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Unformatted text preview: C S1 <0 Y 1 1 B A E C’0 C0 Y0 S0 >0 PVY PVY’ C0 S’0 >0 Note: when the intertemporal budget line swivels clockwise around the endowment p oint because the x-axis intercept becomes smaller while the y-axis intercept Graph ( ) becomes larger. vs. : 33 ECO 204 Chapter 6: Practice Problems & Solutions for Modeling Inter-temporal Consumption in ECO 204 (this version 2012-2013) University of Toronto, Department of Economics (STG). ECO 204, S. Ajaz Hussain. Do not distribute. We have ( ⏟ ) ( as long as Since . this will always be the case. This is true because In fact, as condition is given. ∞ then: [ And as ) then: [ This means that there must be some where the curve intersects with the [ axis. The can be computed by setting 34 ECO 204 Chapter 6: Practice Problems & Solutions for Modeling Inter-temporal Consumption in ECO 204 (this version 2012-2013) University of Toronto, Department of Economics (STG). ECO 204, S. Ajaz Hussain. Do not distribute. ( ) Therefore, the graph looks as follows: S0 Save in T = 0 Borrow in T = 1 -1 0 r r* Borrow in T = 0 Save in T = 1 Now let’s see what happens to as increases [( So ) falls as increases. Graphing vs. 35 ECO 204 Chapter 6: Practice Problems & Solutions for Modeling Inter-temporal Consumption in ECO 204 (this version 2012-2013) University of Toronto, Department of Economics (STG). ECO 204, S. Ajaz Hussain. Do not distribute. ( [ [ -1 ( ) ) [ 0 r (e) Derive the conditions under which an agent will “save” in (and therefore “borrow” at ). According to this condition, will the agent continue to save at as ? What happens to and due to, all else equal, a small increase in Graph vs. and vs. . Answer: To be a saver in T=1 [ ( ( ( ) ) ) [ 36 ECO 204 Chapter 6: Practice Problems & Solutions for Modeling Inter-temporal Consumption in ECO 204 (this version 2012-2013) University of Toronto, Department of Economics (STG). ECO 204, S. Ajaz Hussain. Do not distribute. ( ) [ ( ) ( ) Opposite condition to what we got in d. | | | | FVY PVY The condition for the agent to be a saver at T=1: ( ) If increases then LHS increases. Therefore if increases sufficiently, then the inequality may reverse and the agent may become a borrower at T=1. The other parts of this question are identical to part d. You need to recognize that or or the graph of vs / vs do not change. What changes is the starting point at the graph. (6.7) Some finance courses setup and solve for as in question (6.6) if you solve the UMP: and not and . Show that you get the same expressions for 37 ECO 204 Chapter 6: Practice Problems & Solutions for Modeling Inter-temporal Consumption in ECO 204 (this version 2012-2013) University of Toronto, Department of Economics (STG). ECO 204, S. Ajaz Hussain. Do not distribute. Answer: The inter-temporal UMP was to choose consumption in each period subject to the constraint that equals income: ( ) ( consumption ) To solve the UMP in terms of savings we substitute: Into the UMP budget constraint above to get: ( ( ( )( )( )( ( ) ( ) )( ) ) ( ( ) )(...
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