Download Lecture 11

L11200 Introduction to Macroeconomics 2009/10
Lecture 11:
Consumption, Saving and Investment II
Reading: Barro Ch.7
16 February 2010
Introduction
• Last time:
– Modelled household consumption and saving
decision
– Examined impact of changing income and interest
rates on household consumption
• Today
– Consumption decisions imply a level of saving
– What does this imply for capital accumulation?
Consumption Over Many Periods
• Considered a 2-period consumption decision:
C1  C2 / (1  i1 )  (1  i0 ) ( B0 / P  K0 )  ( w / P)1  L 
( w / P) 2  L / (1  i1 )  ( B2 / P  K 2 ) / (1  i1 )
• Assumed that period 2 was the last period
– Now extend to many periods
– So end-of-period two assets no longer fixed
Beyond Two Periods
• If we extend l.h.s beyond two periods:
C1  C2 / (1  i1 )  C3 / [(1  i1 )  (1  i2 )]...
• And extend rhs beyond two periods:
 (1  i0 ) ( B0 / P  K 0 ) 
( w / P)1  L 
( w / P) 2  L / (1  i1 ) 
( w / P)3  L / [(1  i1 )  (1  i2 )]...
( B2 / P  K 2 ) / (1  i1 ) disappears
• Final term
because there is no ‘end’ period
Multiyear Budget Constraint
• So the ‘multiyear’ constraint is:
C1  C2 / (1  i1 )  C3 / [(1  i1 )  (1  i2 )]...  (1  i0 )  ( B0 / P  K 0 ) 
( w / P)1  L  ( w / P) 2  L / (1  i1 )  ( w / P)3 L  [(1  i1 )  (1  i2 0]  ...
present value of consumption = value of initial assets +
present value of wage increases
• This constraint covers multiple periods:
ultimately covers a household’s lifetime
Temporary vs Permanent Changes
• Over the lifetime of a household, temporary
vs permanent changes in income will have
different effects
– A temporary change in income (e.g. in period 2
only) raises overall resources by a small amount
– The household wants to keep consumption
smooth, so it spreads the extra resource over all
time periods
– So the impact on consumption now is small, the
propensity to consume is less than 1
Temporary vs Permanent Changes
• Permanent changes in income have a much
bigger effect on current consumption
– Income rises in all periods
– So consumption rises in all periods in line with the
increase in income
– The propensity to consume now out of the
increase in income is 1.
– Key issue: an increase in income of £100 today
doesn’t raise consumption today by £100 unless it
is permanent.
Expected vs Unexpected Income
• Whether income is expected also matters
– If households expect a higher future income, they
will factor this into their borrowing decisions and
plan for higher income.
– So when income increases between periods, if it
was expected it has no impact on consumption
– But if households receive an unexpected increase
in income, this will impact of consumption.
Consumption and Investment
• One-period budget constraint
C  (1/ P)  B  K  ( w / P)  L  i  ( B / P)  iK
• Interest rate
i  (R / P   )
C  (1/ P)  B  K  ( w / P)  L  i  ( B / P)  ( R / P) K   K
• This is true for all households
– Across all households, B and ΔB must sum to zero
– So can drop from this equation in aggregate
Consumption and Investment
• Also, know that in equilibrium all income is
paid to labour and capital: Y  (w / P)  L  ( R / P)  K
– So can reduce to
C  K  Y   K
consumption + net investment = real GDP - depreciation
– Net investment depends on consumption. If
consumption is lower, investment will be higher
– This is crucial: it completes the picture of how
household choices determine investment
Review of Macro Model
• Brief review of last 4 lectures
• Want a model of the macroeonomy in order
to understand what might drive fluctuations
and how they impact on the economy
• Model based on ‘microfoundations’ of how
consumers, producers, workers and capital
owners behave
Review I
• Constructed model based on ‘household’
– Household owns a small business, supplies labour,
supplies capital and consumes
– So captures all the essential elements of the
economy
– Households are price takers: markets are perfectly
competitive and continually in equilibrium
Review II
• We setup what households ‘do’ in via the
budget constraint
PC  B  P  K    wL  i  ( B  PK )
• They earn profit, wage income, rental income
and income from bonds
• They use it to consume, save for the future
and invest in more capital
Review III
• We then set out to explain how much income
they earn and what they do with it
– Production: by profit-maximisation, households
combine factors of production to produce output
– In perfectly competitive market the business
makes no profit, but factors of production
(supplies by the household) earn rents
– Exactly the same as in microeconomic model
Review IV
• … and what they do with it
– They spend some and save some, aiming to
smooth their consumption
– This decision is made over many periods
– So consumption depends on overall lifetime
wealth, not just wealth today
– How much they save determines how much is
invested in capital (and so how much output is
produced in the future)
Review V
• Does this model explain reality?
– Sounds plausible, consistent with microeconomics
– Has implications for what will happen in the
economy when variables change
• Next step: incorporate changes in technology
– We found they explained long-run growth
– Maybe changes in technology could also explain
fluctuations
– But only if our model’s predictions are supported
by data
Summary
• Completed the macro model
– Has some limitations (fixed labour and capital
supply)
– But now used to address the data
• Next time: have a closer look at the data on
fluctuations
– Are the prediction of our model consistent with
what we see in the data?