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E Holding y -~ DM:p l+pD constant: (l+e) > 0 -1 e DA:p = - [p - e D p +D- l ] -< 0 The second equation is satisfied if e only if e < -1. condi tion for e ~ 0, the first if and It can also be shown that a necessary and sufficient DA:p (X-) p < 0 and e .!. (X) < 0 DA:p p - is also e < - 1 • Thus the condition guarantees that if the relative price of the non-numeraire good rises, consumption of it will fall while consumption of the numeraire will at least remain constant, that is to say, that the substitution effect, inducing greater consumption of the numeraire, outweighs the decline in income.
34) logarithmically with respect to S, obtaining ~ ~!. dW I dh !. 4 totally, 1. e. , - I is" ass aw dW aDD = ~ aw dW 34 - + and solving for the derivative. I aDD is"3S dS We obtain I sy y - e I I I (- - -) - e (- D:p z z D:y z A M I z=z-) A > 0 under our demand assumptions. Thus an increase in saving at the expense of agricultural consumption will raise the growth rate and the long-run equilibrium capital-labor ratio. However, it will not be as effective as an increase in saving at the expense of consumption of manufactures since income (expressed in terms of manufactures) tends to fall.
16 ) where e D: y e D : p < - 1 where e D:p = y aD ay IT ClD Clp IT p The same system of twelve independent equations can be written for country a and S. It remains to determine the imports of countries S, and their relation to one another. 1), 4As shown in the Appendix to Chapter TWo, the assumption e > 0 implies e D . < -1. , there are no capital movements. 20) Including the twelve independent equations representing country S, there are 28 equations in 27 unknowns. 20). 17) and note that the number of equations equals the number of unknowns.