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Chapter 22 Firm Supply SR: Suppose the firm is a price taker, then the -max problem becomes max y py-c s (y), FOC: p-MC(y)=0. SOC: -MC’(y) (C’’(y))<0 or MC’(y)>0 Two caveats: lie only on the upward-sloping part of the MC and firms may shut down.
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Chapter 22 Firm Supply • SR: Suppose the firm is a price taker, then the -max problem becomes maxy py-cs(y), FOC: p-MC(y)=0. SOC: -MC’(y) (C’’(y))<0 or MC’(y)>0 • Two caveats: lie only on the upward-sloping part of the MC and firms may shut down. • If a firm shuts down, it gets –F. If it operates, it gets py-cv(y)-F. Hence a firm shuts down when –F> py-cv(y)-F or cv(y)/y>p or AVC>p.
AVC<p=MC: So a firm’s supply is the upward sloping part of the MC that lies above the AVC. • Can now work on the producer’s surplus. To produce y units of outputs, the firm incurs extra cost of cv(y). If for these y units, it gets py revenue, then the difference py-cv(y) is the producer’s surplus.
Three ways to measure producer’s surplus. Revenue-variable cost, revenue-the area under the marginal cost, revenue-some combination of both. py-cv(z)-(cv(y)-cv(z))=py-AVC(z)z+yzMC(x)dx • LR: have the option to exit. Hence py-c(y)0 or pc(y)/y=AC. The LR supply curve is the upward sloping part of the LR marginal cost curve that lies above the AC. • CRS: LR MC=LR AC for all y. the supply curve is a horizontal line.
