Question

Consider the cost function C(Q) = 400 + 5Q^2 for Google to produce its new Phone. Using that cost function for the Phone, determine the profit-maximizing output, price and profit (or loss) for the Google Phone, and discuss its long-run implications, under three alternative scenarios:

a.Google Phone is a perfect substitute with a similar product offered by Apple, Samsung and several other Phones that have similar cost functions and that currently sell for $400 each.

b. Google Phone has no substitutes and so is a monopolist, and the demand for the Google Phone is expected to forever be Q = 22 – (1/6)P – note you use the earlier listed cost function.

c. Google Phone currently has no substitutes, and currently the demand for the Google Phone is Q = 80 – (1/5)P, but Google anticipates other firms can develop close substitutes in the future. – note you use the earlier listed cost function.

Answer 1

(a)

Given that Google phones have perfect substitutes, thus, price P = 400.

Given the cost function, profit is given by:

Profit = P. Q - C(Q)

= 400Q - (400 + 5Q^2)

Profit is maximized at the point where MR = MC which gives 400 = 10Q

thus, Q = 40, P = 400, total cost = 8400, total revenue = 16000 and profit = 7600.

(b)

If Google phones is a monopolist, then profit is given by:

Profit = P.Q - C(Q)

= (132 - 6Q)Q - (400 + 5Q^2) which is maximized at MR = MC

this gives: 132 - 12Q = 10Q thus Q = 6, P = 96, profit = (576 - 580) = -4 (loss)

(c)

Profit = TR - TC

= (400 - 5Q)Q - (400 + 5Q^2)

which is maximised at Q = 20, P = 300, Profit = 3600.