倫敦經(jīng)濟(jì)學(xué)院高微講義-企業(yè)理論-wenkub
2022-11-03 10:46:02 本頁面
【正文】 m(w,Q) ? ? ? ...optimal input demands as a function of exogenous variables demand for input i, conditional on output Q We need to examine the first stage of the optimisation process zi* = Hi(w,Q) A function of input prices ...and output level conditional input demand function (our first response function) Result depends on shape of Z z 1 z 2 z 1 z 2 z 1 z 2 z 1 z 2 z2 z1 Take the co ventional case... Map the optimum into (z1,w1)space z2 z1 w1 z1 Start with an arbitrary value of w1 ... Do it again for a lower value of w1 ......and again to get... H1(w,Q) the conditional demand curve ?In the conventional case... ?... the constraint set is convex, with a smooth boundary ?We find the solution is a continuous map... ?... that is single valued. Points to note Result depends on shape of Z z 1 z 2 z 1 z 2 z 1 z 2 z 1 z 2 Z(Q) _ 2 z2 z1 What about the nonconv x case...? again map the optimum into (z1,w1)space Z(Q) _ 2 w1 z2 z1 z1 ...now try a very low value of w1 But what happens in between? a demand correspondence Nonconvex Z : jumps in z* w1 z1 no price yields a solution here multiple inputs at this price The demand correspondence Points to note ?In this case... ?... the constraint set is nonconvex ?We find the solution is a discontinuous map… ?The map is multivalued at the discontinuity. Let us set this difficulty aside... ?Let’s take it for granted that singlevalued inputdemand functions exist. ?How are they related to the cost function? ?What are their properties? ?How are they related to properties of the cost function? Do you remember thes ...? Assume the existence of a conditional input d
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