CFA® Program Curriculum, Volume 2, page 227 To derive the aggregate demand curve, we need to understand the factors that determine
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• Investment is a function of expected profitability and the cost of financing. Expected profitability depends on the overall level of economic output. Financing costs are reflected in real interest rates, which are approximated by nominal interest rates minus the expected inflation rate.
• Government purchases may be viewed as independent of economic activity to a degree, but tax revenue to the government, and therefore the fiscal balance, is clearly a function of economic output.
• Net exports are a function of domestic disposable incomes (which affect imports), foreign disposable incomes (which affect exports), and relative prices of goods in foreign and domestic markets.
^ The IS curve (income-savings) in Figure 2 illustrates the negative relationship between real interest rates and real income for equilibrium in the goods market. Points on the IS curve are the combinations of real interest rates and income consistent with equilibrium in the goods market (i.e., those combinations of real interest rates and income for which planned expenditures equal income).
Figure 2: The IS Curve
Lower interest rates tend to decrease savings (in favor of current consumption) and tend to increase investment by firms because more investments will have positive NPVs when firms’ cost of capital is lower. Therefore, a decrease in interest rates decreases S — I, so that (S - I) < (G - T) + (X - M). In order to satisfy this fundamental relationship, income must increase. Greater income can restore equilibrium in the goods market by increasing savings (which increases S — I), increasing tax receipts (which decreases G - T), and increasing imports (which decreases X - M).
The LM curve (liquidity-money) in Figure 3 illustrates the positive relationship between real interest rates and income consistent with equilibrium in the money market. Higher real interest rates decrease the quantity of real money balances individuals want to hold, so for a given real money supply (M/P constant), equilibrium in the money market requires that an increase in real interest rates be accompanied by an increase in income.
The increase in the demand for money from an increase in income can offset the decrease in demand for money from higher real interest rates and restore equilibrium in the money market.
Figure 3: The LM Curve
Real interest
rate 6% 5%
4%
Y r=4% Y r=5% Y r=6% Real income
For overall equilibrium, the values of real interest rates and income must be consistent with equilibrium in both the goods market and the money market. We illustrate this simultaneous equilibrium as the intersection of the IS and LM curves in Figure 4.
Figure 4: Simultaneous Equilibrium in the Goods Market and the Money Market
The LM curve is drawn for a given level of the real money supply, M/P. Holding the nominal money supply, M, constant, an increase in the price level decreases the real money supply and a decrease in the price level increases the real money supply. Because an increase (decrease) in the real money supply shifts the LM curve downward (upward), we can identify the different combinations of income and real interest rates consistent
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Figure 5: LM Curves for Different Levels of Real Money Supply
Real
The Aggregate Demand Curve
When the IS and LM curves are combined, the point at which they intersect represents the levels of the real interest rate and income that are consistent with equilibrium between income and expenditure (points along the IS curve) and equilibrium between the real money supply and the real interest rate (points along the LM curve). The intersection between the IS and LM curves determines the equilibrium levels of prices and real income (real GDP) for a given level of the real money supply.
The aggregate demand curve shows the relationship between the quantity of real output demanded (which equals real income) and the price level. When we drew the LM curve, we held the real money supply (M/P) constant. Now, if we hold the nominal money supply (A/) constant, changes in the real money supply are due to changes in the price level (P). An increase in the price level will decrease the real money supply (M/P), and a decrease in the price level will increase the real money supply (M/P).
In Panel (a) of Figure 6, Point A is on an LM curve for a lower real money supply (and therefore a higher price level) than Point B. Point C is on an LM curve for a higher real money supply (and therefore a lower price level) then Point B. As a result, the relationship between the price level and real income, given that income is equal to planned expenditures (the IS curve) and money demand is equal to money supply (the LM curve), must be downward sloping. This is the aggregate demand curve [Panel (b) in Figure 6].
The aggregate demand curve slopes downward because higher price levels (holding the money supply constant) reduce real wealth, increase real interest rates, and make domestically produced goods more expensive compared to goods produced abroad, all of which reduce the quantity of domestic output demanded.
Figure 6: Deriving the Aggregate Demand Curve (a) The IS and LM Curves