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Unformatted text preview: 8 6 The Budget Constraint (I)
• The loan market establishes an exchange rate
between periods 1 and 2.
• $1 in period 1 is worth $(1+r) in period 2.
• So the total value of your income in period 1
dollars (its net present value or NPV) is: 1011a – Lecture 8 7 The Budget Constraint (II)
• The budget constraint says that the total amount
spent in period 1 $’s equals the total amount
earned in period 1 $’s.
• That is, the NPV of consumption must equal the
NPV of income.
• This means 1011a – Lecture 8 8 Maximizing Utility
• Now that we have a utility function and a
budget constraint, this is just like any other
utility maximization problem:
c2
y2
max {u(c1 ) + βu(c 2 )}s.t. c1 +
= y1 +
c1 , c 2
1+ r
1+ r €
1011a – Lecture 8 9 The Substitution Method
• We will not solve this with Lagrangians,
but with the substitution method.
• Solve for c2 as a function of c1: 1011a – Lecture 8 10 First Order Conditions (I)
• Our problem becomes: • First order condition is: 1011a – Lecture 8 11 First Order Conditions (II)
• But we have: • Plugging this in: 1011a – Lecture 8 12 The Euler Equation • How do you interpret this?
• Under what assumptions will consumption
rise / fall / stay constant over the two
periods? 1011a – Lecture 8 13 Comparative Statics
• We will find comp...
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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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