ajaz_eco204_2009_chapter_3.2 - University of Toronto...

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University of Toronto, Department of Economics, ECO 204 2009 2010 S. Ajaz Hussain ECO 204 2009 2010 S. Ajaz Hussain (Draft) Chapter 3.2: Intertemporal Consumption & Savings Model 1 Please help improve the course by sending me an e mail about typos or suggestions for improvements In chapter 3.1 we modeled a one period decision of allocating dollar income between dollar consumption and dollar savings. In chapter 3.2, we’ll construct an intertemporal consumption and savings model. In contrast to the one period model, the intertemporal model makes use of interest rates and is the foundation of real interest rates in finance (which is why it’s done in RSM 332). 1. Intertemporal Consumption and Savings Model: Environment Consider an economy with exactly one good: corn . All consumers in this “e corn omy” plan consumption and savings for two periods ܶൌ1 ,2 . 1 Since corn is the only good, consumption, saving and borrowing are in terms of corn. At the beginning of each period, consumers are endowed with corn incomes ܻ in , 2 respectively (see diagram). Of course, endowments vary a consumers and/or time. For instance, you may get more corn in cross T = 1 “Today” T = 2 “Tomorrow” Receive “Endowment” Y 1 (real terms) Consume < “Endowment” C 1 < Y 1 “Save” Save = Y 1 C 1 Consume > “Endowment” C 1 > Y 1 “Borrow” Borrow = C 1 Y 1 Receive “Endowment” Y 2 and Receive Principal + interest on Savings Receive “Endowment” Y 2 but Pay Back Loan + interest 1 Thanks: Mary Magdaluyo, Siyu Wang, Ding Yan ECO 204 (Draft) Chapter 3.2
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University of Toronto, Department of Economics, ECO 204 2009 2010 S. Ajaz Hussain ܶൌ1 than in ܶൌ2 . In turn, your endowments may be greater than your friend who may get more income in than in . Put simply, endowments can be distributed any number of ross consumers and time. 2 ECO 204 (Draft) Chapter 3.2 ways ac In every consumer has to decide whether to save corn or borrow corn. If the consumer borrows corn in she must pay back the loan in ; put another way, you can’t borrow in both and . Similarly, if the consumer borrows saves corn in she must “un save” in (for simplicity, let’s label “un saving” as “borrowing”). In sum, if you borrow in you must save in and if you if you save in you must borrow in . To be able to borrow and save corn, there must be capital markets. That is, if you save corn you deposit the corn in a “bank” (financial intermediary) which lends it to consumer who wish to borrow corn. That you always deposit your savings in a bank is a plausible assumption because if you save corn “under your mattress” (made of corn) it earns zero return whereas if you deposit the corn into a bank, it earns some interest. Denote the nominal interest rate ݅ . Assume the saving and borrowing nominal interest rates are equal: the bank does not earn profits. Now let us introduce prices: is the base period; fix the price level to ܲ ൌ1 . The price level at is denoted ܲ . Notice that: If n ܲ ൌܲ : No InFlatio If ܲ ൏ܲ : InFlation If ܲ ൐ܲ
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ajaz_eco204_2009_chapter_3.2 - University of Toronto...

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