• Chapter 23 Firm Supply
• Key Concept: SR supply is the upward
sloping part of MC that lies above its
AVC.
• LR supply is the upward sloping part of
MC that lies above its AC.
• We also define the producer’s surplus.
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• Chapter 23 Firm Supply
• SR: -max implies
• maxy py-cs(y)
• FOC: p-MC(y)=0
• SOC: -MC’(y)<0
• or MC’(y)>0
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• FOC: p-MC(y)=0.
• SOC: -MC’(y)<0 or MC’(y)>0
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• FOC: p-MC(y)=0.
• SOC: -MC’(y)<0 or MC’(y)>0
• Two caveats:
• lie only on the upward-sloping part of the
MC
• firms may shut down
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• 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.
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• p=MC>AVC
• So a firm’s supply is the upward sloping
part of the MC that lies above the AVC.
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• We now work on the producer’s surplus.
• Recall the consumer’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.
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• Three ways to measure producer’s
surplus.
• Revenue - variable cost
• Revenue - the area under the marginal
cost
• Revenue - some combination of both.
• py-AVC(y)y
=py- y0MC(x)dx
=py-(AVC(z)z+yzMC(x)dx)
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• Revenue - some combination of both.
• The third way is just the area to the left of
the supply curve.
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• We are often interested in the change in
producer’s surplus.
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• Look at the example c(y)=y2+1
• MC=2y
• Hence p=2y or y=p/2 or S(p)=p/2
• π(p)=py-c(y)=pp/2-(p/2)2-1=p2/4-1
• PS=(1/2)(pp/2)=p2/4
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• We now turn to the LR supply.
• LR: firm has the option to exit.
• Hence py-c(y)0 or
p=MCc(y)/y=AC
• The LR supply curve is the upward
sloping part of the LR marginal cost
curve that lies above the AC.
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• CRS
• LR MC=LR AC for all y.
• The supply curve is a horizontal line.
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• The firm is willing to supply any amount
of output at p= cmin
• an arbitrarily large amount of output at
p>cmin
• and zero output at p<cmin
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• Chapter 23 Firm Supply
• Key Concept: SR supply is the upward
sloping part of MC that lies above its
AVC.
• LR supply is the upward sloping part of
MC that lies above its AC.
• We also define the producer’s surplus.
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