Recitation 12

When consumers and investors become more optimistic, the AD curve shifts to the right. In the quantity-theory framework this is equivalent to an increase in velocity \( \dot{v} \), raising nominal spending growth \( \dot{M} + \dot{v} \).

• The new AD curve intersects the SRAS to the right of the original equilibrium.
• The intersection of the new AD with the SRAS \( (E_\pi = 10\%) \) occurs at a higher real GDP growth rate ("High-AD real growth") and a higher inflation rate ("High-AD inflation").
• Since the SRAS is upward-sloping, both real growth and inflation rise above their initial values.

Key intuition: with expected inflation anchored at 10%, a positive demand shock moves the economy up and to the right along the SRAS, temporarily pushing real growth above potential and inflation above 10%.

To fully reverse the AD shock "just right," the central banker tightens monetary policy — reducing money growth \( \dot{M} \) by exactly enough to offset the increase in velocity \( \dot{v} \).

• The AD curve shifts back to the left, returning to its original position: \( AD(\dot{M} + \dot{v} = 13\%) \).
• The economy returns to the original equilibrium: real GDP growth at the potential growth rate, and inflation at 10%.

\[ \pi = 10\% \]

If the central banker perfectly offsets the velocity shock by reducing \( \dot{M} \) by the same amount that \( \dot{v} \) increased, nominal spending growth remains at 13%. The economy stays at the intersection of the original AD curve and the LRAS, and inflation remains exactly 10%.

From the quantity theory:

\[ \dot{M} + \dot{v} = \pi + g_Y \]

With \( \dot{v} = 0 \), potential growth \( g_Y^* = 3\% \), and target inflation \( \pi^* = 2\% \):

\[ \dot{M} = \pi^* + g_Y^* - \dot{v} = 2\% + 3\% - 0\% = 5\% \]

What the central banker should tell the public:

"We are committed to bringing inflation down to 2%. We will set money growth at 5% and maintain it. You should update your inflation expectations to 2%."

Mechanism: the central banker must credibly commit so the SRAS shifts down. If the public believes the announcement and lowers expected inflation to 2%, \( SRAS(E_\pi = 10\%) \) shifts down to \( SRAS(E_\pi = 2\%) \). The new equilibrium is

\[ \pi = 2\%, \quad g_Y = g_Y^* = 3\% \]

Real growth is preserved because the disinflation is costless when fully credible — the economy moves straight down along the LRAS rather than going through a costly recession.

Once expectations are anchored at 2%, the central banker has an incentive to deviate (time inconsistency):

• The central banker could secretly increase money growth above 5% (e.g., back to 13%), shifting AD to the right.
• Because expectations are now anchored at 2%, the economy moves up and to the right along the new \( SRAS(E_\pi = 2\%) \).
• This produces a boom in real GDP growth above potential — politically attractive in an election year.
• The cost (higher inflation) comes later, after the election, when expectations adjust upward and credibility is destroyed for future periods.

To lower the federal funds rate, the Fed must increase the supply of reserves.

• The reserve supply curve is vertical (perfectly inelastic) because the Fed is the monopoly supplier of reserves — it sets the quantity independent of the interest rate.
• Reserve demand is downward-sloping: banks demand more reserves at lower interest rates (opportunity-cost argument).
• To push the equilibrium rate down from 2% to 1.5%, the Fed shifts the vertical supply curve right by conducting open-market purchases (buying Treasury securities, crediting banks with new reserves).
• The new intersection of the rightward-shifted supply with the downward-sloping demand yields the lower equilibrium FFR of 1.5%.

• When the FFR falls to 1.5%, the return on holding reserves at the Fed decreases.
• The opportunity cost of lending falls: banks now give up less by lending out rather than holding reserves at the Fed.
• Banks lend more — not merely because they have more reserves, but because holding reserves has become relatively less attractive.
• Through the money multiplier, the additional lending creates new deposits, enabling further lending.
• The net effect is an increase in the nation's money supply.

This will typically increase aggregate demand.

• A higher money supply raises nominal spending: from the quantity theory, \( AD = \dot{M} + \dot{v} \), so an increase in \( \dot{M} \) shifts AD to the right.
• Lower interest rates also directly stimulate investment and consumption (the interest-rate channel of monetary transmission).
• The rightward shift of AD raises both real GDP growth (in the short run) and inflation.