ECO209Y5 Chapter Notes - Chapter 11: Real Interest Rate, Real Wages, Budget Constraint

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Prof. Javier Ferndez ECO209 Page 1 of 18
Chapter 11 A Real Intertemporal Model with Investment
Chapter 11 A Real Intertemporal
Model with Investment
THE REPRESENTATIVE CONSUMER
The Representative Consumers Budget Constraint
The consumers current budget constraint is:
    
The consumers future budget constraint is:
       
When we arrange for S p & then plug it in to one of the equations (and do some algebra), we get the
consumers lifetime budget constraint:
 
      
The left-hand side is the lifetime consumption & the right-hand side is the lifetime disposable
income. They should equal each other, as throughout the consumers lifetime, they use up
everything.
The Representative Consumers Problem
The representative consumers problem is to choose C, C', l & l' to make themselves as well off as
possible subject to their lifetime budget constraint (above).
Its straightforward to describe the consumer’s optimizing decision in terms of 3 marginal
conditions:
o 
o 
o 
Current Labour Supply
The representative consumers current supply of labour is determined by 3 factors: the current real
wage (w), the real interest rate (r), and lifetime wealth (we).
1) Current Labour Supplied Increases when Current Real Wage Increases
This is true under the assumption that the substitution effect dominates.
Remember that when wage increases, there are 2 effects on leisure. The first is the substitution effect,
where the consumer will decrease consumption of leisure as its price has increased. The second effect
is the income effect, where the consumer consumes more of both l & c as theyre both normal.
2) Current Labour Supplied Increases when Real Interest Rate Increases
The consumer can substitute current leisure for future leisure. The relative price of current leisure
over future leisure is
. Therefore, an increase in the real interest rate, r, given w & w', results in
an increase in the price of current leisure relative to future leisure. Assuming again that the
substitution effect is larger than the income effect, the consumer will want to consume less current
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Prof. Javier Ferndez ECO209 Page 2 of 18
Chapter 11 A Real Intertemporal Model with Investment
leisure and more future leisure (as its become cheaper). This is an intertemporal substitution of
leisure.
3) Current Labour Supplied Decreases when Lifetime Wealth Increases
When there is an increase in lifetime wealth, there will be an increase in current leisure & thus a
decrease in current labour supply since current leisure is assumed to be normal.
Current Labour Supply
The current labour supply curve is labelled N s(r) to indicate that labour supply depends on the current
real interest rate (r).
3
If the real interest rate r increase, the labour supply curve will shift right.
An increase in lifetime wealth (we) causes the labour supply curve to shift left. Note! r is constant
as we increases.
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Prof. Javier Ferndez ECO209 Page 3 of 18
Chapter 11 A Real Intertemporal Model with Investment
Current Demand for Consumption Goods
In the following graph, we show the quantity of current demand for consumption goods by the
representative consumer, for each level of real income Y, holding constant the real interest rate r.
The slope of the curve C d(r) is the MPC, or marginal propensity to consume, which is the amount
that current consumption increases when there is a unit increase in aggregate real income Y.
When theres an increase in r, assuming the substitution effect dominates, there will be a decrease in
demand for current consumption goods because of the intertemporal substitution of consumption.
Also, holding constant r & Y, if theres an increase in we, then the demand curve shifts up.
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