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s... Cij(w, Q) = Hji(w, Q) second derivative Cji(w, Q) = Cij(w, Q) Why...?? And now for a simple result: = ?2 _____ ?wj ?wi ?2 _____ ?wi ?wj Second derivatives mute... The effect of the price of input j on conditional demand for input i Hij(w, Q) = Hji(w, Q) The effect of the price of input i on conditional demand for input j The economic meaning... Now for an even simpler result: Cii(w, Q) = We39。ve put j=i. Special case Hii(w, Q) this must be negative ... so this must be negative too ... and so: Because the cost function is concave in prices: Consider the demand for input 1 conditional demand curve zi wi Hi(w,Q) Hii(w, Q) 0 The conditional demand curve slopes downwards ?Nonconvex Z yields discontinuous H ?Crossprice effects are symmetric ?Ownprice demand slopes downward. For the conditional demand function... The Firm Production Output Supply Ordinary Input Demand Optimisation Comparative Statics The Firm and the Market Conditional Input Demand black box problems max PQ C(w,Q) . Q ? 0 Yields optimal output The second stage problem Q* = S (w, P) supply of output We need to examine the second stage of the optimisation process (our second response function) P Q For a given P read off optimal Q Q CQ C/Q P P Q P Q Q P Q P P P Now let P fall... Note what happens below Average Cost... P Q _ _ Q=S(w,P) no price gives solution here Supply curve z2 Q 0 IRTS here Production function with local IRTS ?Supply curve slopes upward ?Nonconcave G yields discontinuous S ?IRTS means G is nonconcave and so S is discontinuous For the supply function..