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Unformatted text preview: arative statics using the
general method.
â€¢â€ˆ Our FOC can be written: â€¢â€ˆ This is our function â€¢â€ˆ Then we use the equation (where z is the
parameter):
1011a â€“ Lecture 8 14 The Denominator
â€¢â€ˆ First, let us find
. This will be the
denominator in all of our calculations. c2 â€¢â€ˆ If this were not negative, then second order
conditions would fail.
â€¢â€ˆ The sign of a comparative static (with one
endogenous variables) is always the sign of Vxz
1011a â€“ Lecture 8 15 Changes in Income (I)
â€¢â€ˆ Now, let us find . c2 â€¢â€ˆ Hence: 1011a â€“ Lecture 8 16 Changes in Income (II)
â€¢â€ˆ What about second period consumption? 1011a â€“ Lecture 8 17 Changes in Income (III)
â€¢â€ˆ So consumption rises in both periods when
income rises.
â€¢â€ˆ This means that both c1 and c2 are normal goods.
â€¢â€ˆ You can see this must be the case just by
examining the Euler equation (how?): u' (c1 ) = Î² (1 + r) u' (c 2 )
1011a â€“ Lecture 8 18 Changes in the Interest Rate (I)
â€¢â€ˆ Recall that the interest rate is like the price
of first period consumption in terms of
second period consumption.
â€¢â€ˆ So a rise in the interest rate corresponds to
first period consumption getting more
expensive.
â€¢â€ˆ However, changes in the interest rate also
changes your income.
1011a â€“ Lecture 8 19 Changes in the Interest Rate (II)
â€¢â€ˆ Let us find . c2 â€¢â€ˆ Hence: 1011a â€“ Lecture 8 20 Changes in the Interest Rate (III)
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This note was uploaded on 02/09/2013 for the course ECON 1010A taught by Professor Jeffreya.miron during the Spring '11 term at Harvard.
 Spring '11
 JeffreyA.Miron
 Microeconomics

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