Lending to Agribusinesses in Zambia

I + B = Co + Ci / (1 + r_t) — (1 + гь)В / (1 + r_t)

where r_b is the cost of borrowed capital and r_t is the individual’s discount factor, which
takes into account the individual’s risk aversion or intertemporal impatience.

A common source of the demand for loanable funds is entrepreneurs wanting to
take advantage of business opportunities. Consider a situation in which investment
opportunities are too costly to be financed out of current income. That is, I - C₀ for an
individual is small. The borrowed funds B are spent on a risky investment project which
yields returns at a rate r₁. The utility maximizer can attain a higher indifference curve (u₁)
when borrowing to invest in opportunities that allow higher future consumption. When
the investment outcome is successful, lenders receive the borrowed principal (B) plus
interest (at the prior agreed rate, r_b). The investor has greater consumption possibilities in
the future, as seen by the outward shift of the vertical intercept in the budget line (figure
2).

Figure 2. Inter-temporal Utility Maximization with Borrowing

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