Let Q be the number of printer-computer combinations sold in the market and let MC of both these products equal $0.Let the demand for both the products be given as Q = 12 - (P_p + P_c),where P_p and P_c are the prices of printers and computers.What are the profits of each firm when they decide to cooperate,and what happens if they decide to go alone?

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Quizplus · Accepted Answer

The Answer is First,if they decide to cooperate,then the total demand is taken as given and one price is set for the combined product.Thus,the demand curve becomes: Q = 12 - P and inverting this we get:
P = 12 - Q and therefore MR = 12 − 2 Q.If MR = MC,then 12 − 2 Q = 0 and hence Q = 6 units.
This means P = 12 − 6 = $6.Therefore,the revenue from this is $6 x 6 = $36.Now if they decide to go alone,then each firm will set its MR = MC.Then we have the following:
P_c = 12 − P_p − Q and hence its MR_c = 12 − P_p− 2 Q.Likewise for the other company we have,
P_p = 12 − P_c − Q and hence its MR_p = 12 − P_c − 2 Q.
Setting MR_c = MR_p we find P_p = P_c.
Therefore Q = 12 − 2 P_p.So for the printer company,we have
MR_p = 12 − P_p − 2 (12 − 2 P_p)or
MR_p = 12 − P_p − 24 + 4 P_p or
MR_p = − 12 + 3 P_p_.
Setting this equal to MC = $0,we get P_p = $4 = P_c_.
Hence,Q = 12 − 8 = 4 units.
Therefore,the combined revenue is $4 x 4 = $16.
It is better to cooperate and offer combined products.

Let Q Be the Number of Printer-Computer Combinations Sold in the Market