Monopoly Standard Profit Maximization is max r(y)-c(y). With Monopoly this is Max p(y)y-c(y) (the difference to competition is price now depends upon output). FOC yields p(y)+p’(y)y=c’(y). This is also Marginal Revenue=Marginal Cost. This equals p(y)*(1-1/¦ε¦)=c’(y) remember ε=(dy/dp)*(p/y) Notice there is a problem unless ¦ε¦>1.

Example Price is p(y)=120-2y Cost is c(y)=y 2 Profit is p(y)*y-c(y) what is choice of y? What is the competitive equilibrium y? Why is a monopoly inefficient? In a diagram, what is the welfare loss?

Rule of thumb prices Many shops use a rule of thumb to determine prices. Clothing stores may set price double their costs. Restaurants set menu prices roughly 4 times costs. Can this ever be optimal? If q=Ap є what is elasticity? What is price if marginal cost is constant?

Why Monopolies? What causes monopolies? –a legal fiat; e.g. US Postal Service –a patent; e.g. a new drug –sole ownership of a resource; e.g. a toll highway –formation of a cartel/collusion; e.g. OPEC –large economies of scale; e.g. local utility companies.

Patents A patent is a monopoly right granted to an inventor. It lasts about 17 years. There is a trade-off between –loss due to monopoly rights –incentive to innovate.

Natural Monopoly When is a monopoly natural such as in certain public utilities? C(y)=1+y2. P(y)=3-y. Where does p=mc? What is profits at this point for one firm? What happens when another firm enters?

Taxes What happens to the monopoly’s choice under a profit tax? What happens under a quantity tax? –This shifts up the supply/marginal cost curve. –The monopolist chooses where MR=MC so the quantity is reduced. –Consequently, welfare is lower.

Oligopoly A monopoly is when there is only one firm. An oligopoly is when there is a limited number of firms where each firm’s decisions influence the profits of the other firms. We can model the competition between the firms price and quantity, simultaneously sequentially.

Quantity competition (Cournot 1838) Л1=p(q1+q2)q1-c(q1) Л2= p(q1+q2)q2-c(q2) Firm 1 chooses quantity q1 while firm 2 chooses quantity q2. Say these are chosen simultaneously. An equilibrium is where –Firm 1’s choice of q1 is optimal given q2. –Firm 2’s choice of q2 is optimal given q1. If D(p)=4-p and c(q)=q, what the equilibrium quantities and prices. –Take FOCs and solve simultaneous equations. –Can also use intersection of reaction curves.

Quantity competition (Stackelberg 1934) Л1=p(q1+q2)q1-c(q1) Л2= p(q1+q2)q2-c(q2) Firm 1 chooses quantity q1. AFTERWARDS, firm 2 chooses quantity q2. An equilibrium now is where –Firm 2’s choice of q2 is optimal given q1. –Firm 1’s choice of q1 is optimal given q2(q1). –That is, firm 1 takes into account the reaction of firm 2 to his decision.

Stackelberg solution If D(p)=4-p and c(q)=q, what the equilibrium quantities and prices. Must first solve for firm 2’s decision given q1. –Max q2 [(4-q1-q2)-1]q2 Must then use this solution to solve for firm 1’s decision given q2(q1) (this is a function!) –Max q1 [4-q1-q2(q1)-1]q1

Bertrand (1883) price competition. Both firms choose prices simultaneously and have constant marginal cost c. Firm one chooses p1. Firm two chooses p2. Consumers buy from the lowest price firm. (If p1=p2, each firm gets half the consumers.) An equilibrium is a choice of prices p1 and p2 such that –firm 1 wouldn’t want to change his price given p2. –firm 2 wouldn’t want to change her price given p1.

Bertrand Equilibrium Take firm 1’s decision if p2 is strictly bigger than c: –If he sets p1>p2, then he earns 0. –If he sets p1=p2, then he earns 1/2*D(p2)*(p2-c). –If he sets p1 such that c<p1<p2 he earns D(p1)*(p1-c). For a large enough p1<p2, we have: –D(p1)*(p1-c)>1/2*D(p2)*(p2-c). Each has incentive to slightly undercut the other. Equilibrium is that both firms charge p1=p2=c. Not so famous Kaplan & Wettstein (2000) paper shows that there may be other equilibria with positive profits if there aren’t restrictions on D(p).

Collusion If firms get together to set prices or limit quantities what would they choose. D(p)=4-p and c(q)=q. Quantity Max q1,q2 (4-q1-q2-1)*(q1+q2). Price Max p (p-1)*(4-p) This is the monopoly price and quantity! Show all 4 possibilities (Cournot, Bertrand, Collusion, Stackelberg) on the q1, q2 graph?

Anti-competitive practices. In the 80’s, Crazy Eddie said that he will beat any price since he is insane. Today, many companies have price-beating and price-matching policies. They seem very much in favor of competition: consumers are able to get the lower price. In fact, they are not. By having such a policy a stores avoid loosing customers and thus are able to charge a high initial price (yet another paper by this Kaplan guy).