Suppose that a firm faces a demand curve for its product of $P = 10 - Q ^ { d }$ . The corresponding marginal revenue curve is $M R = 10 - 2 Q$ . The firm has a constant marginal cost of $4 per unit. If the firm engages in uniform pricing, what price will the firm charge?
A)$7.
B)$5.
C)$4.
D)$3.

Question

Quizplus · Accepted Answer

The profit-maximizing rule for a firm is to produce the quantity where marginal revenue equals marginal cost. In this case, the marginal cost is constant at $4 per unit. The marginal revenue curve is given by $M R = 10 - 2 Q$ .

Setting marginal revenue equal to marginal cost, we get:

$$10 - 2Q = 4$$

Solving for Q, we get:

$$Q = 3$$

Substituting Q = 3 into the demand curve, we get:

$$P = 10 - Q ^ { d } = 10 - 3 = 7$$

Therefore, the firm will charge a price of $7 per unit. The answer is A). To find the profit-maximizing quantity, we set marginal revenue equal to marginal cost and solve for Q:
10 - 2Q = 4
6 = 2Q
Q = 3
Now that we have the optimal quantity, we can plug that into the demand equation to find the price the firm should charge:
P = 10 - Qd = 10 - 3 = 7
Therefore, the firm should charge $7 per unit if it engages in uniform pricing.

Suppose That a Firm Faces a Demand Curve for Its P=10−QdP = 10 - Q ^ { d }P=10−Qd

Suppose That a Firm Faces a Demand Curve for Its $P = 10 - Q ^ { d }$