Do not distribute b under what conditions will

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Unformatted text preview: Under what conditions will the consumer save corn at ? Characterize: ● The relationship between and ● The relationship between Show all calculations. and Answer To be a saver at , this consumer would have to consume less than her income: [ [ [( [ [( To characterize the relationship between ) [( ) ) [ vs. , we need to first compute [ [ [ . [( ) [( ) [ [ 8 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, we can find out how and are related: ( [ Since ( ) ) for the consumer to be a saver at . To characterize the relationship even better, we need to compute the second order derivative: ( [ Since ( ) ) ( for the consumer to be a saver at Therefore, if the consumer is a saver in ) . This implies a convex relationship. , then as increases, Now, To characterize the relationship between falls and falls at a decreasing rate. vs. , we need to first compute [ [ [( ) [ ( ) [ ( ( ) )( [ Now, we can find out how [ ( . )[( )( ) ) and are related: 9 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. ( )[( )( )( ( ) )[ ( ( ) ) ) ( ( )] ) )[ (which implies ( ( ) ( ( ( Since ( () ) ) ) ) for the consumer to be a saver at . To characterize the relationship even better, we need to compute the second order derivative: ( [ Since ( relationship. ) ) (which implies ( ) Therefore, if the consumer is a saver in ( ) ) for the consumer to be a saver at , then as increases, . This implies a convex falls and falls at a decreasing rate. (6.2) Consider a 3 period economy ( ) with a single good (say, corn). Each consumer receives real income (in units of corn) at the beginning of respectively. Denote the real interest rate by (assume a common at ). {( Suppose a consumer has the following utility function defined over the consumption set ( ) ( ) }: ) That is, the consumer perceives consumption at and literally as perfect substitutes. Under what conditions will calculations. Assume all pecuniary variables . as complements, and consumption at versus and ? State all assumptions and show all Answer: Note: This problem is similar to the one in consumer theory where a consumer perceives food and alcohol as complements, and wine and beer as perfect substitutes for alcohol. The agent’s problem is: ( ) ( ) ( ) ( ) ( ) For simplicity, write this as: ( ) ( ) ( ) 10 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. At the optimum it must be that: We can express the budget constraint in terms of (say) ( ( ( and only: ( ) ) ) ( )( ) ( {( ) ( )} {( ) ( )} {( Note that if then is rising in ) )...
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