Once again, a comparison of (4.26) with the earlier expression (4.10) points to the desirability of keeping the urban price lower than what would have been desirable in the absence of price-productivity effects.
In this appendix, we present the essential details of the model analysed in this chapter. Some of these details are also helpful in the next two chapters.
A is the agricultural land per peasant. The output of the agricultural good per peasant is X ≡ X(A, Lr), where Lr is the variable number of hours a peasant works. (xr, yr) denotes a peasant's consumption of agricultural and industrial goods. Q ≡ X − xr is the surplus of the agricultural good per peasant. Q is positive. pr represents the rural price of the agricultural good in terms of the industrial good. A peasant's budget constraint is(4.A1) A peasant's utility function is Ur(xr, yr, Lr). His indirect utility level, denoted by Vr(pr), is obtained from (4.A2) The envelope theorem yields (4.A3)
where λi is the positive marginal utility of income of a person in sector i.
To understand why the sign of the surplus elasticity,, is not predictable from the standard restrictions on the utility and production functions, we must first consider the simpler case in which a farmer faces a fixed market wage and buys or sells labour services. There are then three effects on the surplus of an increase in pr: output increases because its price is higher; consumption increases because the net profit or rent from land is higher (we assume here that the agricultural good is normal); and consumption decreases because the price of the consumption good is