As explained in Chapter 15, a fall in the interest rate leads to a rise in investment spending, I, which then leads to a rise in both real GDP and consumer spending, C. The rise in real GDP doesn’t lead only to a rise in consumer spending, however. It also leads to a rise in savings: at each stage of the multiplier process, part of the increase in disposable income is saved. How much do savings rise?

In Chapter 10 we introduced the savings–investment spending identity: total savings in the economy is always equal to investment spending. This tells us that when a fall in the interest rate leads to higher investment spending, the resulting increase in real GDP generates exactly enough additional savings to match the rise in investment spending. To put it another way, after a fall in the interest rate, the quantity of savings supplied rises exactly enough to match the quantity of savings demanded. Understanding this relationship is the key to reconciling the two models of the interest rate.

Figure 15A-1 illustrates how the two models of the interest rate are reconciled in the short run. Panel (a) shows the liquidity preference model of the interest rate where MS₁ and MD₁ are the initial supply and demand curves for money, and r₁, the initial equilibrium interest rate, equalizes the quantity of money supplied to the quantity of money demanded in the money market. Panel (b) shows the loanable funds model of the interest rate where S₁ is the initial supply curve, D is the demand curve for loanable funds, and r₁, the initial equilibrium interest rate, equalizes the quantity of loanable funds supplied to the quantity of loanable funds demanded in the market for loanable funds.

In Figure 15A-1 both the money market and the market for loanable funds are initially in equilibrium at E₁ with the same interest rate, r₁. You might think that this would only happen by accident, but in fact it will always be true. To see why, consider what happens in panel (a), the money market, when the Fed increases the money supply from to , pushing the money supply curve rightward, to MS₂, reducing the equilibrium interest rate in the market to r₂, and moving the economy to a short-run equilibrium at E₂.

What happens in panel (b), the market for loanable funds? In the short run, the fall in the interest rate due to the increase in the money supply leads to a rise in real GDP, which generates a rise in savings through the multiplier process. This rise in savings shifts the supply curve for loanable funds rightward, from S₁ to S₂, moving the equilibrium in the loanable funds market from E₁ to E₂ and reducing the equilibrium interest rate in the loanable funds market. Since the rise in savings must exactly match the rise in investment spending, the equilibrium rate in the loanable funds market must fall to r₂, the same as the new equilibrium interest rate in the money market.

In the short run, then, the supply and demand for money determine the interest rate, and the loanable funds market follows the lead of the money market until the equilibrium interest rate in the loanable funds market is the same as the equilibrium interest rate in the money market.

Notice our use of the phrase “in the short run.” Changes in aggregate demand affect aggregate output only in the short run. In the long run, aggregate output is equal to potential output. So our story about how a fall in the interest rate leads to a rise in aggregate output, which leads to a rise in savings, applies only to the short run.

In the long run, as we’ll see next, the determination of the interest rate is quite different, because the roles of the two markets are reversed. In the long run, the loanable funds market determines the equilibrium interest rate, and it is the market for money that follows the lead of the loanable funds market.