## An Example Determining Equilibrium Interest Rates

We take another look at the investor's possible decision to see how it can help in determining equilibrium conditions in the market. The optimum decision could occur in three sections of Figure 1.3: A to B, point B, orBto C. If the optimum occurs in the segment AB, then the investor lends money at the 5% rate. If the optimum occurs at point B, then the investor is neither a borrower nor a lender. Finally, if the optimum occurs in segment BC, the investor borrows against future income at the 5% rate.

In this simple framework, equilibrium in the marketplace is easy to determine. At a 5% interest rate this investor wishes to lend \$2,000, the difference between \$10,000 in income and \$8,000 in consumption. Summing across all investors who wish to lend when the interest rate is 5% gives one point on the supply curve. Similarly summing across investors who wish to borrow at a 5% interest rate gives one point on the demand curve. As the interest rate changes, the amount our hypothetical investor wishes to lend also changes. In fact, if the interest rate is low enough, the investor may change from a lender to a borrower. By

Consumption in period 1

Figure 1.3 Investor equilibrium.

varying the interest rate, the supply and demand curve can be traced out and the equilibrium interest rate determined. The equilibrium interest rate is that rate at which the amount investors wish to borrow is equal to the amount investors wish to lend. This is often called a "market clearing condition." The equilibrium interest rate depends on what each investor's decision problem looks like or the characteristics of a figure like Figure 1.3 for each investor. Figure 1.3 depends on the investor's income in the two periods and the investor's tastes or preferences. Thus, in this simple world, equilibrium interest rates are also determined by the same influences: investors' tastes and investors' income.

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