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# Ch10 - Chapter 10 Intertemporal Choice In this chapter we...

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Chapter 10 Intertemporal Choice In this chapter we model a consumers choice of consumption over time. This is known as intertemporal choice . 10.1 The budget constraint Assume two periods, say, today and tomorrow denoted 1 and 2 respectively. Denote consumption in the respective periods as ( c 1 , c 2 ) and the money the consumer will have in each period as ( m 1 , m 2 ). Assume the relative price of consumption in the two periods is equal to 1. If the consumer can transfer money from period 1 to period 2 by saving (without any interest), but cannot borrow money in period 1 (so he can onely spend a maximum of m 1 ), then the budget constraint looks as follows: 1

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2 CHAPTER 10. INTERTEMPORAL CHOICE The more realistic situation would be the possibility of borrowing across the periods with some interest rate r . Let us derive the budget constraint, while keeping prices in each period as 1 for convenience. If the consumer decides to be a saver so his c 1 < m 1 , then his consump- tion in period 2 will be c 2 = m 2 + ( m 1 - c 1 ) + r ( m 1 - c 1 ) = m 2 + (1 + r )( m 1 - c 1 ) (10.1) Similarly, if the consumer decides to be a borrower so his c 1 > m 1 , then his consumption in period 2 will be c 2 = m 2 - r ( c 1 - m 1 ) - r ( c 1 - m 1 ) = m 2 + (1 + r )( m 1 - c 1 ) which is the same as (10.1) above.
10.1. THE BUDGET CONSTRAINT 3 We can rearrange the budget constraint to get two alternative forms that are useful, namely, the future value form which sets p 2 = 1 and p 1 = (1+ r ) and the present value form which sets p 1 = 1 and p 2 = 1 / (1 + r ). So we have Future value: (1 + r ) c 1 + c 2 = (1 + r ) m 1 + m 2 and

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Ch10 - Chapter 10 Intertemporal Choice In this chapter we...

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