Lending to Agribusinesses in Zambia

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:

where r represents the rate of return between the current and future periods. Combining
the two equations yields a budget constraint of :

÷A

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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