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( )} ( ) {( ) )} ( so that: One can substitute these in the budget constraint to get the actual values for
( ) ( ( ) )
( ) Thus, when:
(
On the other hand, if then is decreasing in ) so that: One can substitute these in the budget constraint to get the actual values for
( )
( (
)
( )
(
) )
( ) Thus, when:
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ECO 204 Chapter 6: Practice Problems & Solutions for Modeling Intertemporal Consumption in ECO 204 (this version 20122013) University of Toronto, Department of Economics (STG). ECO 204, S. Ajaz Hussain. Do not distribute. ( ) (6.3) In this 1 period problem, a consumer allocates her income
function is: ) between consumption ( Assume ( and savings . Her utility ) . (a) Solve the consumer’s UMP. Show all calculations and clearly state any assumptions.
Answer:
By definition, income must be allocated to consumption and savings. The consumer’s UMP is: ( ) s.t. Being an equality constrained optimization problem, set up the Lagrangian: ( ) ( ) The first order conditions (FOCs) are: ( ) From the 1st FOC: Substitute in second FOC:
( ) ( ) 12
ECO 204 Chapter 6: Practice Problems & Solutions for Modeling Intertemporal Consumption in ECO 204 (this version 20122013) University of Toronto, Department of Economics (STG). ECO 204, S. Ajaz Hussain. Do not distribute. Substitute in 3rd FOC: ( ) Thus, the complete solution to this UMP is: ( ) Observe that her savings are always independent of income. This, of course, is due to her quasilinear preferences (recall
( ) then
that
is always independent of income).
(b) Is it possible that this consumer “goes hungry” (i.e. consume nothing)?
Answer:
It is possible that this consumer consumes nothing. From above, note that she always saves a constant dollar amount
(
) and consumes the remainder of her income. Thus, if her income is less than (
) she will consume nothing:
( ) (6.4) An individual lives for two periods (
and ) in an “ecornomy” (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
the nominal interest rate by , inflation by and the real interest by .
Consider a consumer with the following utility function for consumption in
(
) Assume and consumption in ). Denote : . In this question you do not have to derive the intertemporal budget constraint from 1st principles (i.e. you can state the
constraint).
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ECO 204 Chapter 6: Practice Problems & Solutions for Modeling Intertemporal Consumption in ECO 204 (this version 20122013) University of Toronto, Department of Economics (STG). ECO 204, S. Ajaz Hussain. Do not distribute. (a) Calculate the consumer’s optimal consumption in . Show all calculations and clearly state any assumptions. Answer:
The consumer maximizes utility subject to the constraint that intertemporal consumption equals intertemporal
income. The intertemporal budget constraint can be expressed in PV or FV terms: FV Intertemporal Budget Constrai...
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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 Toronto.
 Fall '09
 AJAZHUSSAIN
 Economics, Microeconomics

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