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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.

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