. This happened because wage-setters began forming their expectations based on past inflation, as inflation became more persistent and expectations unanchored (πᵗᵉ = πᵗ⁻¹). The new form, πᵗ − πᵗ⁻¹ = (m + z) − αuᵗ, shows that unemployment now affects the change in inflation rather than its level. Empirical estimates for the US (1970–1995) found πᵗ − πᵗ⁻¹ = 7.4% − 1.2uᵗ, meaning that lower unemployment leads to faster inflation increases. This version is known as theaccelerationist or expectations-augmented Phillips Curve, where low unemployment causes inflation to accelerate over time.