IS-LM Model¶

by Professor Throckmorton
for Intermediate Macro
W&M ECON 304
Slides

Introduction¶

  • The goods market predicts equilibrium output/income, $Y$.
  • The money market predicts the equilibrium interest rate, $i$.
  • The goal is to build a general equilibrium model where there is joint determination of the endogenous variables in equilibrium.
  • In the money market, money demand is already a function of income, $M^d(Y)$.
  • We can modify the goods market so that investment is endogenous to the interest rate, e.g., if the interest rate falls, borrowing is cheaper, and firms invest more in new capital.

LM Curve¶

  • LM is an abbreviation for Liquidity preference (i.e., money demand) equals Money supply.
  • The IS-LM model will live in the interest rate vs. output space, where each axis corresponds to an equilibrium outcome in one of the markets.
  • In the money market, we assumed that the central bank targets the interest rate regardless of the level of money demand, which is a function of income. See the experiment at the end of the money market chapter.
  • Thus, the LM curve is a flat line at the central bank's interest rate target, $i=i^*$, which shifts up or down if the bank changes the target.
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  • Suppose output/income increases.
  • In the money market, money demand increases, which would usually lead to a higher interest rate.
  • However, the central bank increases the money supply to maintain the interest rate at their target $i = i^*$.
  • Thus, the LM curve is flat.

IS Curve¶

  • IS stands for Investment equals Savings, which is one way to describe the equilibrium in the goods market.
  • Relaxing the assumption of exogenous investment in the goods market, let's instead suppose the investment function is $I=I(Y,i)$, i.e., it is endogenous to revenue and the interest rate.
    1. If $Y\uparrow$, then firms receive more revenue and increase investment, $I\uparrow$.
    2. If $i\downarrow$, then it's cheaper to borrow and firms increase investment, $I\uparrow$.
  • Now, if the central bank changes its interest rate target, then investment with change and affect aggregate expenditure and equilibrium output.
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Shifts¶

  • LM shifts when the central bank changes its interest rate target:
    1. LM shifts up for contractionary monetary policy, $\downarrow M^s$ and $\uparrow i^*$.
    2. LM shifts down for expansionary monetary policy, $\uparrow M^s$ and $\downarrow i^*$.
  • IS shifts when something else affects aggregate expenditure, $ZZ$, besides the interest rate:
    1. $\uparrow G$, $\downarrow T$, or $\uparrow c_0$ shift $ZZ$ up and $IS$ right
    2. $\downarrow G$, $\uparrow T$, or $\downarrow c_0$ shift $ZZ$ down and $IS$ left