Scarth_Chapter_2

Macroeconomic Theory: Aggregate Demand and Supply

Author: Faiz Ur Rehman, Department of Economics, IBA, KarachiDate: February 4, 2025Presentation Slides: 1 / 19

Contents

• The Structural Equations

• Short-Run Analysis

• Convergence or Stability Analysis

• Full Equilibrium Analysis

• Alternative Government Policies

The Structural Equations

Key Equations:

1. Y = C + I + G

   • This identity expresses the overall output (Y) as the sum of consumption (C), investment (I), and government spending (G).

2. C = C(Y)

   • Consumption is a function of disposable income (Y); typically associated with the Marginal Propensity to Consume (MPC).

3. I = I(Y, r)

   • Investment depends on income (Y) and the interest rate (r), where higher interest rates generally decrease investment.

4. MP = L(Y, i)

   • The money market equilibrium condition, indicating the demand for money (L) is a function of both income (Y) and the nominal interest rate (i).

5. P˙/P = H((Y − Y¯) / Y¯) + π

   • This equation represents the relationship between the rate of change of the price level (P˙/P) and output relative to potential output (Y¯) along with inflation (π).

Explanation of Equations:

• Equations 1-3 represent the IS (Investment-Savings) relationship, which captures the equilibrium in the goods market.

• Equation 4 represents the LM (Liquidity Preference-Money Supply) relationship, determining equilibrium in the money market.

• Equation 5 shows an expectations-augmented Phillips curve, illustrating the trade-off between unemployment and inflation, focusing on aggregate supply.

Parameters:

• CY, IY > 0: Indicates that consumption and investment are positively related to income.

• Ir < 0: Shows that investment negatively responds to an increase in interest rates.

• LY > 0: Money demand increases with income.

• Li < 0: Money demand decreases with an increase in interest rates.

Assumption:

• Marginal Propensity to Consume (MPC): 0 < CY < 1, suggesting that consumers will spend a portion of any additional income.

Price Assumptions:

• In the short run, prices are often considered fixed, leading firms to adjust production in response to changes in aggregate demand.

Key Features:

• Keynesian Perspective: Fixed prices during the short term can cause output fluctuations driven by demand changes. In the long run, prices adjust, leading to the economy reaching its natural rate of output (Y¯).

• Inflation Relationship: At full employment (Y = Y¯), the actual inflation rate coincides with expected inflation (P˙/P = π). A short-run Phillips curve arises under the condition of zero expected inflation (π).

Model Types:

• Keynesian Model: If the slope of the aggregate supply curve (H) is flat (H′ = 0), indicating demand-driven economy.

• Classical Model: If H' approaches infinity, implying the economy adjusts rapidly to maintain full employment.

Endogenous Variables in Short-Run:

• Y, r, C, I, P˙ - Variables that are determined within the model.

Exogenous Variables:

• G, M, Y¯ - Variables assumed to be determined outside the model and which influence the endogenous variables.

Production Analysis:

• For solving the model, linear approximation techniques are utilized; for example, approximating changes in consumption can be expressed as dC = CY dY.

• A full linear system can be written in change form allowing for comprehensive variable change analysis.

Short-Run Analysis

Short-Run Rewrite:

• Transforming equations for short-run analysis requires defining the relationships between output (Y), interest rates (r), and other determinants.

Multipliers:

• Six primary multipliers are identified:

  • dY/dG: Change in output with respect to government spending.

  • dY/dM: Change in output with respect to the money supply.

  • dY/dP: Change in output with respect to price level adjustments.

  • dr/dG, dr/dM, dr/dP: Sensitivity of interest rates to changes in government spending, money supply, and price levels, respectively.

Denominator Determination:

• Finding determinants through cross-multiplication to establish relationships among variables based on the constructed equations.

Convergence or Stability Analysis

• Derives stability conditions from earlier equations and examines the relationship of output to price to define convergence scenarios.

Negative Slope Condition:

• Establishes convergence of equilibrium under certain conditions where dP˙/dP < 0 demands negative slope for aggregate demand (AD).

Stability Condition:

• Necessary for achieving equilibrium with respect to both IS and LM curves, evaluating shifts in prices and their effect on aggregate demand and supply.

Full Equilibrium Analysis

• In full equilibrium, output equals its natural rate (Y = Y¯), indicating stable prices (P˙ = 0) and no inflation expectations.

• IS-LM approaches dictate how interest rates and price levels find equilibrium based on the response of the economy to changes in the money supply.

Alternative Government Policies

• The role of central banks in determining the demand-driven money supply reflects upon the broader economic impacts, particularly regarding interest rates.

Impacts on Interest Rates:

• Exploring the relationship between nominal and real interest rates during periods of zero inflation (π = 0) sheds light on monetary policy effectiveness.

Matrix Form:

• Establishes connections between changes in price levels and resulting changes in overall demand, assessing the economy’s responsiveness to price fluctuations.

Author: Faiz Ur Rehman, Department of Economics, IBA, KarachiSlide Number: 19 / 19