生产者理论3.ppt

P Q _ _ Q=S(w,P) no price gives solution here Supply curve z2 Q 0 IRTS here Production function with local IRTS z1 Supply curve slopes upward Nonconcave G yields discontinuous S IRTS means G is nonconcave and so S is discontinuous For the supply function... Optimisation The Firm Production Output Supply Ordinary Input Demand Comparative Statics The Firm and the Market Conditional Input Demand Conditional Input Demand Output Supply black box problems demand for input i, conditional on output Q zi* = Hi(w,Q) Q* = S (w, P) supply of output zi* = Hi(w,Q) Q* = S (w, P) 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 uncompensated demand Total= Substitution effect+Output effect Unconditional Demand can be determined from the cost function From Shepherds lemma And Since Can solve Sj(w,P)in terms of C(w,P) Hotelling’s Lemma Prove Assuming one input z The Profit Function and it’s derivatives are But from cost minimisation we know 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 input-price 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 input-price fall: total effect Nonconvex Z may yield a discontinuous D Cross-price effects are symmetric Own-price demand slopes downward Same basic properties as for H function The ordinary demand function... Production Optimisation The Firm Comparative Statics The Firm and the Market 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 b