I = Co + P1C1 ,
(1)
where P1 represents the present cost of future consumption and I represents current
income. The “price” of future consumption is re-written in the financial discounting style
as:
p,= AC ʌ
1 AC1 1 ÷r
(2)
where r represents the rate of return between the current and future periods. Combining
the two equations yields a budget constraint of :
÷A
(3)
1 + r
Utility for this individual is maximized at C0*, C1*. By rearranging the terms in the
budget constraint and substituting for P1, future consumption can also be found:
C1* = (I -Co*) / P1 (4)
C1*= (I - Co*) ( 1 + r) . (5)
Equation (5) means that current savings, (I - C0*), can be invested at rate of return r to
yield C1* in the next consumption period. The concept of utility maximization is
illustrated in figure (1). For a general utility function, U, an individual will choose to
maximize their utility by consuming at point C*1 and C*o, the point of tangency of the
individual’s utility function and the budget constraint.
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