Revised Consumption - Consumption Anthony Murphy Nuffield...

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Consumption Anthony Murphy Nuffield College [email protected]
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Outline Consumption – the biggest component of GDP/national expenditure; a good deal smoother than income . The two period model . Friedman’s permanent income hypothesis PIH - infinitely lived representative agent etc. Modligiani’s life cycle hypothesis LCH – finite life, saving for retirement, population dynamics. Hall’s consumption function – uncertainty, rational expectations and the consumption Euler equation . Euler equations versus (approx.) solved out consumption functions – pros and cons. Example of solved out consumption function for US.
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Basic Two Period Model (1) Diagram: Axes - c 1’ y 1 on horizontal axis (the present) and c 2 ,y 2 on vertical axis (the future). Intertemporal preferences: Regular shaped indifference curves (as opposed to linear or L shaped ones). Less than perfect trade-off between c 1 and c 2 so want to smooth consumption over time. Intertemporal budget line : c 1 +c 2 /(1+r) = y 1 + y 2 /(1+r) (You can add an initial endowment a 0 (1+r) if you want to the RHS of the budget.)
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Consumption tomorrow 0 Indifference curves: Normal case Consumption today Fig. 6.02(a)
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Consumption tomorrow 0 Indifference curves: Zero substitution Consumption today Fig. 6.02(b)
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Consumption tomorrow 0 Indifference curves: Constant substitution Consumption today Fig. 6.02(c)
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Two Period Model (2) Budget constraint is a straight line thru’ (y 1 ,y 2 ) point with slope equal to minus 1/(1+r). No borrowing or lending restrictions. Borrowing and lending rates are the same. Intertemporal budget constraint got by combining period 1 and period 2 budget constraints: c 1 + a 1 = y 1 c 2 = a 1 (1+r) + y 2
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Equilibrium in Two Period Model Equilibrium where highest attainable indifference curve is tangential to the budget line. You may be a borrower (c 1 > y 1 ) or lender (c 1 < y 1 ) in period 1. First order condition (FOC): slope of indifference curve = slope of budget line ie. marginal rate of substitution (MRS) between c 1 and c 2 = 1/(1 + r).
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Consumption tomorrow 0 Optimal consumption: borrower IC 1 IC 2 IC 3 B D R C 1 C 2 M Y 1 Y 2 (i) (i) Consumption today financed on credit (ii) (ii) Consumption loan repayment (including interest) Fig. 6.03 - (1+ r ) Consumption today
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Consumption tomorrow 0 Optimal consumption: lender A Y 1 Y 2 B IC 1 IC 2 IC 3 D R C 1 C 2 (i) (i) Saving from this period’s income (ii) (ii) Additional consumption next period Fig. 6.03 Consumption today - (1+ r )
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FOC and Euler Equation* Suppose preferences are additive over time so U(c 1 ,c 2 ) = u(c 1 ) + β u(c 2 ) where 0 < β < 1 is a discount factor.
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