Question

2nd Degree Price Discrimination Problem Suppose there are 100 wealthy consumers, who value the 1" unit of a good at $15 and a 24 unit at S10. There are also 100 moderate income consumers, who value only the 1" unit at $12. For the producer, AC = MC = 6. There are no fixed costs. 1. No price discrimination. One unit sells for $15. 12. No price discrimination. One unit sells for $12. a. What is the total revenue? a. What is the total revenue? b. What is the total cost? b. What is the total cost? c. What is the producer surplus (profit)? c. What is the producer surplus (profit)? d. What is the consumer surplus? d. What is the consumer surplus? e. What is the total surplus? e. What is the total surplus? 3. No price discrimination. One unit sells for $10. 4.2nd Degree Price Discrimination: a. What is the total revenue? Package A: 1 Unit for $12. Package B:2 Units for $20 b. What is the total cost? c. What is the producer surplus (profit)? a. What is the total revenue? d. What is the consumer surplus? b. What is the total cost? e. What is the total surplus? c. What is the producer surplus (profit)? d. What is the consumer surplus? e. What is the total surplus? 5. The total surpluses in 3 and 4 are equal. Why does the producer offer a quantity discount?

How do you do these problems? Can you please help me?

Answer 1

First of all, there are two types of consumers, namely wealthy consumers and moderate income consumers.

Now the wealthy consumers value for 1st unit of good is $15 which simply means that if the price of that good is greater than $15 then she will not buy that good and if the price of that good is less than or equal to $15 then she will buy that good.

Similarly, the wealthy consumers value the 2nd unit of that good at $10 means that she will buy the 2nd unit only if its price is less than or equal to $10.

The moderate income consumers value 1st unit of good at $12 which means that she will buy the 1st unit of that good only if its price is less than or equal to $12.

Now according to the question, the number of wealthy consumers is 100 and moderate income consumers is also 100. And AC = MC = 6.

1) No price discrimination    (One unit sell for $15)

For this price, the wealthy consumes will only buy the good. And they will buy only 1 unit of it.

a) Total revenue = (No. of consumers buying it) * (Price of the good)

                          = 100 * 15

                          = 1500

b) Total cost = 6 *100

                  = 600

c) Producer Surplus(profit) = Total revenue – Total cost

                                            = 1500 – 600

                                             = 700

d) The Consumer Surplus is the difference between the price that consumers pay and the price that they are willing to pay. In this case which is zero(0) because they are paying $15 and they are willing to pay $15.

e) Total Surplus = Producer Surplus + Consumer Surplus

                         = 700

2) No price discrimination    (One unit sell for $12)

In this case both the types of consumers will buy 1st unit of the good.

a) Total revenue = (No. of consumers buying it) * (Price of the good)

                          = 200 * 12

                          = 2400

b) Total cost = 6 *200

                  = 1200

c) Producer Surplus(profit) = Total revenue – Total cost

                                            = 2400 – 1200

                                             = 1200

d) The Consumer Surplus = (15 – 12)*100

                                          =300

e) Total Surplus = Producer Surplus + Consumer Surplus

                         = 1200 + 300

                         = 1500

3) No price discrimination    (One unit sell for $10)

In this case the wealthy consumers will buy 2 units of the good and the moderate income consumers will buy 1 unit of that good

a) Total revenue = (No. of consumers buying it) * (Price of the good)

                          = 200 * 10 + 100*10

                          = 3000

b) Total cost = 6 *300

                  = 1800

c) Producer Surplus(profit) = Total revenue – Total cost

                                            = 3000 – 1800

                                             = 1200

d) The Consumer Surplus = (15 – 10)*100 + (12 – 10)*100

                                          =500 + 200

                                          =700

e) Total Surplus = Producer Surplus + Consumer Surplus

                         = 1200 + 700

                         = 1900

4) 2nd Degree Price Discrimination

Package A : 1 unit for $12

Package B : 1 unit for $20

Now Package A is affordable for both the types of consumers. But wealthy consumers will not buy Package A because Package B is optimal for them since they are getting 2 units of the good.

a) Total revenue = (No. of consumers buying it) * (Price of the good)

                          = 20*100 + 12*100

                          = 3200

b) Total cost = 6 *200 + 6*100

                  = 1800

c) Producer Surplus(profit) = Total revenue - Total cost

                                            = 3200 – 1800

                                             = 1400

d) The Consumer Surplus will only be for wealthy consumers.

Total willingness to pay = 15 +10 = $25 and they are paying $20

Consumer Surplus = (25 – 20)*100

                                   = 500

e) Total Surplus = Producer Surplus + Consumer Surplus

                         = 1400 + 500

                         = 1900

5) The producer offers a quantity discount to discriminate between the two types of consumers. And there by extracting some of their consumer surplus and thus increasing its own producer surplus(profit).