Question

Intel and Advanced Micro Devices (AMD) are the only two firms that produce central processing units (CPUs), which are the "brains" of computers. While the CPUs produced by the two firms are similar, they are not identical - they are imperfect substitutes for each other (they are differentiated products). As such, they face different inverse demand functions:

p
A
​
=197−15.1q
A
​
−0.3q
I
​

p
I
​
=490−10q
I
​
−6q
A
​

​
where p
A
​
is the price charged by AMD, p
I
​
is the price charged by Intel, q
A
​
is the output of AMD, and q
I
​
is the output of Intel. Each firm faces constant marginal costs of c=40. (a) Determine each firm's best response function. (b) Use the best response functions to solve for the Cournot-Nash equilibrium quantities and prices.

Answer 1

(a) AMD's best response function: q_A = (1/2)(157 - 0.9q_I)

Intel's best response function: q_I = (1/2)(246 - 3q_A)

(b) Cournot-Nash equilibrium quantities and prices:

Equilibrium quantity for AMD (q_A): 64 units

Equilibrium quantity for Intel (q_I): 99 units

Equilibrium price for AMD (p_A): $119.85

Equilibrium price for Intel (p_I): $192.05

Step-by-step explanation:

(a) The best response functions are derived by maximizing the profit function for each firm with respect to its output, considering the output level chosen by the other firm. The best response function for AMD is q_A = (1/2)(157 - 0.9*q_I), and for Intel, it is q_I = (1/2)(246 - 3q_A).

(b) To find the Cournot-Nash equilibrium, we set the two best response functions equal to each other and solve for the equilibrium quantities. By substituting these quantities into the inverse demand functions, we determine the equilibrium prices.

In this case, the Cournot-Nash equilibrium quantities are q_A = 64 units and q_I = 99 units. The corresponding equilibrium prices are p_A = $119.85 and p_I = $192.05.

These quantities and prices represent the output levels and prices at which both firms maximize their profits given the strategic interaction in the market.