Long-Run Labour Supply and Aggregate Demand

Long-Run Labour Supply and Aggregate Demand

Overview of Concepts

  • Labour Market Equilibrium: The interaction of long-run labour supply with labor demand leads to equilibrium in the labour market.
    • Key components include:
    • Long-run aggregate supply (LRAS)
    • Aggregate demand (AD) composed of:
      • Private consumption (C)
      • Investment (I)
      • Government purchases (G)
  • Recommended Readings:
    • Mankiw: Chapter 3.3-3.4
    • Jones: Chapter 4.3
    • Ferreira: Long-Run Labour Supply and Aggregate Demand

Labour Market Equilibrium

  • Endogenous Variables:
    1. Output ($Y$)
    2. Labor ($L$)
    3. Real wage ($W / P$)
  • Equations:
    1. Production function
    2. Labour demand function
    3. Labour market clearing condition: Labour demand = Labour supply
  • Model Parameters:
    1. Productivity parameter ($A$)
    2. Exogenous supplies of capital and labor
  • A solution yields an equilibrium where three unknowns are expressed in terms of parameters and exogenous variables.

Long-Run Labour Supply

  • Workforce Dynamics:

    • Fixed size of workforce: $N = L + U$
    • Unemployment rate: $u = rac{U}{N}$
    • Job dynamics:
    • Fraction $f$ of unemployed find jobs: $fU$
    • Fraction $s$ of employed lose jobs: $sL$

  • In the long-run, steady-state occurs when:
    fU=sLf U = s L

    • This translates to a natural rate of unemployment:
      u = rac{s}{s+f}

  • Key Relationships:

    • Natural level of unemployment:
      U = uN = rac{sN}{s+f}

    • Natural level of employment:
      L = (1-u)N = rac{fN}{s+f}

Labour Market Frictions

  • Why Misalignment Exists:
    1. Not every worker finds a job ($f < 1$).
    2. Workers may leave their jobs ($s > 0$).
  • Minimum Wage Policies: A higher-than-equilibrium minimum wage can:
    • Decrease hiring ($f < 1$)
    • Increase worker separations ($s > 0$)

Long-Run Aggregate Supply (LRAS)

  • Once $L^$ is established, aggregate supply can be defined: Ys=F(L</em>)=YY_s = F(L^</em>) = Y
    • LRAS is a vertical line confirming fixed equilibrium output: Y∗=YY^* = Y
    • The implication is that aggregate demand establishes price levels only, referred to as "Supply-Side Economics".

Components of Aggregate Demand

  • The equation for GDP in the goods and services market is:
    Y=C+I+GY = C + I + G
  • Consumption Components:
    • Non-durables: Food, clothing
    • Durables: Cars, appliances
    • Services: Rents, health care
  • Investment Categories:
    • Residential and business investments
    • Inventory changes (positive/negative)
  • Government Purchases: Includes current expenditures only, leading to impacts on the budget (surplus/deficit).

Financial Market Dynamics

  • Investment Dependencies:
    • Investments depend on real interest rate ($r$), inversely correlated with the rate:
      I=I(r)I = I(r)
  • Savings Function: S=Y−C(Y−T)−GS = Y - C(Y - T) - G
    • National saving = Private saving + Public saving (from tax revenue)
  • Equilibrium Condition: In equilibrium, savings ($S(r)$) equal investment demand ($I(r)$).
  • If $ ext{S} > I(r)$, interest rates are too high leading to a lack of equilibrium. Conversely, $ ext{S} < I(r)$ indicates too low rates.

Next Steps in Study

  • Focus on financial markets and fiscal policy, how these areas interact with overall economic conditions.
  • Explore the roles of money, money supply, and economic implications in macroeconomic models.