Ch 6 Practice

# Thus if then b under what conditions will

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Unformatted text preview: ain. Do not distribute. Now if then ( ) so that the consumer will save whenever: ( ) ( What happens to savings as ) ? Now: ( ) ( [ ( (we need to assume Now if ) ( ) ( ) ( ) ) ). Thus, savings increase when the real interest rate rises. then ( ) so that the consumer will save whenever: ( ) ( What happens to savings as ) ? Now: ( ( (we need to assume ( [ ) ) ) ). Thus, savings increase when the real interest rate rises. (c) Under what conditions will the consumer borrow corn at interest increases? Show all calculations. ? What will happen to borrowings at if the real Answer The consumer will borrow corn at when: We need to consider the two possibilities. 22 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. Now if then ( ) so that the consumer will borrow whenever: ( ( What happens to borrowing as ) ? Now: ( ) ( ) ( [ ( ) [ ( ) [ This will be positive whenever ) ) ( ( ) ( ) ) which means that the consumer will borrow less as real interest rates rise (remember that if consumer is borrowing then she has negative savings so that a positive derivative means that the negative savings becomes a larger number or that she borrows less). The expression will be negative whenever ( ) which means that the consumer will borrow more as real interest rates rise (remember that if consumer is borrowing then she has negative savings so that a negative derivative means that the negative savings becomes a smaller number or that she borrows more). Now if then ( ) so that the consumer will borrow whenever: ( ( What happens to borrowing as ) ) ? Now: ( ( ) ) This means that the consumer will borrow less as real interest rates rise (remember that if consumer is borrowing then she has negative savings so that a positive derivative means that the negative savings becomes a larger number or that she borrows less). 23 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. (6.6) Consider a 2 period economy ( ) with a single good (say, corn). Each consumer receives real income (in units of corn) at the beginning of respectively. The price level at is (i.e. is the base period) and the price level at is . In each period, the consumer can “borrow” or “save” corn at nominal interest rate . In this model, “saving” in a period means that the agent is consuming less than or equal to her income in that period while “borrowing” in a period means that the agent is consuming more than her income in that period. The of total lifetime income is: ( The ) of total lifetime income is: Suppose a consumer has the following utility function over consumption at and : (a) Describe the agent’s preferences over consumption “today” versus “tomorrow”. Graph the con...
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