Consumption is equal to total wage income (
𝑤?
?
), plus dividend income (
?
), minus taxes
(
?
).
This budget constraint (BC) is given by:
?
=
𝑤?
?
+
?
–
?
Accounting for the time constraint we end up with
?
=
𝑤
ℎ
−
?
+
?
–
?
∴
?
= −
𝑤?
+
𝑤ℎ
+
?
–
?
Slope of BC is
−
𝑤
,
and intercept is
𝑤ℎ
+
?
–
T
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Representative Consumer’s Budget Constraint when taxes is greater than dividend
income ( T>
π
)
This figure shows the consumers budget
constraint, line AB, for the case in which taxes
are greater than the consumer’s dividend
income. In this case
?
–
? is negative.
The slope
of the budget constraint is –
w
, and the constraint
shifts with the quantity of nonwage real
disposable income,
π

T.
All points in the
shaded area and on the budget constraint can be
purchased by the consumer. The vertical
intercept is the
maximum quantity of consumption attainable for the consumer, which is what is achieved if
the consumer works
h
hours and consumes no leisure. The horizontal intercept is the
maximum number of hours of leisure that the consumer can take and still be able to pay the
lump sum tax.
Representative Consumer’s Budget Constraint when dividend income is greater than
taxes ( T<
π
)
This figure shows the consumers budget
constraint when taxes are less than dividend
income, in which case
?
–
? is positive.
This
implies that the budget constraint is kinked.
Consumption bundles in the shaded area and
on the budget constraint are feasible for the
consumer; all other consumption bundles
are not feasible. The kink in the budget
constraint can be seen to be as a result of the
fact that the consumer cannot consume more
than
h
hours of leisure. Thus, at point B we
have
?
=
h,
which implies that the number of hours worked by the consumer is zero. Points
along BD all involve the consumer working zero hours and consuming some amount C
≤
?
–
?
— that is, the consumer always has the option of throwing away some of his dividend
income. Even though the consumer does not work at point B we have C =
?
–
?
> 0, as
dividend income exceeds taxes.
Consumer Optimization
To determine what choice of consumption and leisure the consumer makes, we assume that
the consumer is rational. This means the consumer knows his or her own preferences and
budget constraint and can evaluate which feasible consumption bundle is best
.
Therefore, the
consumer can make an informed optimization decision and can therefore optimize his
behaviour. The consumer chooses the consumption bundle that is on his or her highest
indifference curve, while satisfying
his or her budget constraint.
Optimization in this case implies that
the marginal rate of substitution of
leisure for consumption equals the
real wage.
The consumption bundle represented
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by point H, where an indifference curve is tangent to the budget constraint, is the optimal
consumption bundle for the consumer. Points inside the budget constraint, such as J, cannot
be optimal (more is preferred to less), and points such as E and F, where an indifference curve
cuts the budget constraint, also cannot be optimal. A consumer would ot choose point J as it is
 Summer '18