A firm offers two differentiated products, X and Y and faces two types of consumers, types A and B. There are equal numbers of each type of consumers ¡V so, for simplicity, assume there is just one of each type. The valuations of the two types of customers of the two products are summarized in the table below. Assume (for simplicity) that the marginal cost of manufacture of X and Y is identical, constant and equal to zero:

Customers
& Products X-cheapticket Y-VIPticket
Type A 10 15
Type B 12 25

(a)If the firm offers good X for a price of 11 and good Y for a price of 26, which (if any) product will each consumer type buy (if she only wants to buy one)?

(b)If the firm offers good X for a price of 9 and good Y for a price of 24, which (if any) product will each consumer type buy (if she only wants to buy one)?

(c)Calculate the profits earned by the firm on each of the set of prices in parts (a) ¡V (b). Can you propose prices for X and Y to achieve higher profits?

(d)How does the consumer surplus for Type B on good X limit the price that can be set for good Y (to get Type B to select good Y)? Is there a positive or negative relationship between the price on good X and the price that can be charged on good Y? Why (if we want both consumers to purchase a good) does this imply that the price on good X should be set leaving Type A with zero consumer surplus?

I'm guessing you tried to cut-and-paste a table. Alas, you made need to type in all the info.

To determine which product each consumer type will buy, we need to compare the valuations of the products with the prices being offered by the firm.

(a) If the firm offers good X for a price of 11 and good Y for a price of 26, we compare the valuations of each consumer type with the respective prices:

- For Type A:
- Valuation of X: 10
- Valuation of Y: 15
Since the price of X (11) is lower than its valuation (10), Type A will select good X.

- For Type B:
- Valuation of X: 12
- Valuation of Y: 25
Since the price of X (11) is lower than its valuation (12) and the price of Y (26) is higher than its valuation (25), Type B will select good X.

Therefore, Type A will buy good X and Type B will also buy good X.

(b) If the firm offers good X for a price of 9 and good Y for a price of 24, we repeat the same comparison:

- For Type A:
- Valuation of X: 10
- Valuation of Y: 15
Since the price of X (9) is lower than its valuation (10), Type A will select good X.

- For Type B:
- Valuation of X: 12
- Valuation of Y: 25
Since the price of X (9) is lower than its valuation (12) and the price of Y (24) is lower than its valuation (25), Type B will select good Y.

Therefore, Type A will buy good X and Type B will buy good Y.

Now let's move on to calculating the profits earned by the firm on each set of prices:

(a) At prices of X = 11 and Y = 26:
- Number of Type A customers buying X = 1
- Number of Type B customers buying X = 1
- Total revenue = (price of X * Number of Type A customers) + (price of X * Number of Type B customers) = (11 * 1) + (11 * 1)
- Total revenue = 22

(b) At prices of X = 9 and Y = 24:
- Number of Type A customers buying X = 1
- Number of Type B customers buying Y = 1
- Total revenue = (price of X * Number of Type A customers) + (price of Y * Number of Type B customers) = (9 * 1) + (24 * 1)
- Total revenue = 33

To achieve higher profits, the firm needs to set prices such that more customers choose to buy their goods. Based on the previous calculations, it seems that setting a lower price for X (9) and a higher price for Y (24) resulted in higher total revenue and thus higher profits. However, further analysis is needed to find the optimal prices that maximize profits.

The consumer surplus for Type B on good X limits the price that can be set for good Y. Consumer surplus is the difference between the valuation of a good and the price paid. If the price of Y is too high, Type B will choose to buy X instead, as X provides a higher consumer surplus for them.

The relationship between the price on good X and the price that can be charged on good Y is negative. As the price of X decreases (assuming the valuations remain constant), the consumer surplus for Type B on good X increases, making them more likely to choose X over Y. To incentivize Type B to select Y, the price of Y needs to be lower than the potential consumer surplus for Type B on X.

To ensure that Type A has zero consumer surplus, the price on good X should be set equal to or slightly higher than their valuation. This reduces their incentive to switch to an alternative, resulting in higher profits for the firm.