Dominick Salvatore Schaums Outline of Microeconomics, 4th edition Schaums Outline Series 2006

100 CONSUMER DEMAND THEORY [CHAP. 4
Fig. 4-37 Fig. 4-38
(a) If the individual borrows all of the personal period 2 income to spend in period 1, the level of expenditures
in period 1 would be $157.14 ($100 þ $60/1.05). On the other hand, if the individual lends all
of the personal period 1 income, the expenditures in period 2 would be $165 [60 þ ($100 1.05)]. This
gives the individuals the budget line shown in Fig. 4-37.
(b) For the individual to be in equilibrium by lending $20 out of period 1 income, one of the indifference
curves (showing this individual’s utility derived from period 1 versus period 2 consumption) must be
tangent to the budget constraint at the point where the individual saves and lends $20 out of period 1
income. This is shown in Fig. 4-38. At the equilibrium point E, the marginal rate of substitution of
present for future consumption or time preference of this individual is equal to the market rate of interest
of 5%. The individual’s consumption is $80 in period 1 and $81 [$60 þ ($20 1.05)] in period 2. This
type of analysis can be extended to more than two periods.
4.42 Suppose that an individual has an income, M ¼ $100, and a maximum number of hours, T ¼ 24 per week,
available to consume products X (for example, a movie) and Y (for example, a restaurant meal).
P x ¼ P y ¼ $10, and the time required to consume X and Y is t x ¼ 2 h and t y ¼ 3 h, respectively. (a)
Derive and plot the money and time budget constraints of this individual. (b) On a separate graph, draw indifference
curve I, giving the equilibrium point where both money and time are binding constraints; alternative
indifference curve I 0 , giving an equilibrium point where T only is the binding constraint; and another alternative
indifference curve, I 0 , giving an equilibrium point where M is the only binding constraint. (c) How can
the individual’s equilibrium position be improved when only M or only T is the binding constraint?
(a) The money budget constraint is
The time budget constraint is
($10)X þ ($10)Y 4 100
(2 h)X þ (3h)Y 4 24 h
The inequalities indicate that the individual can be on or inside the particular budget lines shown in
Fig. 4-39. To these, we might add X, Y 5 0 to prevent negative values for X and Y.
(b) In Fig. 4-40, OCEB is the feasible region (or regions) which satisfies both constraints simultaneously.
Point E is the equilibrium point at which both constraints are binding. Point F is an alternative equilibrium
point where T only is the binding constraint, and point G is another alternative equilibrium point
where M is the only binding constraint.