Intel and AMD, the primary producers of computer central
processing units (CPUs), compete with one another in the mid-range chip
category (among other categories). Assume that global demand for mid-range
chips depends on the quantity that the two firms make, so that the price (in
dollars) for mid-range chips is given by and where the quantities
are measured in millions. Each midrange chip costs Intel $60 to produce. AMD’s
production process is more streamlined; each chip costs them only $48 to
(a) Write the profit function for each firm in terms of qIntel
and qAMD. Find each firm’s best-response rule.
(b) Find the Nash equilibrium price, quantity, and profit
for each firm.
(c) (Optional) Suppose Intel acquires AMD, so that it now
has two separate divisions with two different production costs. The merged firm
wishes to maximize total profits from the two divisions. How many chips should each
division produce? What is the market price and the total profit to the firm?