Computer monitors and computer processors are perfect compliments with a market

Question

Computer monitors and computer processors are perfect compliments with a market demand of Q=500-Pmonitor-Pproccessor. Currently two companies produce each of the goods separately at a marginal cost of 10 each. That is the marginal cost of an additional processor and monitor combo is 20.

i) Given this circumstance derive the individual demand curves each producer faces for their respective good. [Hint: write the Qmonitors as a function of both the monitor and processor price].

ii) Given the marginal cost of 10 and this demand curve solve for the optimal price for each good as a function of the others price. [That is for the company that produces monitors take the FOC with respect to the price of monitors and solve].

iii) Solve for the equilibrium price of the monitor and processor. [Hint: This is the same issue of plugging in the optimal pricing function for one good and solving for another]. iv) Given these prices solve for the total price and equilibrium quantity of monitors/processors.

v) Now suppose the companies were to merge and the company produced a monitor/processor bundle at a marginal cost of 20. What is the equilibrium price and quantity sold of this bundle.

vi) Suppose instead of a merger that the market for monitors was perfectly competitive. That is monitors are sold at a price of $10. What is the computer processors price and what is the equilibrium quantity of monitors and processors sold?

Explanation / Answer

a)The individual demand curve each producer faces is Q=Pmonitor- Pprocessor.

b)First solve for the company that produces monitors take the FOC with respect to the price of monitor.Taking FOC,we get optimal price which is equal to 1.

C) Equilibrium price of monitor and processor is equal to 1.

d) Equilibrium quantity will be equal to 498 and equilibrium price is equal to 1.

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