Week 13

Managerial Economics

Order of Business

• Homework

• Assigned Lectures

• Other Material

• Lectures for Next Week

Homework-Last Week

Pashigian, Chapter 10, Exercise 3

Since marginal cost is zero, I assume each firm can produce the entire market demand. This sounds to me like a "winner take all bidding situation". The demand curve for firm A for instance would be equal to zero when its price was above that of firm B, and equal to 60-P when its price was below B's. That means a Nash Equilibrium at a price of zero, with the firms splitting the market of 60; each firm would produce 30. Each firm then loses $50, assuming fixed costs of $50. If the firms merged, they would act like a monopoly and force the price to 30, and market demand to 30.

Now suppose you were working with the FTC. If the merger does not go through, neither firm will stay in the business. No consumer surplus will be generated. But if the merger goes through, there will be consumer and producer surplus generated. Thus I would support the merger as the lesser of two evils.

Pashigian, Chapter 10, Exercise 4

If they build plants of fixed and limited production capacity, then they can effectively prohibit their customer from employing a winner take all strategy against them. For example, suppose the competitive solution would have production of 20 units and the monopoly solution would have production of 10 units. If each builds a plant capable of producing 5 units, then they cannot be subject to a price war. Between them, they will only build 10 units for that is all they can produce.

Pashigian, Chapter 10, Exercise 10

No just because you have a dominant strategy does not mean that strategy will maximize profits.

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The demand curve for a particular product is given by

Q = 630000-300p.

The marginal cost of producing the product is $400. Two firms produce the product, working as a Cournot Duopoly. Plot their reaction functions. Given their reaction functions, calculate the quantity produced and the market price for the product.

A

B

A

B

255,000

510,000255,000

510,000 Each firm produces 170,000

Market price is $93.33

Accept a lot of round off

The industry demand curve for widgets is given by

Q = 240 - 10 P

Initially there are ten plants producing widgets. Each plant belongs to a different firm. (Indeed, there is a law restricting each firm to one plant). Nine of the ten plants have a cost function

16 + q2

The tenth plant (Acme) has an exemption from environmental laws so that its cost function is

9 + q2

•Assuming initially that only these ten firm/plants may produce widgets, determine the equilibrium price and quantity of widgets, as well as the profits of each firm, including Acme.

Each firm has a MC = 2q, so each firm’s supply is q = P/2. Since there are 10 firms total industry supply is 10(P/2) = 5P.

Since supply and demand must equal

240-10P = 5P

Solving P =16. Total quantity demanded is 80, each firm produces 8. Profits. Each firm has revenue of $144. Nine firms have costs of 16 + 82

=$80, or profits of $64. Acme’s profits are $71.

•Now assume that other firms may open a (single) plant and produce widgets if they wish. If they do, their cost function will be the same as the nine plants. Determine the equilibrium price of widgets, the number of firms in the industry, the quantity of widgets produced by each firm, and the profits of each firm, including Acme.

Lets find the minimum of the AC function. AC is 16/q + q, and MC = 2q. Since MC = AC at the minimum of the AC function, we solve 16/q +q = 2q, and get q = 4. At that level of output MC = AC =8. That will be the price.

Total demand is 240-10(8) =160.

Since each firm produces 4, there must be 40 firms. Each firm except Acme will have zero profits; Acme will have profits of $7.

•Now suppose that Acme Widgets, the owner of the first plant, is given a legal monopoly to produce widgets, but is also given the right to open as many other plants as it wishes. Determine how many plants Acme will operate, the number of widgets it will produce at each plant, the price it will charge for widgets, and its profits. (Break on 1 plant)

LRMC = 8 (we see that from the previous problem).

We want to know MR. To get that, note that the monopolist’s revenue function is

R = PQ = (24-0.1Q)Q = 24Q –0.1Q2

Thus

MR = 24 - 0.2Q

Since MR = MC for a monopolist, we can solve to get Q = 80. It will sell at a price of $16.

To get profits, remember that revenues are (80)($16)= $1440. Costs are $8 each or $640. So profits are $800. EXCEPT for the $7 extra profit Acme makes on its first plant, so profits turn out to be $807.

•Now suppose that widgets are subject to a $1 tax. What happens to Acme's supply curve?

•Now suppose that widgets are subject to a $1 tax. What happens to Acme's supply curve?

Silly! A monopolist does not have a supply curve

Homework-Due this Week

The demand for a product is

Q = 600-2p.

The marginal cost of producing a product is zero, but each firm in the business has a fixed cost of $20.

(a) Initially two firms are producing the product in a Cournot Duopoly. How many units are being produced? At what price are they being sold? What is each firm's profit?

(b) Now suppose a third firm enters the business. We know this is not technically a Cournot duopoly, but we know how to extend the model. With three firms, how many units are being produced? At what price are they being sold? What is each firm's profit?

(c) These profits will be a signal to other firms to enter the business, so a fourth firm will enter. And so on. How many firms will eventually enter? When firms stop entering, what price will the product be sold for? How many firms will there be? (Hint: don’t forget the fixed cost).

The industry demand curve for widgets is given by Q = 600 - 10 P. Initially there are forty plants producing widgets. Each plant belongs to a different firm. (Indeed, there is a law restricting each firm to one plant). Each plan has costs equal to

27 + 3q2

where q is the number of widgets produced by each plant.

(a) Assuming initially that only these forty firms/plants may produce widgets, determine the equilibrium price and quantity of widgets, as well as the profits of each firm.

(b) Now assume that other firms may open a (single) plant and produce widgets if they wish. If they do, their cost function will be the same. Now determine the equilibrium price of widgets, the number of firms in the industry, the quantity of widgets produced by each firm, and the profits of each firm.

(c) Now suppose that Acme Widgets is given a legal monopoly to operate widgets, but is also given the right to open as many plans as it wishes. Determine how many plants Acme will operate, the number of widgets it will produce at each plant, the price it will charge for widgets, and its profits.

(d) Derive Acme’s supply curve.

The industry demand curve for widgets is given by

Q = 650 - 8 P

Initially there are ten plants producing widgets. Each plant belongs to a different firm. (Indeed, there is a law restricting each firm to one plant). Each plant has a cost function

25 + q2

where q is the number of widgets produced by each plant.

(a) Assuming initially that only these ten firm/plants may produce widgets, determine the equilibrium price and quantity of widgets.

(b) Now assume that other firms may open a (single) plant and produce widgets if they wish. If they do, their cost function will be the same as the ten plants.

(c) Now suppose that a new technology makes it possible to build plants with a cost of

4 + q2

Once there has been time to adjust, what will be the equilibrium price of widgets?

(d) How many widgets will the old plants produce?

(e) How many new plants will come into being? (Assume none of the old plants leave the industry).

Lectures for This Week

• Agency Problems

• Expense Preference

•Agency Problems

•Expense Preference

Lectures for Next Week

• Price Discrimination-A Primer

• Price Discrimination with Self Identification

• Price Discrimination in Action

• Three Discrimination Problems

• Solution to Three Discrimination Problems

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