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

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Prof. Javier Fernández 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 Consumer’s Budget Constraint

The consumer’s current budget constraint is:

The consumer’s 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

consumer’s 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 consumer’s lifetime, they use up

everything.

The Representative Consumer’s Problem

The representative consumer’s problem is to choose C, C', l & l' to make themselves as well off as

possible subject to their lifetime budget constraint (above).

It’s straightforward to describe the consumer’s optimizing decision in terms of 3 marginal

conditions:

o

o

o

Current Labour Supply

The representative consumer’s 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 they’re 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

Prof. Javier Fernández ECO209 Page 2 of 18

Chapter 11 – A Real Intertemporal Model with Investment

leisure and more future leisure (as it’s 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.

Prof. Javier Fernández 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 there’s 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 there’s an increase in we, then the demand curve shifts up.