Question

After intense lobbying, your gourmet popcorn firm has been awarded the sole license for selling popcorn in the Hampton Roads region. No other firms may sell gourmet popcorn in the region and imports into the region are prohibited and packages are subject to inspection.

The inverse demand function for the gourmet popcorn market and marginal revenue function are:

P = 574.1 - 13.64*Q

MR = 574.1 - 2*13.64*Q

And you know your firm has the following cost and marginal cost functions:

C(Q) = 427.73 + 5.92*Q + 9.98*Q^2

MC(Q) = 5.92 + 2*9.98*Q

What is the total revenue from the sale of your firm's gourmet popcorn?

Answer 1

Consider the given problem here the particular firm will act as a monopolist after the intense lobbying. So, here the monopolist will maximize its profit by the following condition.

=> MR = MC, => 574.1 - 2*13.64*q = 5.92 + 2*9.98*q, => 574.1 - 5.92 - 27.28*q = 19.96*q.

=> 568.18 = 27.28*q + 19.96*q = 47.24*q, => q = 568.18/47.24 = 12.03, => q=12.03.

Now, the demand function is given by, “P = 574.1 - 13.64*q = 574.1 - 13.64*12.03 = 410.01, => P = 410.01.

So, here the profit maximizing price and the out are given by, “P=410.01” and “q=12.03” respectively. So, here the total revenue is given by, “TR = P*q = 410.01*12.03 = $4,932.42.