New Keynesian Business Cycles Model

Motivation. Unlike the Real Business Cycle Model or the Coordination Failure Business Cycle Model, in reality it’s pretty hard for companies to change prices, wage contracts to change, etc. This is called the menu cost, and we assume this is so big that firms can’t change the prices $P$ in the short term. We still have the same Intertemporal Consumption-Leisure Optimization (Full General Equilibrium) model and the Money Market but with the key difference: Price levels $P$ are fixed.

Now assume that for some stupid reason the central bank increases money supply in order to decrease interest rates. Note that:

• ass. Sticky Prices. Price level $\bar{P}$ is fixed no matter what.
• ass. Demand-Determined Output. The output is always demanded, not supplied. At a given $r$, the $Y^{\ast }$ is read off from the $Y^d$ curve, not the $Y^s$ curve.
• The labor demand curve is irrelevant. Read the $N^{\ast }$ off the production function $F(\cdot )$ based on $Y^{\ast }$ from the $Y^d$ curve Then:

1. Central bank sets target interest rate $r^{\ast }$, and matches the $M^s$ to target that interest rate
2. Households…
   1. Demand more at lower $r^{\ast }$
   2. Decrease labor supply (work tomorrow instead)
3. Firms…
   1. Start producing more to match the higher demand $Y^{\ast }$ at new lower $r^{\ast }$
   2. Employ more people at new higher wage $w^{\ast }$ to meet higher demand
   3. Liquidy demand expands as rates decrease and output increases, to meet the new Money supply at the same $\bar{P}$