Ch 6 Intertemporal Consumption

# Eco 204 s ajaz hussain do not distribute the right

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Unformatted text preview: et constraint and noting that the left side equals 11 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. the right side3: ( ) ( ) ( ) ( ) Remember: the real inter-temporal budget constraint always passes through the endowment point. As such, in contrast to consumer theory, the budget line will not swivel on either intercepts. For example, suppose the real interest rises (when would this happen?). In that case, the x-axis intercept falls (since as ), the y-axis intercept increases (since as ), and the budget line slope increases, so that: Suppose ↑ ( E ) ( ) Before we do some UMPs, let’s think about what the position of the optimal choice vis a vis the endowment point – what would this tell us? Take a look at the graph below which shows the optimal choices and endowment points of three agents A, B and C: 3 After all, how do you check if a line goes through a point? 12 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 C Agent B Agent A A E E= E ( ( ) C ) ( ) B 45o 45o 45o Notice all three agents’ endowment point is above the 45 degree line: this means that income at is greater than their income at . Notice that: or that all three agents’ Agent A’s optimal choice is above the 45 degree line so that she consumes more at than at and that which means she saves at allowing her to consume more than her income at (in fact, notice that ) Agent B’s optimal choice is below the 45 degree line so that she consumes more at than at and that which means she borrows at due to which she consumes less than her income at (in fact, notice that ) Agent C’s optimal choice coincides with the endowment point which means that she neither saves or borrows at which means that she must consume all her income at . This shows that if an agent saves when she’s young she gets to consume more than her income when she’s old; if an agent borrows when she’s young she must consume less than her income when she’s old; and that if an agent neither saves or borrows when she’s young then she must consume all her income when she’s old. In particular, agents can’t save or borrow in both periods. Based on our discussion, the general inter-temporal UMP model is: ( ) ( ) ⏟( ) 13 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. For convenience, denote the of the total life-time real income as model can be succinctly expressed as: ( ) ( with which the general inter-temporal UMP ) We now do specific cases of the inter-temporal UMP. 3. Cobb-Douglas Inter-temporal UMP Model Consider an agent who perceives consumption at choice must have some corn in both periods (i.e. utility model: and as imperfect substitutes and who at the optimal ). We can represent her preferences by the Cobb-Douglas Where are utility parameters and the utility functio...
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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- Toronto.

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