Two Period CE Model with Production

1
Two Period CE Model with Production

• Optimal Consumption and Labor Supply
• Competitive Equilibrium
• Productivity Shocks

2
2-Period Model with Labor-Leisure Choice

• Previously assumed output/income y1,y2 was
  exogenous. Now we incorporate the ideas of
  optimal labor-leisure choice and production from
  the one period model.
• Household ? consume, work, save in each period
• Firms ? employ labor to produce output
• Labor Market ? market clearing wages
• Good Market ? market clearing interest rate
• No government sector (for now)

3

• Households
• subject to
• where lt 1 Nt.
• Solving for s in period 1 and substituting into
  period 2
• (BC)

4

• Solving for s in period 1 and substituting into
  period 2
• (BC)
• An optimal choice of c1,c2 and N1s ,N2s
  solving (BC) and
• (H1)
• (H2)
• (H3)

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• Implications
• (i) As long as substitution effect gt income
  effect, dN1/dw1 gt 0 and dN2 /dw2 gt 0.
• Labor supply in each period increases with the
  wage rate.
• (ii) As long as substitution effect gt income
  effect, dN1/dr gt 0.
• Labor supply in the current period increases
  with the interest rate.

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• (iii) Increases in wealth (e.g. P or lower T w/
  gov) decreases labor supply.
• Graphically
• (i) ? upward sloping NS curve
• (ii) ? Higher r will shift NS right
• ? Upward sloping output supply (Ys) curve.
• (iii) ? Higher wealth shifts NS left

7

• Firms
• Period 1
• ?
• Period 2
• ?

8

• Competitive Equilibrium (no gov)
• Goods y1 c1
• y1 c1
• Credit s 0
• Labor N1d N1s
• N2d N2s
• EX Temporary vs permanent productivity shocks.