The optimal consumption bundle for the consumer is at point A, where the MRS is equal to

(1+r). The consumer is a lender as the consumption bundle chosen implies positive savings,
with E being the endowment point.
A Consumer Who is a Borrower
In this figure, the initial endowment point is at E and the
consumer chooses point A where (c, c’) = (c*, c’*).
At
this point, the quantity the consumer borrows in the first
period is –s = c*  y – t, or the distance DB.
The optimal consumption bundle is at point A. Because
current consumption exceeds current disposable income,
savings is negative, and so the consumer is a borrower.
An Increase in Current Income for the Lender
When current income increases, lifetime
wealth increases from
we
1
to
we
2
. The lifetime
budget constraint shifts out, and the slope of
the constraint remains unchanged, because the
rea interest rate does not change. Initially, the
consumer chooses A, and he or she chooses B
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after current income increases. Current and future consumption both increases as both are
normal goods and current consumption increase by less than the increase in current income.
In this figure, the initial endowment point is at E1, and the consumer initially chooses the
consumption bundle represented by point A. In this figure we have shown the case of a
consumer who is initially a lender. We suppose that the current period income increase from
y
1
to
y
2
. As a result, the budget constraint shifts to the right by the amount
y
2
– y
1
, which is the
distanceE1E2, where E2 is the new endowment point. The slope of the budget constraint
remains unchanged, as the real interest rate is the same. Because current and future
consumption are normal goods, the consumer can now choose a consumption bundle
represented by a point like B, where consumption in both periods has risen from the previous
values. Current consumption increases from c1 t oc2 and future consumption increase from
c’1 to c’2. Thus, if current income increases, the consumer, the consumer wishes to spend this
additional income over both periods and not consume it all in the same period. Therefore, the
increase in current income is the distance AD, while the increase in current consumption is
the distance AF, which is less than the distance AD. As a result, an increase in current income
causes an increase in consumption in both periods and an increase in savings.
An Increase in Future Income
An increase in future income increases lifetime wealth from we1 to we2, shifting the lifetime
budget constraint to the right and leaving its slope unchanged. The consumer initially chooses
point A, and he or she chooses B after the budget constraint shifts. Future consumption
increases by less than the increase in future income, saving decreases and current
consumption increases.
In this figure we show that the effects of
an increase in income from y1 to y2.
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 Summer '18