A monopolist%u2019s demand function is given by P = 80 %u2013 3Q (with MR = 80 %

Question

A monopolist%u2019s demand function is given by                                     

                                      P = 80 %u2013 3Q

                                      (with MR = 80 %u2013 6Q).

          Its total cost function is

                                      TC = 20Q + 200

                                      (with MC = 20).

(i)           Using algebra determine the profit maximizing output, price and optimal profit for the firm.

           (ii)      Suppose that instead of maximizing profit, the firm wants to maximize total revenue.                     Using algebra determine the optimal output, price, profit and revenue for the firm.

Explanation / Answer

given

P=80-3Q ( here the symbol %u2013 is not clear so i assumed negative if positive i will give those set of answers)

TR=Q*P=80Q-3Q^2

given TC=20Q+200

so profit= TR-TC

=80Q-3Q^2-20Q-200

=60Q-3Q^2-200

maximum profit is obtained by differentiating profit wrt Q

so u get

60-6Q=0

so Q=10

now

answer

output=10

price=80-60=20

profit=600-300-200=100

when total revenue is maximized

similar procedure

differentiate wrt Q

so u get

80-6Q=0

Q=13.33

quantity cant be in fraction so we assume it to be 13

so P=80-39=41

output=13

price=41

profit=60*13-3(13)^2-200=-434

if any doubts plz ask

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