How would the Intel-AMD equilibrium in the Solved Problem 13.2 change if AMD fac

Question

How would the Intel-AMD equilibrium in the Solved Problem 13.2 change if AMD faced the same demand function as Intel? Intel and Advanced Micro Devices (AMD) are the only two firms that produce central processing units (CPUs), which are the brains of personal computers. Both because the products differ physically and because Intel's advertising "Intel Inside" campaign has cvinced some consumers of its superiority, consumers view the CPUs as imperfect substitutes. Consequently, the two firms inverse demand functions differ PA 490-104A-q and Pi 490-10q 6qA where price is dollars per CPU, quantity is millions of CPUs, the subscrip ndicates Intel, and the subscript A represents AMD. Each firm faces a constant marginal cost of m- $165 per unit. (For simplicity, we will assume there are no fixed costs.) Solve for the Cournot equilibrium quantities and prices. The Cournot equilibrium quantities are Amillion CPUs and million CPUs. (Enter numeric responses using real numbers rounded to two decimal places.)

Explanation / Answer

Inverse demand functions:

PA=490-10qA-6qI

PI=490-10qI-6qA

Two identical firms, as both produces CPU – AMD produces qA and Intel produces qI.

Therefore, q1 + q2 = Q

Marginal Cost= $165

Profit maximising condition for a firm, MC = MR

Rewriting inverse demand function:

P=490-10(qA+qI)-6(qA+qI)

P= 490-16qA-16qI

Total Revenue:

AMD: 490qA-16qA2-16qAqI

Intel: 490qI-16qAqI-16qI2

Marginal Revenue:

AMD:(490-16qI)-32qA

Intel: (490-16qA)-32qI

Profit maximisation :

AMD: (490-16qI)-32qA = 165

(1) 32qA+16qI= 325

Intel: (490-16qA)-32qI = 165

(2) 16qA+32qI= 325

By, Solving equation (1) and (2), we get the cournot equilibrium quantities:

qA=6.77 million CPUs

qI= 6.77 million CPUs

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