The Goods Market and the IS Relation
Equilibrium in the goods market exists when production, Y, is equal to the demand for goods, Z. This condition is called the IS relation.
In the simple model developed previously, the interest rate did not affect the demand for goods. The equilibrium condition was given by: $Y = C(Y - T) + \overline I + G$
Investment, Sales, and the Interest Rate
Investment depends primarily on two factors:
- The level of sales (+)
The interest rate (-)
$I = I(Y, i)$(Y是销售水平, i是利率)
Determining Output
Taking into account the investment relation, the equilibrium condition in the goods market becomes: $Y = C(Y - T) + I(Y, i) + G$
For a given value of the interest rate i, demand is an increasing function of output
- An increase in output leads to an increase in income and also to an increase in disposable income
- An increase in output also leads to an increase in investment
The demand for goods is an increasing function of output. Equilibrium requires that the demand for goods be equal to output:
- two characteristics of ZZ(需求函数):
- Because it’s assumed that the consumption and investment relations in Equation $Y = C(Y - T) + I(Y, i) + G$ are linear, ZZ is, in general, a curve rather than a line
- ZZ is drawn flatter than a 45-degree line because it’s assumed that an increase in output leads to a less than one-for-one increase in demand
Deriving the IS Curve
- The Derivation of the IS Curve
- An increase in the interest rate decreases the demand for goods at any level of output, leading to a decrease in the equilibrium level of output
- Equilibrium in the goods market implies that an increase in the interest rate leads to a decrease in output. The IS curve is therefore downward sloping
Shifts of the IS Curve
- Changes in factors that decrease the demand for goods, given the interest rate, shift the IS curve to the left. Changes in factors that increase the demand for goods, given the interest rate, shift the IS curve to the right.
An increase in taxes shifts the IS curve to the left:
使IS曲线向右移动的做法：增加政府支出，减税，扩张性财政政策(利率下降)等
Financial Markets and the LM Relation
The interest rate is determined by the equality of the supply of and the demand for money: $M = \$YL(i)$
M = nominal money stock
- $YL(i) = demand for money
- $Y = nominal income
i = nominal interest rate
The LM relation: In equilibrium, the real money supply is equal to the real money demand, which depends on real income, Y, and the interest rate, i: $\frac{M}{P} = YL(i)$
Nominal GDP = Real GDP multiplied by the GDP deflator: $\$Y = YP$, equivalently: $\frac{\$Y}{P} = Y$
Deriving the LM Curve
- The Derivation of the LM Curve
- An increase in income leads, at a given interest rate, to an increase in the demand for money. Given the money supply, this increase in the demand for money leads to an increase in the equilibrium interest rate
- Equilibrium in the financial markets implies that an increase in income leads to an increase in the interest rate. The LM curve is therefore upward sloping
Shifts of the LM Curve
An increase in money causes the LM curve to shift down:
- An increase in the money supply shifts the LM curve down; a decrease in the money supply shifts the LM curve up
国家增加货币供给会使LM曲线向下移
Putting the IS and the LM Relations Together
- IS relation: $Y = C(Y - T) + I(Y, i) + G$
- LM relation: $\frac{M}{P} = YL(i)$
- Equilibrium in the goods market implies that an increase in the interest rate leads to a decrease in output. This is represented by the IS curve. Equilibrium in financial markets implies that an increase in output leads to an increase in the interest rate. This is represented by the LM curve. Only at point A, which is on both curves, are both goods and financial markets in equilibrium.
Fiscal Policy, Activity, and the Interest Rate
Fiscal contraction(紧缩性财政政策), or fiscal consolidation, refers to fiscal policy that reduces the budget deficit(削减赤字, 减小政府支出)
An increase in the deficit is called a fiscal expansion(扩张性财政政策)
Taxes affect the IS curve, not the LM curve
对$Y = c(Y - T) + I(Y, i) + G$中G的调控和对c(Y - T)的调控
Monetary contraction(紧缩性货币政策), or monetary tightening, refers to a decrease in the money supply(减少货币供给)
An increase in the money supply is called monetary expansion(扩张性货币政策)
Monetary policy does not affect the IS curve, only the LM curve
A monetary expansion leads to higher output and a lower interest rate:
Using a Policy Mix
- Investment = Private saving + Public saving I = S + (T – G)
- A fiscal contraction may decrease investment. Or, looking at the reverse policy, a fiscal expansion — a decrease in taxes or an increase in spending—may actually increase investment
How Does the IS-LM Model Fit the Facts?
Consumers are likely to take some time to adjust their consumption following a change in disposable income
Firms are likely to take some time to adjust investment spending following a change in their sales
Firms are likely to take some time to adjust investment spending following a change in the interest rate
Firms are likely to take some time to adjust production following a change in their sales