Answer:
Quantity = 59 units
Price = $111
Step-by-step explanation:
The Demand function is given by
[tex]P = 170 - Q[/tex]
The Marginal cost is given by
[tex]MC = 52[/tex]
We are asked to find the quantity and price of goods.
Firstly, obtain the Marginal revenue function from the demand function
The Total revenue is given by
[tex]TR = P \times Q \\\\TR = (170 - Q) \times Q \\\\TR = 170Q - Q^2[/tex]
The Marginal revenue is the derivative of the Total revenue,
[tex]MR = \frac{d}{dQ} (TR) = 170Q - Q^2 \\\\MR = \frac{d}{dQ} (TR) = 170 - 2Q \\\\[/tex]
Assuming that the monopolist maximizes profits,
[tex]MR = MC \\\\170 - 2Q = 52\\\\2Q = 170 - 52\\\\2Q = 118\\\\Q = 118/2\\\\Q = 59[/tex]
Therefore, the quantity is 59 units.
The price of each good is
[tex]P = 170 - Q \\\\P = 170 - 59 \\\\P = 111[/tex]
Therefore, the price is $111.
