Ch 6 Intertemporal Consumption

76 units suppose at you borrow 100 since the nominal

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Unformatted text preview: interest rate is therefore 10%: Scenario # 2: Inflation rate of 5% Suppose you borrow $100 In real terms, you’ve borrowed 100 units ( ) ( ) Pay back In real terms, you’re paying back 104.76 units Suppose at you borrow $100. Since the nominal interest rate is 10%, in you will pay back $110. Now look at this problem in real terms (in terms of corn). Observe there is 5% inflation here ( ). When you took out a loan of $100, you really borrowed 100 units of corn. When you pay back the loan, you do so in dollars ($110). In terms of corn however you’re paying back $110/$1.05 = 104.762 or almost 105 units of corn. That is, you borrowed 100 units of corn and are paying back (approximately) 105 units of corn: the “real” interest rate is therefore (approximately) 4.76% (observe how the Fisher approximation gives the same answer). This example demonstrates what you saw in ECO 100 macro: in an inflationary economy, borrowers “win” (and lenders “lose”) because in real terms borrowers pay back less than what they borrowed. Similarly, in a deflationary economy, borrowers “lose” (and lenders “win”) because in real terms borrowers pay back more than what they borrowed. Next, we assume that at the price of a unit of corn is and that at the price of a unit of corn is allow for inflation/deflation between and and denote the rate of inflation by where: . We Notice that: ( 3. Inter-temporal UMP Model Consider an agent who lives for two periods ) in an economy with one good (corn). At the beginning of , the 5 ECO 204 Chapter 6: Inter-temporal Consumption (this version 2012-2013) University of Toronto, Department of Economics (STG). ECO 204, S. Ajaz Hussain. Do not distribute. agent is endowed with corn income (the dollar value of which is ) and at the beginning of , the ( ) ). At agent is endowed with corn income (the dollar value of which is the agent can save/borrow corn at a nominal interest rate of . She has preferences over consumption at and represented by a utility function ( ). We model this agent’s choice of consumption by the inter-temporal UMP model: ( ) ⏟ ( ) Unlike the consumer theory UMP, in the inter-temporal UMP total (lifetime) expenditure always equal total (lifetime) income. Recalling the time value of money from Math 133 we see that the inter-temporal budget constraint can be expressed: ⏟ ● First, let’s examine the Present Value ( { } ⏟ ) Inter-temporal Nominal Budget Constraint: { } ( { } }} } ( ) {{ {{ }} ) This is a nominal budget constraint (in terms of dollars). Next, we examine the Future Value ( { } ) Inter-temporal Nominal Budget Constraint: { } ( ) { ( ) This too is a nominal budget constraint (in terms of dollars). One can work with either the or inter-temporal budget constraint and in ECO 204 we will work with constraint. As such, the agent’s choice of consumption is modeled by the inter-temporal UMP model: ( ) budget ⏟ ( ) 6 ECO 204 Chapter 6: Inter-temporal Consumption (this version 2012-2013) University o...
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This note was uploaded on 03/20/2014 for the course ECON 204 taught by Professor Ajazhussain during the Fall '09 term at University of Toronto.

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