Question 1 · Introducció a la Macroeconomia UPF 2021

Diagrams for parts (a), (b), (d), and (g)

Solución: a. Standard IS-LM: Downward-sloping IS curve, horizontal LM curve at $r = \bar{r}$. Equilibrium output $Y$ at the intersection. b. Shock in $Q$: The IS curve shifts leftward to $IS'$. Output contracts from $Y$ to $Y'$, while $r$ remains unchanged at $\bar{r}$. d. Fiscal expansion: Higher $G$ and lower net $T$ shift the IS curve rightward from $IS'$ toward $IS''$, offsetting the output contraction. g. Asset purchases lowering $x$: Stimulates investment, shifting the IS curve rightward from $IS'$ toward $IS''$ at given policy rate $r$.

a) Clarify the slope of each schedule and identify joint equilibrium.

Solución: The vertical axis represents the real interest rate $r$ and the horizontal axis represents output/income $Y$. The LM curve is horizontal at $r = \bar{r}$ because the central bank targets the interest rate directly through open-market operations. The IS curve is downward-sloping: a higher real rate increases the cost of capital, dampening investment and aggregate demand, which reduces equilibrium output via the multiplier. The intersection of IS and LM gives joint equilibrium in the goods and financial markets.

b) Describe the qualitative adjustments in output and the real interest rate after an increase in Q.

Solución: An increase in perceived crisis risk $Q$ reduces both consumer confidence and business investment sentiment. For any given policy rate $r$, aggregate expenditure falls, shifting the IS curve inward to the left (from IS to IS'). Because the central bank holds $r$ fixed, output contracts from $Y$ to $Y'$, while the real interest rate remains unchanged at $\bar{r}$.

c) Directional effect of the pandemic shock on C, I, Y, and r

Solución: Consumption ($C$): ↓ decrease; Investment ($I$): ↓ decrease; Production ($Y$): ↓ decrease; Income ($Y$): ↓ decrease; Real interest rate ($r$): → constant / unchanged

d) Depict the graphical impact of expansionary fiscal measures relative to the post-shock position.

Solución: The expansionary fiscal packages (increases in $G$ and transfers / tax relief lowering net $T$) increase autonomous demand, shifting the IS curve rightward from IS' toward IS''. On the diagram, this partially or fully offsets the initial contraction in output, moving the equilibrium back toward the initial level of economic activity.

e) Impact of expansionary fiscal package on C, I, Y, and r

Solución: Consumption ($C$): ↑ increase; Investment ($I$): ↑ increase; Production ($Y$): ↑ increase; Income ($Y$): ↑ increase; Real interest rate ($r$): → constant / unchanged

f) Why did the ECB decide not to lower its key interest rates further?

Solución: Because nominal policy rates were already at or below zero, the monetary authority was constrained by the Effective/Zero Lower Bound (liquidity trap conditions). Further expansion of conventional high-powered money supplies cannot meaningfully compress nominal policy rates any further.

g) Explain how asset purchase programs reducing the risk premium x impact the IS-LM equilibrium.

Solución: By purchasing massive quantities of private and public debt, the central bank provides liquidity and compresses credit spreads, effectively lowering the risk premium $x$. With a lower borrowing cost $r + x$, firms face cheaper financing, which stimulates investment and shifts the IS curve rightward from IS' toward IS'' at the given policy rate $r$. Output expands toward potential without altering the policy rate.