Economics - Monopoly?

Question

Assume there are only two producers of tennis rackets: Wilson and Prince. The market demand for tennis rackets is depicted by the algebraic formula P = 100 - Q, where P stands for price and Q stands for quantity of rackets. If the market were monopolized, the resulting formula for the monopolist's marginal revenue would be MR = 100 - 2Q, where MR stands for marginal revenue. Assume that both producers face a constant marginal cost of $40 and that there are no fixed costs.

3.1. If Wilson and Prince form a cartel and each agrees to produce one half of the monopolist's profit-maximizing output, how many rackets would each manufacturer produce?

Answer 1

P=100-Q

TR=P*Q=100Q-Q^2

MR=100-2Q

MC=40

MR=MC

100-2Q=40

60=2Q

Q=30

P=100-30=70

TR=P*Q=70*30=2100

TC=40*Q=40*30=1200

Profit=TC-TR=2100-1200=900

Total rackets produced=30

Each produces=30/2=15

Answer: Each produces 15 rackets

Answer 2

In Economics, monopoly (also "Pure oligopoly") exists when a specific individual or enterprise has sufficient control over a particular product or service to determine significantly the terms on which other individuals shall have access to it.  Monopolies are thus characterized by a lack of economic competition for the good or service that they provide and a lack of viable substitute goods.  Alternatively (a modern and less common usage), it may be used as a verb or adjective to refer to the process  by which a firm gains persistently greater market share than what is expected under perfect competition. The latter usage of the term is invoked in the theory of monopolistic competition.

Answer 3

i thought you meant monopoly the board game. ha ha

Answer 4

If they form a cartel, then a new company will come in and figure out how to produce tennis rackets at a lower cost.  That would force Wilson and Prince to lower their prices to stay in business.  There is always competition, even in other forms.  For example, if the price of tennis rackets was higher than people were willing to pay, they would find a new recreational activity instead.  Sure, there will still be the rich, faithful people who will play tennis, but Prince and Wilson wouldn't be making money that way.  

On another note, cartels don't really stay together long because companies are known to try to out-compete the other members of the cartel.  If Wilson and Prince agreed to sell rackets at exactly the same price and not try to out-perform the other company, why wouldn't they just merge into one company in the first place?  Really, it's just a way to try to convince the other to keep their prices artificially higher so that you can stay in business and compete with them.  Not really a good thing for the consumer.

Answer 5

Each would produce 15 rackets