Question

Aqua Pure has a natural monopoly on providing water to households in a local apartment complex. They can provide water at an average cost of ATC = 240/Q + 6, and a constant marginal cost of MC = $6. Demand for water in the apartment complex is given by P = 40 – 0.5Q. What is Aqua Pure’s unregulated monopoly price, the socially optimal price, and the fair-return price?

Monopoly Price: $ _______

Socially Optimal Price: $ _______

Fair-Return Price: $ ________

Answer 1

i)

P=40-0.5Q

Total Revenue=TR=P*Q=(40-0.5Q)*Q=40Q-0.5Q^2

Marginal Revenue=dTR/dQ=40-Q

Monopoly output can be determined by setting MR=MC

40-Q=6

Q=34

P=40-0.5Q=40-0.5*34=$23 (Monopoly price)

ii)

Socially optimal price=MC=$6

iii)

Fair return output can be determined by setting P=ATC

40-0.5Q=(240/Q)+6

34-0.5Q=(240/Q)

34Q-0.5Q^2=240

Q^2-68Q+480=0

Q^2-60Q-8Q+480=0

Q*(Q-60)-8*(Q-60)=0

(Q-60)*(Q-8)=0

Q=60 or Q=8

We will consider the higher value of Q

Q=60

P=40-0.5Q=40-0.5*60=$10

Fair return price=$10