Your computer needs an operating system (OS; price p1) and application software (App; price p2). The demand for the combination is given by Q = 600 – 20P, where P = P1 + P2. The marginal costs are zero.
- Find the optimal price and quantity if the OS and App are provided by separate firms.
- Find the optimal price and quantity if the OS and App are provided by a single integrated firm.
The price of the operating system is given by P1 and the price of the application software is P2. The demand for both of them is given by Q = 600 - 20*P with P = (P1 + P2) with the marginal costs being zero.
The utility of the two is given by 600*P - 20P^2. The marginal utility is 600 - 40*P.
The optimal price and quantity can be determined when the marginal utility of the consumer falls to 0.
If the operating system and application software are provided by separate firms, both the firms would like to have as large a portion of P as possible. The When the marginal utility is 0, 600 - 40P = 0 or P = 15. At P = 15, the consumer can buy 300 units of software. The allocation is optimal when the consumer buys 150 units at $15 of each software.
If a single firm is providing both the software, the consumer is free to buy 300 units of either the operating system or the application software at $15 each.