Question

What is the slope of a consumer’s lifetime budget constraint when plotted in a c vs c' diagram?

Answer 1

The Two-Period Consumption Model

We want to create a model that captures this concept of transitory and

permanent income, and which can therefore distinguish between temporary and

permanent shocks to our economy.

Introducing the Two-Period Model (It has two periods)

The first period represents today, the current time period.

The second period represents tomorrow, the future time period.

Transitory income effects will only effect the first time period, whereas

permanent income effects will effect both current and future consumption.

Below is an indifference curve for a consumer. Notice that they have smooth

preferences over current and future consumption.

Glossary:

c1 current consumption

c2 future consumption

U utility

Indifference Curve shows all the bundles of c1 and c2 that give the consumer the

same level of utility. Higher indifference curves represent higher utility/ being

better off.

The Lifetime Budget Constraint
c +c′1 + r= y − t +y′ − t′1 + r
◮ The budget constraint in the future period implies that
s =c′ − (y′ − t′)1 + r
◮ Replace this expression for s in the current period budget
constraint to get
c +c′ − (y′ − t′)1 + r| {z }s= y − t
◮ Rearranging gives the lifetime budget constraint above

c +c′1 + r= y − t +y′ − t′1 + r
◮ The LHS of the lifetime budget constraint is the
present value of lifetime consumption
◮ The RHS of the lifetime budget constraint is the
present value of lifetime disposable income or wealth
◮ Present value means:
in terms of period 1 consumption goods
◮ The problem, then, is to choose consumption today and
tomorrow (c and c′) to be as well off as possible
◮ Once the consumer has chosen c and c′, savings (s) can
be found either from the current or future budget constraint

c′ = (1 + r)(y − t) + y′ − t′ − (1 + r)c

c′ = (1 + r)we − (1 + r)c
where we is present-value disposable income (or wealth), i.e.
we = y − t +y′ − t1 + r
◮ The intercept of the budget constraint is (1 + r)we
◮ The slope of the budget constraint is −(1 + r)

The Lifetime Budget Constraint Graphically
◮ The vertical intercept ((1 + r)we)
is what could be consumed
tomorrow if nothing were
consumed today
◮ The horizontal intercept (we) is
what could be consumed today if
nothing were consumed
tomorrow
◮ The slope of the line BA is
−(1 + r)
◮ All points in the shaded area are

Point E is the endowment pointfeasible consumption bundles
or bundle
◮ The consumer consumes his/her
endowment bundle (point E) if
savings are exactly zero (s = 0)
◮ To consume points on the line
BE, the consumer must be a
lender (s > 0)
◮ To consume points on the line
EA, the consumer must borrow
(s < 0)