Question 2 · Introducció a la Macroeconomia UPF 2021

Graphical diagrams for parts a, b, c, d, and e

Solución: a. WS-PS diagram: The horizontal PS line $\frac{W}{P} = \frac{1}{1+m}$ shifts downward to $\frac{1}{1+m'}$. The downward-sloping WS curve remains unchanged. The equilibrium moves from point $A$ to point $A'$, characterized by a lower real wage and a higher natural rate of unemployment $u'_n > u_n$. b. Phillips curve diagram: In the $(\bar{\pi}_t - \bar{\pi}_{t-1}, Y)$ space, the PC line has a positive slope and crosses the horizontal axis (zero change in inflation) at potential output $Y_n$. When potential output falls to $Y'_n$, the curve shifts leftward/upward to $PC'$, intersecting the horizontal axis at $Y'_n$. c. IS-LM-PC diagram (part c): In the top panel (IS-LM), the IS curve shifts substantially leftward to $IS'$ so that equilibrium output $Y_1^*$ is strictly below the new lower potential output $Y'_n$. In the bottom panel (PC), output $Y_1^*$ corresponds to a negative output gap $(Y_1^* - Y'_n < 0)$ on $PC'$, resulting in decelerating inflation $(\bar{\pi}_t - \bar{\pi}_{t-1} < 0)$. d. IS-LM-PC diagram (part d): Fiscal expansion shifts the IS curve rightward back to the original position $IS'' = IS$, yielding output $Y_2^* = Y_n$. Because potential output is now $Y'_n < Y_n$, on curve $PC'$ this corresponds to a positive output gap $(Y_2^* - Y'_n > 0)$ and accelerating inflation $(\bar{\pi}_t - \bar{\pi}_{t-1} > 0)$. e. IS-LM-PC diagram (part e): The recommended fiscal stimulus shifts the IS curve rightward to $IS'''$, intersecting the LM curve at exactly the new potential output $Y = Y'_n$. This closes the output gap on $PC'$, stabilizing inflation $(\bar{\pi}_t - \bar{\pi}_{t-1} = 0)$.

a. (0.3 points) Using the wage-setting (WS) and price-setting (PS) equations, depict the medium-run labor market equilibrium before and after the shock. State the mathematical equations for both curves and provide an economic interpretation of the changes in the natural unemployment rate and real wages.

Solución: Wage Setting (WS): $\frac{W}{P^e} = F(u, z)$ Price Setting (PS): $\frac{W}{P} = \frac{1}{1+m}$ Equilibrium condition ($P = P^e$): $F(u_n, z) = \frac{1}{1+m}$ The increase in markup from $m$ to $m'$ lowers the equilibrium real wage to $\frac{1}{1+m'}$ and increases the natural rate of unemployment ($u'_n > u_n$), reducing potential output ($Y'_n < Y_n$).

b. (0.3 points) Graphically illustrate the Phillips curve (relating output $Y$ to the change in inflation $\bar{\pi}_t - \bar{\pi}_{t-1}$) before and after the pandemic. Write down the equation of the Phillips curve and explain the shift in potential output from $Y_n$ to $Y'_n$.

Solución: Phillips Curve: $\bar{\pi}_t - \bar{\pi}_{t-1} = \frac{\bar{\alpha}}{L}(Y_t - Y_n)$ With the decline in potential output from $Y_n$ to $Y'_n$, the output level consistent with stable inflation shifts left, shifting the Phillips curve upward/leftward from $PC$ to $PC'$.

c. (0.3 points) Suppose the crisis not only affects locked-down sectors, but also depresses general consumer and business confidence, such that aggregate demand contracts by an amount greater than the reduction in potential output. Represent the short-run equilibrium in an IS-LM-PC diagram. Is this point a medium-run equilibrium? Describe the behavior of output and inflation.

Solución: Output falls to $Y_1^* < Y'_n < Y_n$ due to a strong leftward shift of the IS curve. Inflation decelerates ($\bar{\pi}_t - \bar{\pi}_{t-1} < 0$). This is not a medium-run equilibrium because inflation is decreasing rather than stable.

d. (0.3 points) Suppose the fiscal authority expands public expenditure $G$ by exactly the amount needed to compensate for the drop in private consumption and investment. Show the new short-run equilibrium on the IS-LM-PC diagram. Is this sustainable as a medium-run equilibrium if the lockdown persists?

Solución: Output returns to $Y_2^* = Y_n$. Because potential output is permanently lower at $Y'_n$, there is a positive output gap ($Y_2^* > Y'_n$), causing inflation to accelerate. This is not sustainable in the medium run because monetary policy would have to increase interest rates to stop inflation from accelerating.

e. (0.3 points) Propose an alternative, more suitable policy mix for this economy instead of the one outlined in part 2.4. Justify your answer using macroeconomic reasoning and an IS-LM-PC diagram.

Solución: An optimal policy mix expands fiscal spending moderately so that aggregate demand aligns with the new potential output $Y = Y'_n$ ($IS'''$). This stabilizes inflation ($\bar{\pi}_t - \bar{\pi}_{t-1} = 0$) and avoids excessive debt accumulation and overshooting.