chap 13

Introduction to IS–LM Model

• This chapter covers important concepts related to the IS–LM model.

  • Relationship of IS curve to:

  • Keynesian cross

  • Loanable funds model

  • Relationship of LM curve to:

  • Theory of liquidity preference

  • Determination of income and interest rate in the short run when the price level (P) is fixed.

Contextual Background

• Recap from Chapter 12: Introduction to aggregate demand and aggregate supply model.

  • Long Run Characteristics:

    • Prices are flexible.

    • Output determined by factors of production and technology.

    • Unemployment equals its natural rate.

  • Short Run Characteristics:

    • Prices are fixed.

    • Output determined by aggregate demand.

    • Unemployment is negatively related to output.

Development of the IS–LM Model

• This chapter fully develops the IS–LM model that serves as the foundation for the aggregate demand curve.

  • Focus is on short-run scenarios where the price level remains fixed (horizontal Short Run Aggregate Supply curve).

  • Future chapters will address closed-economy cases (Chapters 13 and 14) and open-economy cases (Chapter 15).

Keynesian Cross Model

• Overview of the Keynesian cross, a simple closed-economy model determining income through expenditure (originating from J.M. Keynes).

  • Key Notation:

    • I = Planned investment

    • PE = C + I + G = Planned expenditure

    • Y = Real GDP = Actual expenditure

  • Important Concept: Difference between actual expenditure and planned expenditure equals unplanned inventory investment.

Elements of the Keynesian Cross

• Consumption Function: C = C(Y – T)

  • Where G = Government purchases, T = Taxes.

  • The planned investment is treated as exogenous: I = .

• Planned Expenditure Equation:

  • $PE = C(Y - T) + I + G$

• Equilibrium Condition:

  • $Y = PE$

Graphical Representation of Planned Expenditure

• Graph showing planned expenditure (PE) versus income/output (Y).

  • Representation of a consumption function with a slope defined by Marginal Propensity to Consume (MPC).

Graphical Representation of Equilibrium Condition

• Graph illustrating the equilibrium condition where planned expenditure equals actual expenditure.

  • The 45-degree line in the graph indicates points where actual expenditure equals planned expenditure.

Adjustment to Equilibrium

• Explanation of how economic adjustments lead to equilibrium:

  • Unplanned drop in inventory leads to an increase in income.

  • Conversely, unplanned inventory accumulation results in a decrease in income.

Impact of Increased Government Purchases

• An increase in government purchases raises planned expenditure (PE) by an amount $ΔG$.

  • Movement from equilibrium A to B results in an increase in income greater than the increase in G.

  • Higher income leads to higher consumption, initiating a multiplier process until a new equilibrium ($Y_2$) is reached.

Calculating Changes in Income (ΔY)

• Using the equilibrium condition:

  • $ΔY = ΔC + ΔI + ΔG$

  • Since I is fixed:

  • $ΔY = (MPC imes ΔY) + ΔG$

  • Reorganizing gives a formula:

  • $rac{ΔY}{1 - MPC} = ΔG$

Definition of the Government Purchases Multiplier

• A measure of income increase resulting from a $1 increase in G:

  • $Y = rac{ΔG}{1 - MPC}$

  • Example when MPC = 0.8 yields 5 as the multiplier:

  • $rac{1}{0.2} = 5$

  • This means an increase in G results in a greater rise in income.

Understanding the Multiplier Effect

• Initial increase in government spending leads to an equal initial increase in income.

• Higher income generates more consumption (C), leading to more income and perpetuating the cycle.

Impact of Tax Decrease

• A decrease in taxes increases planned expenditure by $MPC imes ΔT$.

  • This shifts equilibrium from A to B, leading to a rise in income greater than the tax decrease if $MPC > 0.5$.

Solving for Changes in Income (Tax cut)

• Utilizing the equilibrium condition:

  • $ΔY = MPC imes (ΔY - ΔT)$

  • Final formula derived:

  • $rac{ΔY}{1 - MPC} = -MPC imes ΔT$

Definition of the Tax Multiplier

• Measure of income change resulting from a $1 increase in T:

  • $Y = - rac{ΔT}{1 - MPC}$

  • For $MPC = 0.8$, the tax multiplier becomes:

  • $- rac{0.8}{0.2} = -4$

Negative Impact of Tax Increase

• A tax increase causes a reduction in consumption, which in turn reduces overall income.

  • The tax multiplier, in absolute value, is greater than one if $MPC > 0.5$.

The IS Curve

• Definition and Functionality:

  • A graphical representation of all combinations of real interest rates (r) and income (Y) that lead to goods market equilibrium.

  • Equation for the IS curve:

  • $Y = C(Y - T(r)) + I(r) + G$

Deriving the IS Curve

• Description of the negative slope:

  • A decrease in the real interest rate induces higher planned investment and thereby increases income.

  • Summary of the relationship: the lower the interest rate, the higher the income level.

Effects of Fiscal Policy on the IS Curve

• Fiscal policy shifts the IS curve.

• Increased government spending shifts the IS curve to the right due to increased planned expenditure at all values of r.

  • The horizontal distance of the IS shift:

  • $rac{ΔY}{1 - MPC} = ΔG$

Tax Changes and the IS Curve

• An increase in taxes shifts the IS curve to the left.

• The size of the shift can be expressed:

  • $- rac{ΔY}{MPC} = ΔT$

Theory of Liquidity Preference

• Introduced by John Maynard Keynes.

• Basic premise that the interest rate is determined by the supply and demand for money.

Money Supply

• Definition of real money balances as a fixed quantity:

  • $M/P = s$

Money Demand

• Demand for real balances is defined as:

  • $(M/P)_{d} = L(r)$

• Graphical representation shows equilibrium point determining interest rate (r*).

How the Fed Raises Interest Rates

• The Federal Reserve's actions to reduce the money supply increase interest rates.

Case Study: Monetary Tightening

• December 1970s Economic Conditions:

  • Inflation above 10%.

  • Fed's policies designed to reduce money supply.

• Predicted effects on nominal interest rates analyzed through:

  • Short Run: Model using liquidity preference.

  • Long Run: Model using quantity theory and Fisher effect.

• Historical interest rates observed reflecting this model's predictions.

The LM Curve

• Explanation and function of the LM curve:

  • Depicts combinations of r and Y equating money supply and demand.

  • Equation for LM curve:

  • $rac{M}{P} = L(r, Y)$

Deriving the LM Curve

• As income increases (from $Y<em>1$ to $Y</em>2$), demand for money rises, leading to increased interest rates, thus shifting the LM curve upward.

Characteristics of LM Curve

• Upward slope explanations:

  • Increased income raises money demand, leading to excess demand at current interest rates, which necessitates a rise in rates for market equilibrium.

Shifts in LM Curve due to Money Supply Changes

• A decrease in money supply shifts the LM curve upwards, illustrating higher interest rates.

Short-Run Equilibrium

• The short-run equilibrium represents the combination of interest rate (r) and income (Y) satisfying equilibrium conditions simultaneously in goods and money markets:

  • $Y = C(Y - T) + I(r) + G$

  • $rac{M}{P} = L(r, Y)$

Summary and Connection of IS-LM Model to Economics

• The IS-LM model integrates the Keynesian cross and liquidity preference theories, explaining short-run economic fluctuations.

• It elucidates aggregate demand and short-run impacts resulting from various economic policies and shocks.

Overview of the Next Chapter

• In the upcoming Chapter 14, analyses will be conducted using the IS–LM model to explore policy impacts and shocks, focusing on deriving the aggregate demand curve from the IS–LM framework and utilizing both IS–LM and Aggregate Demand – Aggregate Supply models to comprehend short-run and long-run effects.