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Lecture 4

Lecture 4.docx

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James Bruce

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Lecture 4 Individual Firm’s Supply The supply function for a firm gives the profit maximizing quantity of output as a function of market price. Found where SMC = P and SMC is upward-sloping and P>min of AVC (if P0 - So just set SMC = P - y/2=P - y*=2P 3 2 Ex. A firm has VC = y /3-5y +45y. What is the SR supply? - SMC = dVC/dy = y -10y+45 - dSMC/dy = 2y-10 - y= 5 - At y=5, SMC = 25-50+45 = 20 - AVC = VC/y = y /3-5y+45 - dAVC/dy=2y/3-5 = 0 - y=15/2 - AVC(15/2) = 75/4-150/4+180/4=105/4 - So for P<=105/4, y*=0. For P>=105/4, P=SMC - P = y -10y+45 2 - y2-10y+45-P=0 - y -10y+25+20-P=0 - (y-5) +20-P=0 2 - (y-5) =P-20 - Y=5+sqrt(P-20) - So supply function: y* = {0 if P<=105/4 || 5+sqrt(P-20) if P>=105/4} Market Supply Function (SR): total desired (π-maxing) output in a market as a function of market price. Given a market with n firms with individual supply functions y*(p) i=1,2,in, the market supply is Y*(P)= SUM(y(P)) on [1,n] i 1/2 1/2 Ex. A market has 200 firms. They each have z1 z2 and w1=w2 =1. 100 of them have 4 units of input 2 (which is fixed in the SR). The other 100 firms have 25 units of input 2. What is the market supply function? 1/2 1/2 - y = z1 z2 - z1*=y /z2 2 - VC = w1z1* = y /z2 - SMC = dVC/dy = 2y/z2 (>AVC = y/z2) - So P = SMC gives individual firm supply. - P=2y/z2 - yi(p)=Pz2/2 - Y*(P) = SUM(1-200) (y(p)) = 100(P(4)/2) + 100(P(25)/2) i - Y*(P) = 200P + 1250P = 1450P  market supply function ^ TEST UP TO ABOVE ^ - covers everything up to and including market supply Review SR Cost and Product Curves TP = F(z1,z2) MP1=dTP/dz1, AP=TP/z1 VC=w1z1, FC=w1z2 STC=VC+FC SAC=STC/y AVC=VC/y AFC=FC/y SMC=dVC/y=dSTC/dy MP=w/SMC and AP=w/AVC Marg>Avg Avg increasing Marg=AvgAvg constant Marg
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