108
and, MP = x=b
0(A P) (P AV P = (M P) ( P )=MV P.
y y
Therefore,
AVP =MVP =r(1+ i) + i + I.
The shadow prices and MVPs of capital for cotton, rice, sesame, and sorghum are summarized in Table 24.
The derived demand functions are discontinuous step functions. The discontinuities result from discrete quantities of capital being used in the linear program; it is for these specified levels that the shadow prices are given. The functions all demonstrate the expected relationship between MVP and quantity of capital; decreasing marginal productivity is indicated as larger amounts of the input are used.
Although the shadow prices for capital differ slightly between
semesters, the MVP from only one of the semesters was chosen to derive the demand curve with respect to each crop. In no case, however, would the choice of one semester over the other affect the general outcome of the supply and demand analysis.
At the point where total capital requirement--total cost of production 3_-i s reached, the MVP-l is equal to the interest rate. At higher levels of capital, when it ceases to be a scarce resource, the MVP is not meaningful in a programming framework. The contribution of the input beyond this point is assumed to be zero. Demand Derived from Regression Analysis
The demand for the non-traditional cash inputs was derived for
3These costs were rounded-off from-the costs calculated in the study.