Question

A​ monopoly's cost function is CQ and its the demand for its product is pQ where Q is​ output, p is​ price, and C is the total cost of production. Determine the profit-maximizingLOADING... price and output for a monopoly.

Answer 1

Answer:

The answer is "70 units".

Explanation:

In the given question some equation is missing which can be defined as follows:

$C = 1.5Q^2+40Q\\\\P=320-0.5Q$  

Monopolistic functions are used where Marginal Profit = Marginal Cost where marginal revenue and marginal cost stand for the MR and  MC.

Finding the value of MR :

$\ MR = \frac{\partial TR}{\partial Q}$

       $= \frac{\partial PQ}{\partial Q} \\\\= \frac{\partial (320-0.5Q)Q}{\partial Q}$

       $= \frac{\partial (320Q -0.5Q^2)}{\partial Q}\\\\ = \frac{\partial Q (320 -0.5Q)}{\partial Q}\\\\ \ by \ solving \ we \ get \\\\ = 320 - Q...(1)$

Calculating the value of the MC:

$MC = \frac{\partial TC}{\partial Q}$

        $=\frac{\partial (1.5Q^2 + 40Q)}{\partial Q} \\\\=\frac{\partial Q (1.5Q + 40)}{\partial Q}\\\\ \ by \ solve \ value \\\\ = 3Q + 40....(2)$

compare the above equation (i) and (ii):

$\to 320 -Q = 3Q+40\\\\\to 320 -40 = 3Q+ Q\\\\\to 280 = 4Q\\\\\to 4Q =280 \\\\\to Q= \frac{280}{4}\\\\\to Q= 70$