Question

Question 3 Tries remaining: 2 for the price searcher's product is given by: 100-20P Points out of 8.34 Calculate the price the monopolist will charge. P Flag question (Do not include a dollar sign in your response. Round to the nearest two decimals.) Suppose that a price-searcher monopolist had a total cost function given by: TC= 20 + 0.5Q +0.2a. The demand Answer: Check

Answer 1

A monopolist will charge that price at which his profits are maximum. So, we'll try to find the price at which his profits are maximum.

Profit = Total Revenue (TR) - Total Cost (TC)

TR = Price*Quantity

Quantity (Q) = 100 - 20P => P = 5 - Q/20

So, TR = (5 - Q/20)*Q

= 5Q - Q²/20

Profit = (5Q - Q²/20) - (20 + 0.5Q + 0.2Q²)

Differentiating w.r.t Q and equating it to 0, we get

5 - 2Q/20 - (0.5 + 0.4Q) = 0

=> 5 - 0.1Q - 0.5 - 0.4Q = 0

=> 0.5Q = 4.5

=> Q = 9

Now we know that P = 5 - Q/20, substituting Q = 9, we get

P = 5 - 9/20 = 4.55