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Lecture 3

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James Bruce

Lecture 3 Comparative Statics Endogenous variable: one which the models attempts to explain Exogenous variable: one which the model treats as given/fixed and uses to explain the model Eg. In the cost-min model: endogenous = costs, costs of production exogenous = outputs, input costs, production technology Comparative statics: the systematic analysis of how the exogenous variables affect the endogenous ones - Changes in Output: how does the firm’s cost-minimizing input bundle change as desired output changes (but not input costs) o Normal input: one for which the cost- minimizing quantity increases as output increases o Inferior input: one for which the cost-min. quantity falls as output increases. It is downward sloping if one input is normal and the other is inferior - Input Costs: suppose the cost of one input, say input one, changes while output and the other input’s (#2) cost remain unchanged. Suppose there is dim. MRTS and w1 inc. Do costs of production increase or is it possible that, by substituting away from the now more costly input, it lowers its costs of production (below what they were prior to w1 inc.)? o W1 inc gives steeper isocosts which was initially at A. After w1 inc, move to B. o Old cost at A = old cost at G(since A,G are on the same isost) o Old cost at G< new clost at G (since w1 inc and z1>0 at G) o New cost at G = new cost at B (since B/G on same new isocost) o Therefore old ost at A < new cost at B o Therefore cost of production increases if the cost of an input increases o (So long as z1 >0 at every cost minimizing bundle prior to w1 inc, we get the same result) - Eg. A firm has a production function y = (z1 +z2 ). What is the output expansion path? o MP1/MP2 = w1/w2 1/2 1/2 -1/2 1/2 1/2 -1/2 o (2(z1 +z2 )*z1 /2)/ (2(z1 +z2 )*z2 /2) = w1/w2 o z2 /z1 1/2= w1/w2 2 o z2 = (w1/w2) z1 o Homothetic production function: one for which the O.E.P is a line through the origin  Relationship Between LR and SR Costs: - The LAC curve is the lower envelope of all possible SAC curves - Every point on the LAC is a point on some SAC - At any level of output, LAC < SAC for every SAC curve 1/2 1/2 - Ex. For a firm with y = z1 z2 facing w1 = 1 and w2 = 1, show that LAC is the lower envelope of the SAC curves (input 2 fixed in SR) o For input 2 fixed at z2, y = z1 z2/2 2 o z1* = y /z2 o STC = w1z1* + w2z2 o STC = y /z2 + z2 (w1, w2 = 1) o SAC = STC/y = y/z2 + z2/y
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