nhi 106 Lecture_3

Long-Run Labour Supply and Aggregate Demand Notes

Presented by Miguel H. Ferreira, Queen Mary University of London

Overview of Key Concepts

  • Long-Run Labour Supply: The topic primarily focuses on the interaction between the long-run supply of labor and the long-run aggregate demand, leading to labor market equilibrium.

  • Aggregate Demand Components:

    • Private Consumption: Expenditures made by households.

    • Investment: Spending on capital goods.

    • Government Purchases: Government expenditures on goods and services that contribute to economic activity.

Labour Market Equilibrium

  • Understanding Equilibrium:

    • Determined where labor supply meets labor demand.

    • Key variables in equilibrium:

    • Output (Y)

    • Labor (L)

    • Real Wage (W/P)

Model Components

  • Equilibrium Model consists of:

    1. Production Function: Represents the relation between output and inputs.

    2. Labour Demand Curve: Represents the relationship between wage levels and the quantity of labor demanded.

    3. Labour Market Clearing Condition: States that labor demand should equal labor supply.

  • Parameters in the Model:

    1. Productivity Parameter (A): Reflects the efficiency of labor input.

    2. Exogenous Supplies of Capital and Labor: Inputs treated as fixed inputs in the model.

  • General Equilibrium: Occurs when all markets (labor, goods) clear simultaneously.

Equilibrium Real Wage

  • Output Formula: Y^* = A L^{1-\alpha}

    • Labor Calculation:
      L^* = L

    • Rental Wage Rate:
      W^* = MPL

Long-Run Labour Supply Dynamics

  • Understanding Workforce Size:

    • Total workforce is fixed:
      N = L + U

    • Where U is unemployment and l is the total number of employed individuals.

  • Steady-State Condition and Translation:

    • Job Finding Rate (f) and Separation Rate (s) lead to steady-state equation:
      fU = sL

    • Rearranging leads to:
      u = \frac{s}{s+f}

    • Defines the Natural Rate of Unemployment in the long-run.

  • Natural Level of Employment:

    • U = uN = \frac{sN}{s+f}

    • L = (1-u)N = \frac{fN}{s+f}

Labour Market Frictions

  • Understanding Labor Frictions:

    • Reasons for non-zero values of s and f:

    1. Minimum Wage Policies: Can lead to a higher than equilibrium wage, impacting hiring and firing processes.

Long-Run Aggregate Supply

  • Relationship to Aggegate Demand:

    • Output determined by long-run labor supply leads to a fixed long-run aggregate supply (LRAS) curve which is vertical on the graph.

    • The output does not fluctuate with demand changes, illustrating Supply-Side Economics.

    • Aggregate demand stabilizes the price level (P), concluding that aggregate supply is defined.

Critique of the Model

  • Model Limitations:

    • Although it calculates the natural rate of unemployment, it fails to address origins of unemployment.

    • Does not elucidate the time delays in job finding or losing jobs.

Summary of Functions

  • Labour Demand Function (Ld): Endogenously determined by technology, price-level, and wage rates.

  • Labour Supply Function (Ls): Determined by job finding/separation rates and total worker pool (N).

  • Market Equilibrium Result:

    • Long-run (W,L) determined by the interaction of Ld and Ls, leading to clear outputs by the labour supply limitations.

Long-Run Aggregate Demand Components

  • GDP Identity: Y = C + I + G

    • Components Explained:

    • Consumption (C): Expenditures on non-durables, durables, and services.

    • Investment (I): Encompasses residential, business, and inventory investments.

    • Government Purchases (G): Differentiated from total government spending, only current period expenditures are considered.

Simple Model of Consumption

  • Disposable Income Impact on Consumption:

    • Consumption expressed as:
      C = C(Y - T)

    • Specific example:
      C = 100 + 0.3(Y - T) where 0.3 is the marginal propensity to consume (MPC).

Investment Function

  • Dependence on Real Interest Rate (r):

    • High r inhibits investment due to increased opportunity cost of not investing, hence the investment function decreases as r increases.

Government Financial Mechanics

  • Relation Between Government Income and Expenditure:

    • Government revenues (T) come from households and firms:

    • Government budget structure with assumptions for simplicity:

    • Balanced Budget: When G = T

    • Budget Deficit: When G > T

    • Budget Surplus: When G < T

Equilibrium in Goods Market

  • Aggregate Demand and Supply Equilibrium:

    • Demand Equation:
      Y^d = C(Y - T)+I(r)+G

    • Aggregate Supply Equation:
      Y^s = F(K,L^*) = Y

    • Equilibrium condition:
      Y^s = Y = Y^d and several aggregate components become exogenous leading to demand solely based on interest rates (r).

Financial Market Dynamics

  • Interaction between Savings and Investments:

    • Equilibrium is achieved when:
      S(r) = I(r)

    • Equilibrium Condition:

    • If supply of savings exceeds investment demand, it indicates a high interest rate, while if the investment demand is greater, the interest rate is too low.

Future Topics to Explore

  • Upcoming sessions will focus on the Dynamics of Financial Markets and the impacts of Fiscal Policy, particularly the role of money and supply in the economy.