What is the equilibrium price and quantity decided by the monopolist?
The firm produces at MR=MC
converting the demand curve to the inverse demand curve to find MR function
Q=800-P
P=800-Q
MR=800-2Q ........ An MR curve is double sloped than an inverse linear demand curve
MC=change in TC =first differentiation of TC=dTC/dQ=2Q
equating MR=MC
800-2Q=2Q
4Q=800
Q=200
P=800-200=600
the quantity is 200 units and the price is $600
What is the average cost at the equilibrium quantity?
ATC=TC/Q=Q^2/Q=Q=200
ATC is $200
How much profit does the monopolist make at the equilibrium price and quantity?
Profit =(P-ATC)*Q
=(600-200)*200
=80000
the profit is $80000
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