One-Period Macro Model

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One-Period Macro Model

• Households Firms
• Competitive Equilibrium

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Households

• Chooses Labor Supply (Ns), leisure (l 1- Ns),
  and consumption (c) to
• subject to
• given w real wage rate and a household
  wealth.

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• Optimal values of c,l, given w and a, solves

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• Implications
• (i) Changes in wealth creates a pure income
  effect
• dc/da gt 0
• dl/da gt 0 and dN/da lt 0
• (ii) Changes in real wages creates both an
  income and substitution effect
• dc/dw gt 0 and dN/dw ??

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Figure 4.12 Real Wage in the United States,
19802003
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Figure 4.13 Average Weekly Hours in the United
States, 19802003
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The workweek and real GDP per person in 36
countries
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Firms

• Chooses labor demand (Nd) and output Y to
  maximize profits (P)
• subject to
• (assuming fixed level of K)
• z Productivity/Technology Shock (Solow
  Residual)

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Figure 4.20 The Solow Residual for the United
States
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• Optimal values of N,Y, given w, solves
• Implications
• (i) dN/dw lt 0 (Labor Demand Curve)
• (ii) dN/dz gt 0 (Productivity Shock)

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Competitive Equilibrium (CE)

• Households ? c,Ns given a and w.
• Firms ? Y,Nd given w.
• Households are the owners of firms and takes
  profits as given a P Y wN
• Market-Clearing
• Nd Ns N 1l (labor mkt)
• Y c (Goods Mkt)

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• A competitive equilibrium is c,N,Y,w
  solving

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Pareto Optimality

• An allocation is Pareto Optimal if no other
  feasible allocation can make someone else better
  off without making anyone else worse off.
• The competitive equilibrium (CE) is Pareto
  Optimal.
• Verify Social Planning Problem / Robinson
  Crusoe.

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Productivity Shocks

• An increase in z
• Income effect ? () C and () l
• Substitution Effect ? () C and (-) l
• Hence dc/dz gt 0 and dN/dz ??
• In the case where both effects are roughly equal,
  Y and w increases.
• Classic Example is energy prices and GDP.

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Figure 5.11 Deviations from Trend in Real GDP
and the Solow Residual
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Figure 5.12 The Relative Price of Energy
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One Period CE Model with Government

• Government sector
• (i) Collects revenues from taxes (T).
• (ii) Purchases goods and services (G)
• Assume balanced budget (G T)
• Household wealth (a) P - T
• Goods Market Clearing Y C G
• Labor market Clearing Nd Ns

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CE Model with Government

• Households ? c,Ns given a and w.
• Firms ? Y,Nd given w.
• Households are the owners of firms and takes
  profits as given a P-T
• Market-Clearing
• Nd Ns N 1l (labor mkt)
• Y cG (Goods Mkt)

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• A competitive equilibrium given G is
  c,N,Y,w solving

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Effects of Government Purchases

• Negative Income Effect
• dc/dG lt 0
• dl/dG lt 0 ? dN/dG and dY/dG gt 0
• du(c,l)/dG lt 0
• Stabilization Policy The government can use
  government purchases to stabilize output from
  productivity shocks (dG/dz gt 0) but it will lead
  to a further decrease in economic welfare.

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The Growth Rate of U.S. Real Gross Domestic
Product since 1870
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Figure 5.7 GDP, Consumption, and Government
Expenditures
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Comparison with IS-LM

• Both predict
• (i) dY/dG gt 0
• (ii) Government purchases can be used to
  stabilize GDP and business cycles.
• Differences
• (i) CE model predicts dC/dG lt 0
• (ii) There is full crowding out of consumption
• (iii) Fiscal policy will not improve welfare of
  the representative consumer.