Ch 6 Practice

# Do not distribute b under what conditions will

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

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 ) )...
View Full Document

## 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.

Ask a homework question - tutors are online