This preview shows page 1. Sign up to view the full content.
Unformatted text preview: straint (in “real” terms) on a
plot and interpret the and axis intercepts and slope. intertemporal budget Answer:
Let’s use the monotonic transformation
The agent considers and . to be imperfect substitutes.  
  ⁄

⁄   This implies that if the agent consumes one more unit of corn today she just forego units of corns tomorrow to remain equally happy.
FV Budget Constraint (in “real” terms):
( )
( (
) )
( ) Yaxis intercept is:
Set
24
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. ( ) Xaxis intercept:
Set
(
( Slope: ( )
) (
( )
) ). This implies that if the agent consumes one more unit of corn today, she must give up (
) units of corn tomorrow to
remain on the budget line. The slope can also be interpreted as the ratio of “Price of 1 unit corn today” to “Price of 1
unit of corn tomorrow” either in PV terms or FV terms.
In FV Terms:
    In PV Terms: FVY Demand curve for good 1 PVY (b) Solve the consumer’s intertemporal UMP for
What happens if the of ? If it’s easier, feel free to make up values for , and the of (for example: in terms of the parameters.
or ). Answer:
25
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. The intertemporal UMP is to choose consumption in each period subject to the constraint that consumption equals income: ( ) ( ) ( )( Use the definition of real interest rate: ( Where )( to transform the UMP into: ( Set (since )( ) ) is the base period) to get: ( )( ( ) ( )( ) )( ( ( )( ( ) ( ) ) ( The ) ) ) ) budget constraint is in terms of the real interest rate. Use the hint and work with the log CobbDouglas utility function:
( ) ( ) Setup the Lagrangian:
26
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. ( [ ) ( ) The FOCs are: ( [ ( ) ) ( ) Rearrange and equate the first two FOCs: ( ) () We can substitute this in the ( ) budget constraint:
( ( ) ) ( ( () ( ) ) )[ ( ( [ ( ) ( [ ) ) ( ) ) 27
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. [ That is, consumption in (in the present period) is a constant fraction
( () () )
( [ [( That is, consumption in of the PV income. Now for ) ) (in the future) is a constant fraction of the FV income (that’s neat!). Finally, we can calculate , which by the envelope theorem, is the marginal utility of “income”:
[ ( )
( [
Applying the envelope theorem the MU of a small increase in We can solve for Recall that (
) ) income is: using any of the first two FOCS. For example, the second FOC implies: [( ) so that: [( [( ) ) 28 ECO 204 Chapter 6: Practice Problems & Solutions for Modeling In...
View
Full
Document
 Fall '09
 AJAZHUSSAIN
 Economics, Microeconomics

Click to edit the document details