ECON 330 Lecture 10.5 Tuesday, October 23

No new material, a small number of workouts (math)

So far we did… The competitive model The monopoly equilibrium, the DWL. The equilibrium of the dominant firm Price elasticity of demand, Consumer Surplus,

What is coming after the Bayram break Model of Oligopoly Cournot Bertrand Stackelberg NASH equilibrium, some game theory One time versus repeated interaction in oligopoly models.

HWK#2, second question

A monopolist has AC = MC = c A monopolist has AC = MC = c. The market demand is Q = P–e, where e > 1. The price elasticity of demand is constant for all prices and is equal to –e. Compute the increase in the monopoly price if the marginal cost is increased by one dollar. How does the answer depend on the value of e?

Use the formula

Here comes the first question…

Consider a market with 9 firms Consider a market with 9 firms. All firms use the same production technology and have the following cost function c(q) = 0.5q2. The market demand is given by Q(p) = 10 – p.

For all 9 firms the cost function is c(q) = 0. 5q2 For all 9 firms the cost function is c(q) = 0.5q2. The market demand is Q(p) = 10 – p. Compute the competitive equilibrium (price, quantity, consumer surplus, producer surplus, etc).

The cost function is c(q) = 0.5q2. The market demand is Q(p) = 10 – p. Now suppose one of these firms is not happy with competitive behavior (take market price as given and assume you can sell any quantity at that price) and decides to try price setting behavior instead. The remaining 8 firms continue to behave competitively. In this new scenario the experimenting firm sets the price, given that price the other firms choose their quantities to max their profit. (You can say that the experimenting firm behaves like a dominant firm.)

The cost function is c(q) = 0.5q2. The market demand is Q(p) = 10 – p. What price will the price setting firm set? (Its goal is profit maximization.) Compute the price elasticity of the residual demand at the profit maximizing price

Now consider the slightly more realistic situation Now consider the slightly more realistic situation. A dominant firm is created by the merger of 5 firms. The remaining 4 firms remain independent. It can be shown that the marginal cost of the dominant firm is MC(q) = q/5.

The cost function is c(q) = 0.5q2. The market demand is Q(p) = 10 – p. Compute the profit maximizing price for the dominant firm. Show that the members of the dominant firm make less profit than the independent firms.

After this… You should to be able to do the following mathematical ….

A market with two identical firms. The cost function is c(q) = 0.1q2+q. The market demand is Q = 14 –2P. A. Compute the competitive equilibrium price quantity profits etc. B. One of the firms behaves like a dominant firm, sets the price, the other behaves competitively. Compute equilibrium price quantity profits etc. C. The two firms collude and form a single firm that becomes a monopoly. The marginal cost function for the monopoly is 0.1q+0.5. Compute the monopoly equilibrium price quantity profits etc.

Next question

The market demand is Q = 20 –2P The market demand is Q = 20 –2P. We will consider two scenarios: A monopoly, and a dominant firm. A. There is a monopoly firm with MC = 2.   B. There is a dominant firm with MC = 2, and a group of small firms with MC = 4 and a total capacity of K = 2.

Compute the monopoly equilibrium price, quantity, CS, and PS. Compute the dominant firm equilibrium price, quantity, CS, and PS.

Under which market structure is the DWL larger? Comment.  For scenario B compare the true DWL to the estimated DWL with the Harberger and the Cowling & Mueller methods.