Question

Linda and Alberto consume the same product. They have the following demand curves for this product:

Q _Linda = 500 – 10 P

Q _Alberto = 500 – 20 P

The marginal cost (MC) for the firm is $10.

• Calculate the prices when the firm discriminates between the two consumers. (15 points) Please explain how you got your answer.
• Is this a good strategy, or should the firm charge the same price to both of them? (10 points) Please explain how you got your answer.

Answer 1

Answer : 1) For Linda :

Q = 500 - 10P

=> 10P = 500 - Q

=> P = (500 - Q) / 10

=> P = 50 - 0.1Q

TR (Total Revenue) = P * Q = (50 - 0.1Q) * Q = 50Q - 0.1Q^2

MR (Marginal Revenue) = TR / Q = 50 - 0.2Q

For price discrimination the profit maximizing condition is MR = MC. So,

50 - 0.2Q = 10

=> 50 - 10 = 0.2Q

=> 40 = 0.2Q

=> Q = 40 / 0.2

=> Q = 200

From demand function we get,

P = 50 - (0.1 * 200)

=> P = $30

So, here the firm charges $30 price level for Linda.

For Alberto :

Q = 500 - 20P

=> 20P = 500 - Q

=> P = (500 - Q) / 20

=> P = 25 - 0.05Q

TR = P*Q = (25 - 0.05Q) * Q = 25Q - 0.05Q^2

MR = TR / Q = 25 - 0.1Q

For price discrimination the profit maximizing condition is MR = MC. So,

25 - 0.1Q = 10

=> 25 - 10 = 0.1Q

=> 15 = 0.1Q

=> Q = 15 / 0.1

=> Q = 150

From demand function we get,

P = 25 - (0.05 * 150)

=> P = $17.5

So, here the firm charges $17.5 price level for Alberto.

2) In case of single price market demand becomes the sum of Linda and Alberto's demand.

P = (50 - 0.1Q) + (25 - 0.05Q) = 50 - 0.1Q + 25 - 0.05Q

=> P = 75 - 0.15Q

TR = P*Q = (75 - 0.15Q) * Q = 75Q - 0.15Q^2

MR = TR / Q = 75 - 0.3Q

For single price monopoly the profit maximizing condition is MR = MC. So,

75 - 0.3Q = 10

=> 75 - 10 = 0.3Q

=> 65 = 0.3Q

=> Q = 65 / 0.3

=> Q = 216.67

From demand function we get,

P = 75 - (0.15 * 216.67) = 75 - 32.5

=> P = $42.5

Total revenue of firm from single price = P * Q = 42.5 * 216.67 = $9,208.48 .

Total revenue from price discrimination = Revenue from Linda + Revenue from Alberto = (30 * 200) + (17.5 * 150) = 6000 + 2625 = $8,625.

Now we can see that the total revenue is higher in single price strategy. As the cost does not changes and the total revenue is higher in single price strategy hence the firm will earn higher profit by using single price strategy. So, the firm should charge same price for both Linda and Alberto.