Chapter 10 In this chapter, We focus on the short run, and temporarily set aside the question of whether the economy has the resources to produce the output demanded. We examine the determination of r and Y when the price level, P, is given. We then establish the relationship between the price level and the real GDP 0
the IS Outline curve, and its relation to: the Keynesian cross the loanable funds model the LM curve, and its relation to: the theory of liquidity preference how the IS-LM model determines income and the interest rate in the short run when P is fixed 1
The Keynesian Cross A simple closed economy model in which income is determined by expenditure (spending). Notation: I = planned investment PE = C + I + G = planned expenditure Y = real GDP = actual expenditure Spending Balance: aggregate spending (planned expenditure) consistent with the income that the public bases its spending decisions on. 2
Elements of the Keynesian Cross consumption function: govt policy variables: C = C ( Y T ) G = G, T = T for now, planned investment is exogenous: I = I planned expenditure: PE = C ( Y T ) + I + G equilibrium condition: actual expenditure = planned expenditure Y = PE 3
The equilibrium value of income PE planned expenditure PE =Y PE =C +I +G income, output, Y Equilibrium income 4
An increase in government purchases PE At Y 1, there is now an unplanned drop in inventory PE =C +I +G 2 PE =C +I +G 1 G so firms increase output, and income rises toward a new equilibrium. PE 1 = Y 1 Y Y PE 2 = Y 2 5
Solving for Y Y = C + I + G Y = C + I + G = C + G = MPC Y + G Collect terms with Y on the left side of the equals sign: (1 MPC) Y = G equilibrium condition in changes because I exogenous because C = MPC Y Solve for Y : 1 Y = G 1 MPC 6
The government purchases multiplier Definition: the increase in income resulting from a $1 increase in G. In this model, the govt purchases multiplier equals Y G = 1 1 MPC Example: If MPC = 0.8, then Y 1 = = 5 G 1 0.8 An increase in G causes income to increase 5 times as much! 7
Why the multiplier is greater than 1 Initially, the increase in G causes an equal increase in Y: Y = G. But Y C further Y further C further Y So the final impact on income is much bigger than the initial G. 8
An increase in taxes Initially, the tax increase reduces consumption, and therefore PE: PE PE =C 1 +I +G PE =C 2 +I +G C = MPC T so firms reduce output, and income falls toward a new equilibrium PE 2 = Y 2 Y At Y 1, there is now an unplanned inventory buildup PE 1 = Y 1 Y 9
Solving for Y Y = C + I + G = C eq m condition in changes I and G exogenous ( Y T ) = MPC Solving for Y : (1 MPC) Y = MPC T Final result: MPC Y = T 1 MPC 10
The tax multiplier def: the change in income resulting from a $1 increase in T : Y T = MPC 1 MPC If MPC = 0.8, then the tax multiplier equals Y 0.8 0.8 = = = T 1 0.8 0.2 4 11
is negative: A tax increase reduces C, which reduces income. The tax multiplier is smaller than the govt spending multiplier: Consumers save the fraction (1 MPC) of a tax cut, so the initial boost in spending from a tax cut is smaller than from an equal increase in G. 12
Deriving the IS curve PE PE =Y PE =C +I (r 2 )+G r I PE =C +I (r 1 )+G PE I Y r Y 1 Y 2 Y r 1 r 2 Y 1 Y 2 IS Y 13
The IS curve def: a graph of all combinations of r and Y that result in goods market equilibrium i.e. actual expenditure (output) = planned expenditure The equation for the IS curve is: Y = C ( Y T ) + I ( r ) + G 14
The Slope of the IS curve A fall in the interest rate motivates firms to increase investment spending, which drives up total planned spending (PE ). To restore equilibrium in the goods market, output (a.k.a. actual expenditure, Y ) must increase. Question: what does the IS curve look like if investment does not depend upon the interest rate? 15
Fiscal Policy and the IS curve We can use the IS-LM model to see how fiscal policy (G and T ) affects aggregate demand and output. Let s start by using the Keynesian cross to see how fiscal policy shifts the IS curve 16
Shifting the IS curve: G At any value of r, G PE Y so the IS curve shifts to the right. PE PE =Y PE =C +I (r 1 )+G 2 PE =C +I (r 1 )+G 1 The horizontal distance of the IS shift equals r r 1 Y 1 1 Y = G Y 1 MPC Y 1 Y 2 Y 2 IS 1 Y IS 2 Y 17
Shifting the IS curve: T At any value of r, T C PE so the IS curve shifts to the left. PE PE =Y PE =C 1 +I (r 1 )+G PE =C 2 +I (r 1 )+G The horizontal distance of the IS shift equals r r 1 Y 2 Y 1 Y MPC Y = T 1 MPC Y Y 2 Y 1 IS 2 IS 1 Y
The Theory of Liquidity Preference Due to John Maynard Keynes. A simple theory in which the interest rate is determined by money supply and money demand. CHAPTER 1 The Science of Macroeconomics 19
Money supply The supply of real money balances is fixed: r interest rate ( M P ) s ( M P ) s = M P M P M/P real money balances CHAPTER 1 The Science of Macroeconomics 20
Money Demand and The LM curve Now let s put Y back into the money demand function: ( M P ) d = L( r, Y ) The LM curve is a graph of all combinations of r and Y that equate the supply and demand for real money balances. The equation for the LM curve is: M P = L( r, Y ) CHAPTER 1 The Science of Macroeconomics 21
Deriving the LM curve r (a) The market for real money balances r (b) The LM curve LM r 2 r 2 L (r, Y 2 ) r 1 r 1 L (r, Y 1 ) M 1 P M/P Y 1 Y 2 Y CHAPTER 1 The Science of Macroeconomics 22
The Slope of the LM Curve An increase in income raises money demand. Since the supply of real balances is fixed, there is now excess demand in the money market at the initial interest rate. The interest rate must rise to restore equilibrium in the money market. CHAPTER 1 The Science of Macroeconomics 23
More on the Slope of the LM Curve How does the LM curve look like if Money demand does not depend upon the interest rate? Money demand does not depend upon income? Money demand is extremely sensitive to the interest rate? CHAPTER 1 The Science of Macroeconomics 24
How M shifts the LM curve r (a) The market for real money balances r (b) The LM curve LM 2 r 2 r 2 LM 1 r 1 L (r, Y 1 ) r 1 M 2 P M 1 P M/P Y 1 Y CHAPTER 1 The Science of Macroeconomics 25
Example: Shifting the LM curve Suppose a wave of credit card fraud causes consumers to use cash more frequently in transactions. Use the liquidity preference model to show how these events shift the LM curve. CHAPTER 1 The Science of Macroeconomics 26
Example: Shifting the LM curve r (a) The market for real money balances r (b) The LM curve LM 2 r 2 r 1 L (r, Y 1 ) L (r, Y 1 ) r 2 LM 1 r 1 M 1 P M/P Y 1 Y CHAPTER 1 The Science of Macroeconomics 27
The short-run equilibrium The short-run equilibrium is the combination of r and Y that simultaneously satisfies the equilibrium conditions in the goods & money markets: r LM Y = C ( Y T ) + I ( r ) + G M P = L( r, Y ) Equilibrium interest rate CHAPTER 1 The Science of Macroeconomics IS Equilibrium level of income Y 28
The Big Picture Keynesian Cross Theory of Liquidity Preference IS curve LM curve IS-LM model Explanation of short-run fluctuations Agg. demand curve Agg. supply curve Model of Agg. Demand and Agg. Supply CHAPTER 1 The Science of Macroeconomics 29
Preview of Chapter 11 In Chapter 11, we will use the IS-LM model to analyze the impact of policies and shocks. learn how the aggregate demand curve comes from IS-LM. use the IS-LM and AD-AS models together to analyze the short-run and long-run effects of shocks. CHAPTER 1 The Science of Macroeconomics 30
1. Keynesian cross Chapter Summary basic model of income determination takes fiscal policy & investment as exogenous fiscal policy has a multiplier effect on income 2. IS curve comes from Keynesian cross when planned investment depends negatively on interest rate shows all combinations of r and Y that equate planned expenditure with actual expenditure on goods & services CHAPTER 1 The Science of Macroeconomics 31
Chapter Summary 3. Theory of Liquidity Preference basic model of interest rate determination takes money supply & price level as exogenous an increase in the money supply lowers the interest rate 4. LM curve comes from liquidity preference theory when money demand depends positively on income shows all combinations of r and Y that equate demand for real money balances with supply CHAPTER 1 The Science of Macroeconomics 32
5. IS-LM model Chapter Summary Intersection of IS and LM curves shows the unique point (Y, r ) that satisfies equilibrium in both the goods and money markets. CHAPTER 1 The Science of Macroeconomics 33