Scenario: Tobac Co. is a monopolist in the cigarette market in Nicotiana Republic, where the U.S. dollar is used as the official currency. The firm faces the demand curve shown below. The firm has a constant marginal cost of $2.00 per pack. The fixed cost of the firm is $50 million. To answer the questions below, it is useful to know that the equation of the (inverse) demand curve is P = 8 - 0.04Q, where Q is the quantity demanded (in millions of packs) and P is the price per pack (in $). Also, you should draw in the marginal revenue curve.

-Refer to the scenario above.Tobac Co.'s total revenue is maximized when it sells ________ packs of cigarettes at ________ per pack.

Question

Scenario: Tobac Co. is a monopolist in the cigarette market in Nicotiana Republic, where the U.S. dollar is used as the official currency. The firm faces the demand curve shown below. The firm has a constant marginal cost of $2.00 per pack. The fixed cost of the firm is $50 million. To answer the questions below, it is useful to know that the equation of the (inverse) demand curve is P = 8 - 0.04Q, where Q is the quantity demanded (in millions of packs) and P is the price per pack (in $). Also, you should draw in the marginal revenue curve.
 
-Refer to the scenario above.Tobac Co.'s total revenue is maximized when it sells ________ packs of cigarettes at ________ per pack.

Quizplus · Accepted Answer

To find the quantity where total revenue is maximized, we need to first find the quantity where marginal revenue equals marginal cost. 
Since the marginal cost is constant at $2.00, the marginal revenue is simply the derivative of the total revenue:
MR= TR' = (P × Q)' = Q + P × Q' 
Setting MR equal to $2.00, we get: 
2 = Q + (8-0.08Q) (-0.04)
2= Q-0.32Q +0.32
Q=100 million
To find the price at this quantity, we can use the demand equation: 
P= 8- 0.04Q
P=8-0.04(100)= $4.00 
Therefore, Tobac Co.'s total revenue is maximized when it sells 100 million packs of cigarettes at $4.00 per pack.