[范里安版中级微观经济学英文版课件]Lecture 5. Intertemporal Choices.ppt

A change in the interest rate is just like the change of price. As there are endowments, price changes have two effects on purchasing power. Ordinary income effect. Endowment income effect: When the interest rate (or price) changes, the value of the endowments and thus the money income also changes. Slutsky Equation * The Slutsky identity is now Define For optimal choice: There could be Slutsky Equation * The Slutsky equation becomes If ?r→0, then The Slutsky equation is Slutsky Equation * If the interest rate changes continuously, the Slutsky equation is If lender, (m1-c1)0, total effect is negative. If borrower, (m1-c1)0, total effect is ambiguous. Slutsky Equation (?) (-) (+) (?) * Present Value for Several Periods Given an interest rate r $y saved at the start of period 1 becomes $y(1+r)2 at the start of period 3. So, The future value two period from now of $y is  Similarly, the present value of $y available at the start of the third period is * Present Value for Several Periods If there is $yn available at the start of each period n, The total present value of these lumps of income is Period 1 2 3 … n Income PV y1 y1 y2 y3 yn … y1/(1+r) y1/(1+r)2 y1/(1+r)n-1 … * Budget Constraint for Several Periods If there are three periods, the budget constraint will have the form  Similarly, if there are n periods, the budget constraint will have the form  * Conclusion: A consumer prefers a stream of money that has a higher present value (PV) to one with lower PV. Condition: the consumer can borrow and lend freely at a constant interest rate The consumer’s preference on consumption doesn’t effect the result Reason: A stream of money with a higher PV gives a consumer more consumption possibilities in every period. Use of Present Value * Use of Present Value c2 c1 (m’1, m’2) (m1, m2) (m’1, m’2) has a higher PV than (m1, m2), and gives the consumer a higher utility. * Two applications of present value If there are two