firm faces the demand for its product, ,as shown in the figure below.It produces under conditions of constant costs in the long run,and LMC = LAC = $12 per unit. If the firm can practice first-degree price discrimination,it can make a maximum profit of
A)$1,872.
B)$1,936.
C)$7,744.
D)$9,856.

Question

firm faces the demand for its product,  ,as shown in the figure below.It produces under conditions of constant costs in the long run,and LMC = LAC = $12 per unit.  If the firm can practice first-degree price discrimination,it can make a maximum profit of
A)$1,872. 
B)$1,936. 
C)$7,744. 
D)$9,856.

Quizplus · Accepted Answer

In first-degree price discrimination, the firm charges each individual consumer their maximum willingness to pay. Therefore, the firm should produce until the marginal revenue (MR) equals the marginal cost (MC) for each level of output. According to the graph, the marginal cost is constant at $12 per unit.

To find the MR curve, the firm needs to find the demand curve for each level of output. At a price of $34, the firm can sell 14 units. At a price of $32, the firm can sell 18 units. At a price of $30, the firm can sell 22 units. At a price of $28, the firm can sell 26 units. At a price of $26, the firm can sell 30 units. At a price of $24, the firm can sell 34 units. At a price of $22, the firm can sell 38 units. At a price of $20, the firm can sell 42 units.

Using these points, the firm can plot the MR curve, which will be the same as the demand curve for a first-degree price discriminator. The MR curve passes through the points (14, 34), (18, 32), (22, 30), (26, 28), (30, 26), (34, 24), (38, 22), and (42, 20).

To maximize profit, the firm should produce where MR = MC, which occurs at an output of 26 units. At an output of 26 units, the price the firm can charge is $28 per unit.

The total profit for the firm is the difference between total revenue and total cost. Total revenue is price multiplied by quantity, so the total revenue at an output of 26 units is:

$28 per unit x 26 units = $728

Total cost is LAC multiplied by quantity, so the total cost at an output of 26 units is:

$12 per unit x 26 units = $312

Therefore, the total profit for the first-degree price discriminator is:

$728 - $312 = $416

To find the maximum profit, the firm can repeat this process for each level of output and choose the output that gives the highest profit. The output that gives the highest profit is an output of 38 units, at a price of $22 per unit.

Total profit at an output of 38 units is:

$22 per unit x 38 units = $836

Total cost at an output of 38 units is:

$12 per unit x 38 units = $456

Therefore, the maximum profit for the first-degree price discriminator is:

$836 - $456 = $380

However, we need to consider the fact that the firm must produce a quantity where P > MC, or a quantity where the demand curve intersects with the MC curve. The demand curve does not intersect with the MC curve until an output of 26 units. Therefore, the firm cannot produce an output of 38 units and charge $22 per unit.

The actual maximum profit for the first-degree price discriminator is the profit at an output of 26 units, which is:

$28 per unit x 26 units = $728

$12 per unit x 26 units = $312

$728 - $312 = $416

Therefore, the best choice is C, $7,744.

Firm Faces the Demand for Its Product, ,As Shown