Optimal Pricing Strategy and Associated Profit

To determine the optimal pricing strategy for Adobe’s Photoshop software and the associated profit, we need to consider the values of both household users and graphic designers for the different versions of the software: Full Version (CMYK colors) and Discount Version.

Let’s denote the prices as follows:

• Full Version price: $P_F
• Discount Version price: $P_D

And the values for each customer segment are:

• Value of Full Version for Household User: $339
• Value of Discount Version for Household User: $300
• Value of Full Version for Graphic Designer: $600
• Value of Discount Version for Graphic Designer: $400

For the optimal pricing strategy, Adobe should set prices that maximize its total profit. We can approach this by comparing the profits generated from each customer segment and version of the software. Since the marginal cost of production is $0, profit is equal to revenue.

Household Users:

For the Household User segment, the optimal pricing strategy is to offer the Discount Version at a price lower than the value they place on it. This means:

$P_D ≤ $339

If we set $P_D = $300, Adobe’s profit from Household Users for the Discount Version would be: Profit = Number of Household Users × (Value of Discount Version – Cost) = 1 × ($300 – $0) = $300

Graphic Designers:

For the Graphic Designer segment, the optimal pricing strategy depends on whether Adobe can capture the higher value they place on the Full Version.

If Adobe charges $600 for the Full Version, the profit from Graphic Designers for the Full Version would be: Profit = Number of Graphic Designers × (Value of Full Version – Cost) = 1 × ($600 – $0) = $600

However, if Adobe charges $400 for the Discount Version, it can capture more graphic designers as customers: Profit = Number of Graphic Designers × (Value of Discount Version – Cost) = 1 × ($400 – $0) = $400

Conclusion:

In this case, the optimal pricing strategy is as follows:

• Charge Household Users $300 for the Discount Version, resulting in a profit of $300.
• Charge Graphic Designers $400 for the Discount Version, resulting in a profit of $400.

The total profit for Adobe would be $300 + $400 = $700.

Part 2: Largest Value $X for Price Discrimination

Price discrimination involves charging different prices to different customer segments based on their willingness to pay. To implement price discrimination, Adobe would need to set prices such that the more price-sensitive segment (Household Users) pays a lower price compared to the less price-sensitive segment (Graphic Designers).

The largest value $X can take while still implementing price discrimination can be determined by setting the price of the Discount Version for Household Users at $X, while ensuring that it’s lower than the value they place on it:

$X ≤ $339

This ensures that price discrimination is maintained, where Household Users pay less than Graphic Designers for the same version of the software. For example, if Adobe sets $X = $250, price discrimination would still be maintained, as Household Users pay $250 while Graphic Designers pay $400 for the Discount Version.

In summary, the largest value $X can take is $339, which is the value that maintains the distinction between the pricing for Household Users and Graphic Designers, allowing Adobe to implement price discrimination.