生產者理論知識(ppt 55頁)-全文預覽
【正文】 ut Now put together the two stages of the optimisation process By substitution: Hi(w, S(w, P)) Di(w, P) demand for input i (unconditional ) =: (our third response function) Differentiate for the unpensated demand (.)(.)(.)(.) jiQijij SHHD ?? (.)(.)(.)(.) jiQijij SHHD ??Total= Substitution effect+Output effect Unconditional Demand can be determined from the cost function From Shepherds lemma (.)),(ijij HQC ?w (.)),(ijij HQC ?wAnd (.)),( iQiQ HQ ?wSince pQC Q ?),( wCan solve Sj(w,P)in terms of C(w,P) Hotelling’s Lemma QPSPp ???? ),(),( ww? iiizPDwp ???? ),(),( ww?Prove Assuming one input z The Profit Function and it’s derivatives are ],[]),[(),( pwwzpwzpGwp ??? zzwpGwzzzpG wzwwzw ?????? )(? GzwpGwzzpGGpzppzp ?????? )(?But from cost minimisation we know wpG z ?Consider the demand for input 1 Change in cost conditional demand curve price fall z1* z1 w1 H1(w,Q) initial price level ...and allow the price of input 1 to fall inputprice fall: substitution effect Notional increase in factor input if output target is held constant price fall z1* z1 w1 Original conditional demand curve ordinary demand curve z1** Conditional demand curve at new output level inputprice fall: total effect ?Nonconvex Z may yield a discontinuous D ?Crossprice effects are symmetric ?Ownprice demand slopes downward The ordinary demand function... Production Optimisation The Firm Comparative Statics The Firm and the Market Production Overview... The Firm Production The Short Run Optimisation Comparative Statics The Firm and the Market A Special Case ? T his is not a moment in time
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