Ch 6 Practice - University of Toronto Department of...

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University of Toronto, Department of Economics (STG). ECO 204, S. Ajaz Hussain. Do not distribute. 1 ECO 204 Chapter 6: Practice Problems & Solutions for Modeling Inter-temporal Consumption in ECO 204 (this version 2012-2013) Department of Economics (STG), ECO 204, Sayed Ajaz Hussain _________________________________________________________________________________________________ P RACTICE P ROBLEMS W ITH S OLUTIONS TO C HAPTER 6: Modeling Inter-temporal Consumption 1 Updated: 1/21/2013 Fixed typos are in yellow (6.1) 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. Denote the real interest rate by (assume a common at ). Suppose a consumer has the following utility function defined over the consumption set {( ) } : ( ) ( ) Assume all pecuniary variables . (a) Derive an expression for the of (Future Value of Total Lifetime Income), and the of (Present Value of Total Lifetime Income). State all assumptions and show all calculations. (b) Under what conditions will the consumer save corn at ? Characterize: The relationship between and The relationship between and Show all calculations. (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 as complements, and consumption at versus literally as perfect substitutes. Under what conditions will and ? State all assumptions and show all calculations. Assume all pecuniary variables . (6.3) In this 1 period problem, a consumer allocates her income between consumption and savings . Her utility function is: 1 Thanks to Akber Nafeh for preparing these problems and solutions. Also thanks to Samantha Pettinato.
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University of Toronto, Department of Economics (STG). ECO 204, S. Ajaz Hussain. Do not distribute. 2 ECO 204 Chapter 6: Practice Problems & Solutions for Modeling Inter-temporal Consumption in ECO 204 (this version 2012-2013) ( ) Assume . (a) Solve the consumer’s UMP. Show all calculations and clearly state any assumptions. (b) Is it possible that this consumer “goes hungry” (i.e. consume nothing)? (6.4) An individual lives for two periods ( and ) in an “e -corn- omy” (i.e. the only good is corn). Her real income (measured in corn) is in and in time . is the base period so that and allow for the possibility of inflation (i.e. it may be that ). Denote the nominal interest rate by , inflation by and the real interest by . Consider a consumer with the following utility function for consumption in and consumption in : ( ) Assume . In this question you do not have to derive the inter-temporal budget constraint from 1 st principles (i.e. you can state the constraint). (a) Calculate the consumer’s optimal consumption in . Show all calculations and clearly state any assumptions.
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