Question

5, The inverse demand curve a pure monopoly faces is P = 120-20. The firm's cost curve is TC 10+o (a) Compare the monopoly outcome to that of perfect competition. (b) Determine how much consumers are harmed by monopoly relative to perfect competition (i.e. determine the change in consumer surplus). (c) Determine the deadweight loss ofmonopoly.

Answer 1

Answer
a)
Monopoly produces at MR=MC
MR=120-4Q ....... An MR curve is double sloped than the demand curve
MC is a change in total cost and a change in function found by differentiation
MC=dTC/dQ=2Q

equating MR+MC
120-4Q=2Q
6Q=120
Q=20
P=120-2*20
P=$80

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A perfectly competitive firm produces at MC=P
equating MC=P
2Q=120-2Q
4Q=120
Q=30
P=120-2*30
P=$60

the monopoly produces 20 units, and perfect competition produces 30 units, and monopoly charges $80 and perfect competition charges $60
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b)
A consumer surplus is the area below demand curve and above price and left of the quantity
under perfect competition
CS=0.5*(Y-intercept of the demand curve-P)*Q
=0.5*(120-60)*30
=900
under monopoly
CS=0.5*(120-80)*20
=400
the decrease in consumer surplus =900-400=$500
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c)
DWL is the loss in total surplus because of lower output than the efficient output
DWL=0.5*(monopoly price -monopoly MC)*(difference between quantities)
monopoly MC=10+20*2=$50
DWL=0.5*(80-50)*(30-20)
=$150
the DWL is $150

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