Question

Tri.Optimum, LLC holds a monopoly license in their industry. They face a market demand of ? = 250 − 4?; ?(?) = 200 + 50?.

a. What are TO’s maximum monopoly profits?

b. By what percentage has the consumer surplus been reduced compared to the social optimum?

Answer 1

a)

A monopoly produces at MR=MC

MC is a change in the total cost and a change in function found by differentiation of the function, and here it is total cost function.

MC=dTC/dQ=50

MC=50

MR=250-8Q.......... An MR funtiion is double sloped than a linear inverse demand funtion.

equating MR=MC

250-8Q=50

8Q=200

Q=25

P=250-4*25=150

the firm produces 25 units and charges price of $150

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total revenue =P*Q=25*150=3750

total cost =200+50Q=200+50*25=1450

profit=TR-TC

=3750-1450=2300

the profit is $2300

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B)

Monopoly consumer surplus is

CS=0.5*(Y axis intercept of the demand curve -P)*Q

=0.5*(250-150)*25

=1250

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A social optimum output is at MC=P

equating the P=MC

250-4Q=50

4Q=200

Q=50

P=MC=50

CS=0.5*(250-50)*50

=5000

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change in CS =5000-1250=3750

%change in CS =(change in CS//CS of at the social optimum level of output)*100=(3750/5000)*100

=75

the % decrease in CS is 75%