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.

Example Price is p(y)=120-2y, this implies marginal revenue is Total cost is c(y)=y 2. This implies marginal cost is What is the monopoly’s choice of y (mr=mc) and profits? What is the competitive equilibrium y (price=mc) and firms profits? Why is a monopoly inefficient? Someone values a good above its marginal cost. 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 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: “Natural Monopoly”. Such as when at competitive price is below average cost. (I like two firms cannot make a profit no matter what price is set, but one firm can.)

Patents A patent is a monopoly right granted to an inventor. It lasts about 17 years. For the government: there is a trade-off between –loss due to monopoly rights. –incentive to innovate. For the company –Must decide between patent and trade secret. –Minus side of patent is that it expires and is no longer secret (competitors can perhaps go around it). –Minus side of trade secret is that there is no legal protection, but lasts forever. For example, Coca Cola. –Strategy – protective, delay or shelve? License (temporarily remove competition).

24.06 Natural Monopoly where a firm cannot make a profit with competitive pricing.

Natural Monopoly Take C(y)=1+y 2. P(y)=3-y. Notice the c entails a fixed cost of 1. Where does p=mc (mc is 2y)? What is profits at this point for a single firm that meets the whole demand? What happens when another firm enters? They can’t charge a price close to competitive equilibrium and survive. Monopoly (mr=3-2y)? Y=3/4. If two firms try to split this output, they still lose money. (Actually, two firms that split output can do better than this by setting Y=1. Why?) Do they still lose money? Government should allow a monopoly but force a price cap. What should happen if C(y)=1.1+y 2 ? C(y)=1.6+y 2 ? The last has demand below average cost.

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.