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Ch 6 Practice

Eco 204 s ajaz hussain do not distribute and now

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Unformatted text preview: “save” in condition, will the agent continue to “save” at as ? (and therefore borrow at ). According to this Answer: To be a “saver” at , this consumer would have to consume less than her income: [( [( ) ) [( ) There are many ways to express the borrowing condition. Here is one way, useful for graphing saving/borrowing diagrams. The agent saves in when: [( ) [( ) 50 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. [( ( The agent “saves” in ) ) [( ( ) ) when: The agent will “save” in (the optimal bundle will be to the right of the endowment point) when the corners line is flatter than the endowment point ray: Agent borrows in t = 0, “saves” in t = 1 C1 FVY Y0 < Y1 E Y1 S1 < 0 C1 α/β Y0 C0 PVY C0 S0 < 0 Observe how the condition for is independent of the real interest rate which means that once a borrower at the agent will always be a borrower regardless of the real interest rate (albeit the level of borrowings will change). (e) What happens to and due to, all else equal, a small increase in ? Graph Answer: From above, the condition for the agent to save in vs. and vs. . is: Now, as the inequality is preserved which means that she will continue to save in ? Let’s see: . But will she save more as 51 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. so long as [( ) ) [( [( ) [( ) [( [( ( ( ) [( then so long as ) [( Note how as ) (i.e. the agent is saving at [( Formally: ⏟) [( ): ( ⏟ ) ) ) ) ) The derivative is always negative and given that the agent is saving (i.e. ) this means that as then : Agent saving in t = 0, “borrowing” in t = 1 Suppose r ↑ Agent continues to save in t = 0 but S0 ↓ C1 FVY S’1 < 0 S < 0 1 C’1 C1 A B Y0 > Y1 E Y1 α/ β C0 C’0 Y0 S’0 > 0 PVY C0 S0 > 0 52 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. The graph of and depends on whether the agent is intrinsically a saver or a borrower. She will be a saver at where savings are: [( Because if ) the graph has a negative slope since: ( ⏟ [( ) ) Take the 2nd derivative to see if the graph is linear, strictly concave/convex: ( [( ⏟ Because As and , the second derivative is always positive so that the graph is strictly convex. -1 then: ) then: [( And as ) [( As ) then because ) : [( ) Agent will save at t = 0 if α/β > Y1/Y0 S0 Save in t = 0 Borrow in t= 1 -1 r 0 By the same token if the agent is a borrower at if where borrowing (negative savings) are: 53 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 20...
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