Computronium Interactive (CI)'s business model is to rent out computing time on its super computers CI has two types of potential customers of equal number 10 aca demic and 10 business clients CI charges each customer a monthly subscription fee F in exchange for the right to purchase any amount of computing time at a usage fee of P cents per second of computing time Each academic customer has the demand function QA 8 PA, where PA is the usage fee that academic institutions are charged each business customer has the demand QB 10PB, where PB is the usage fee that business institutions are charged The quantities QA and QB are measured in millions of seconds per month The marginal cost to CI of additional computing time is constant at 2 cents per second, and CI has no fixed cost (a)(5 marks) First, suppose that CI can distinguish between academic and business customers and can successfully charge them different usage fees PA and PB but the subscription fees for both types are fixed to zero (i e FA FB 0) What usage fees PA and PB would maximise CI's profits What would its profits be in this case (b)(6 marks) Now consider the same situation as in part (a) but without the assumption that the subscription fees FA and FB have to be zero So now CI can set different, potentially positive subscription fees for each customer type What subscription fees FA and FB and what usage fees PA and PB should CI charge each group to maximise its profits What would its profits be in this case (c)(7 marks) For this part and the next, suppose instead that CI cannot distinguish between the two types of consumers and cannot successfully price discriminate i e CI has to charge the same subscription fee F and usage fee P to both types of customers What usage fee P would maximise CI's profits if F 0 What would its profits be in this case (d)(7 marks) Now consider the same situation as in part (c) but without the assumption that the subscription fee F has to be zero If P 2, what subscription fee F should CI charge to maximise its profits What would its profits be in this case

The Answer is in the image, click to view ...

Answered step by step

Verified Expert Solution

Link Copied!

Question

1 Approved Answer

Posted on Jun 23, 2024

Computronium Interactive (CI)'s business model is to rent out computing time on its super computers. CI has two types of potential customers of equal number:

Computronium Interactive (CI)'s business model is to rent out computing time on its super computers. CI has two types of potential customers of equal number: 10 aca- demic and 10 business clients. CI charges each customer a monthly subscription fee F in exchange for the right to purchase any amount of computing time at a usage fee of P cents per second of computing time. Each academic customer has the demand function QA = 8 PA, where PA is the usage fee that academic institutions are charged; each business customer has the demand QB = 10PB, where PB is the usage fee that business institutions are charged. The quantities QA and QB are measured in millions of seconds per month. The marginal cost to CI of additional computing time is constant at 2 cents per second, and CI has no fixed cost.

(a)(5 marks) First, suppose that CI can distinguish between academic and business customers and can successfully charge them different usage fees PA and PB but the subscription fees for both types are fixed to zero (i.e. FA = FB = 0). What usage fees PA and PB would maximise CI's profits? What would its profits be in this case?
(b)(6 marks) Now consider the same situation as in part (a) but without the assumption that the subscription fees FA and FB have to be zero. So now CI can set different, potentially positive subscription fees for each customer type. What subscription fees FA and FB and what usage fees PA and PB should CI charge each group to maximise its profits? What would its profits be in this case?
(c)(7 marks) For this part and the next, suppose instead that CI cannot distinguish between the two types of consumers and cannot successfully price discriminate: i.e. CI has to charge the same subscription fee F and usage fee P to both types of customers. What usage fee P would maximise CI's profits if F = 0? What would its profits be in this case?
(d)(7 marks) Now consider the same situation as in part (c) but without the assumption that the subscription fee F has to be zero. If P = 2, what subscription fee F should CI charge to maximise its profits? What would its profits be in this case?