Consider a monopolist that faces the following equations: Market demand for mono

Question

Consider a monopolist that faces the following equations: Market demand for monopolist's product: Q = 100 - P TC for monopolist: TC = 20Q + 3/10 Q^2 Write the demand equation in terms of Q. Given the above information, what is the profit maximizing price and quantity for the monopolist? Calculate the monopolist's total profits. Suppose the monopolist is regulated to produce where price equals average total cost (average cost pricing). Calculate the quantity the monopolist will produce and the price that will be charged after regulation. Calculate the level of profits for the regulated monopoly. What do you think happens to the consumer surplus under regulation compared to a scenario with no regulation? What do you think happens to deadweight loss when we move from an unregulated to a regulated monopolist?

Explanation / Answer

(a)Market Demand Q = 100-P

Total cost for monopolist TC= 20Q + 3/10Q2

To simply the above, we can write P = 100 – Q

We know that Total Revenue TR = Price * Q

Therefore TR = (100 –Q) * Q = 100Q – Q2

MR equal to 1st order derivatives of TR i.e. dy/dx (100Q –Q2) = 100 -2Q

We know TC = 20Q + 3/10Q2 ………………………..Given in the question

The first order derivatives of MC = dy/dx (TC) = 20 +6Q/10

Now equate the MC=MR

Thus the demand equation in terms of Q is written as 20 +6Q/10 =100 -2Q.

(b)Profit maximizing price and quantity

We need to equate MC =MR

Value of Q from the above equation is 30.76

Putting the value in the equation MC =MR

We get Quantity as 38.456

Price = 61.544

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