Agricultural household models The profit effect X a* = X a* ( pa , pm , w,Y * ) ( = X a* pa , pm , w,Y * ( pa , w, A) ) How does the HH’s demand for the ag staple (Xa*) Δ when the price of the ag staple (pa) s (assuming it is a normal, non-Giffen good)? Does it or ? ¶ X a* ¶ X a* = ¶ pa ¶ pa (?) (-) + Y *=const ¶ X a* ¶Y * × ¶Y * ¶ pa (+) (+) What would we have concluded if we had used a standard consumer demand model for Xa? 1 Agricultural household models The profit effect (cont’d) Using the Slutsky equation (see extra slides or Sadoulet & de Janvry 1995 for details), we can rewrite the expression as: ¶ X a* ¶ X a* = ¶ pa ¶ pa -X * × a U =const ¶ X a* ¶Y * * +Q × ¶ X a* ¶Y * or, equivalently: ¶ X a* ¶ X a* = ¶ pa ¶ pa (-) • • • * + (Q - X U =const * )× a ¶ X a* ¶Y * (+) Q*-Xa*? What is Let’s call this M*. What is the the sign of M* (marketable surplus) for net buyers vs. net sellers? What can we say about the effect of an increase in pa on Xa* for net buyers vs. net sellers? 2 1 Slutsky equation: shows relationship b/w Marshallian (M) & Hicksian (M) demand functions ¶x M ¶x H ¶x M Slutsky equation: -x = ¶p ¶p ¶y (1) ¶x M is holding y constant. ¶p ¶x H H H is holding U constant. x = x ( p,U ), so ¶p Recall x M = x M ( p, y), so ¶x ¶x ¶x -x (2) = ¶ p y=const. ¶ p U =const. ¶ y Can rewrite Slutsky as Apply Slutsky to get profit effect equation in terms of marketable surplus (Q*-Xa*) · · · We already showed that: Per Slutsky (2): ¶ X a* ¶ X a* = ¶ pa ¶ pa ¶ X a* ¶ pa Plug (4) into (3): = ¶ pa Y =const ¶ pa = - X a* ¶ X a* ¶Y * - X a* U =const (4) ¶ X a* ¶ X a* ¶Y * ¶Y * + × (5) ¶Y * ¶ pa * ¶Y ¶(p + wT ) ¶( paQ - wL + wT ) = = = Q* (6) ¶ pa ¶ pa ¶ pa * * · Note that: · Plug (6) into (5), rearrange terms, and simplify: ¶ X a* ¶ pa × (3) ¶Y * ¶ pa U =const ¶ X a* ¶ pa ¶ X a* ¶Y * Y *=const ¶ X a* * ¶ X a* + = Y * =const ¶ X a* ¶ pa + (Q* - X a* ) U =const ¶ X a* ¶Y * 4 2