Question

Consider the cost function C(Q) = 25000 + Q2 (or MC= 2Q) for Apple Inc. to produce the iPhone. Note that the company has fixed costs of $25,000. Also, the demand for Apple’s iPhone is given by P = 400 - 3Q (and its MR = 400 - 6Q).

Using that cost function for the iPhone, determine the profit maximizing output and price for the iPhone as well as profits, and discuss its long-run implications, under three alternative scenarios. (Hint: Use Hand-written Class Notes to answer these questions.)

a. Apple’s iPhone is a perfect substitute with the Motorola Droid and several other smart phones that have similar cost functions and that currently sell for $200 each (as in perfect competition model). Should the company stay in business in the long-run?

b. Apple’s iPhone has no substitutes and so is a monopolist, and the demand for the iPhone is expected to forever be P = 400 - 3Q (or Q = 133.33 – (1/3)P) (as in monopoly) Should the company stay in business in the long-run?

c. Apple’s iPhone currently has no substitutes, and currently the demand for the iPhone is P = 400 - 3Q (or Q = 133.33 – (1/3)P), but Apple anticipates other firms to produce close substitutes in the future (as in monopolistic competition in the future) Should the company stay in business in the long-run?

d. If it operates in an oligopolistic market, how can Apple use price and non-price strategies (methods of competition) to compete effectively in the smart-phone market? (No need for calculations)

Answer 1

Consider TC=25000+25000+2Q=50000+2Q

TR=P*Q=(400-3Q)Q= 400Q-3Q^2

Now to have profit maximising output, MR=MC and MR'<=MC'

thus, 2Q=400-6Q

thus Q=50.

output is 50 units.

Now At Q=50,To find wether this output is profit maximising price let us first calculate MR' and MC'

MR'=-6 and MC'=2

thus MC'>=MR'

Thus this is profit maximising output.

Now price assosciated with Q=50 is

P=400-3(50)....Resubstituting Q=50 in DD equation

P=250$

Profit maximising price is 250$

Totalprofit is TC-TR=50000+100-(400*50)+(3*2500)

Profit = 50100-(20000+7500)

Profit= 50100-27500

At Profit maximising output and price Profit=22500$

Under long Run,

1) Motorola phones that are sold at 200$ currently in longrun would have higher demand as the price is quite low than Apples 250$. Thus DD for Apple I phones might decrease in longrun qwing to the fact that Motorola phones are their perfect substitutes at ceteris paribus.Apple should not stay in business for longrun.

2) If apple is momnopolist,surely they can stay in business for long run.As their dd is not changing.But that is quite a hypothetical situation to be.

3)Though the rival firms in monopolistic competetion decide to produce the close substitutes still they will not be perfect substitutes.Thus Being differentiated products, Aplle still ahs a chance to capturre the market.And can surely be in the business for long run.

4)One best way is to set their price after the rival firms set their price assuming constant output.But this is quite unrealistic(Cournots duopoly model).Thus apple should assume rivals will have constant price and determine its own price and focus on changing output at that price acording to Edgeworths model in oligopoly.It is relatively stable to Bertrands model.