5-- Case Study- Economic for Strategic decision

MBA 681 Economics for Strategic Decisions Prepared by Yun Wang

1. How does firm maximize profit. 2. Poduction decision in the perfect competitive market. 3. Production decision in monopolistic competitive market. 4. Production decision in oligopoly. 5. Production decision in monoply. 6. Two special models in oligopoly market.

1. How a Firm Maximizes Profit:

All firms try to maximize profits based on the following equation:

Profit = Total Revenue − Total Cost

The rules we have just developed for profit maximization are:

1. The profit-maximizing level of output is where the difference between total revenue and total cost is greatest, and

2. The profit-maximizing level of output is also where MR = MC.

Notice: All of these rules do not require the assumption of market type; they are true for all firms with different market structures (perfect competition, monopolistic competition, oligopoly, monopoly)!

The Four Market Structures:Structures

Market Structure

Characteristic Perfect Competition Monopolistic Competition Oligopoly Monopoly

Type of product Identical Differentiated Identical or differentiated Unique

Ease of entry High High Low Entry blocked

Examples of industries

 Growing wheat  Poultry farming

 Clothing stores  Restaurants

 Manufacturing computers  Manufacturing automobiles

 First-class mail delivery  Providing tap water

2. Profit Determination in Perfect Competitive Market: A firm maximizes profit at the level of output at which marginal revenue equals marginal cost.

The difference between price and average total cost equals profit per unit of output.

Total profit equals profit per unit of output, times the amount of output: the area of the green rectangle on the graph.

In the graph on the left, price never exceeds average cost, so the firm could not possibly make a profit.

The best this firm can do is to break even, obtaining no profit but incurring no loss.

The MC = MR rule leads us to this optimal level of production.

The situation is even worse for this firm; not only can it not make a profit, price is always lower than average total cost, so it must make a loss.

It makes the smallest loss possible by again following the MC = MR rule.

No other level of output allows the firm’s loss to be so small.

Identifying Whether a Firm Can Make a Profit Once we have determined the quantity where MC = MR, we can immediately know whether the firm is making a profit, breaking even, or making a loss. At that quantity,

• If P > ATC, the firm is making a profit

• If P = ATC, the firm is breaking even

• If P < ATC, the firm is making a loss

Even better: these statements hold true at every level of output.

However, if the price is too low, i.e. below the minimum point of AVC, the firm will produce nothing at all.

The quantity supplied is zero below this point.

3. Profit Determination in Monopolistic Competitive Market: (1 of 3)

In the short run, a monopolistic competitive firm might make a profit or a loss.

The situation where the firm is making a profit is above.

Notice that there are quantities for which demand (price) is above ATC; this is what allows the firm to make a profit.

Now the firm is making a loss.

Notice that there is now no quantity for which demand (price) is above ATC; this firm must make a (short-run) economic loss, no matter what quantity it chooses.

In the long run, the firm must break even.

Notice that the ATC curve is just tangent to the demand curve. The best the firm can do is to produce that quantity.

There is no quantity at which the firm can make a profit; the ATC curve is never below the demand curve.

In the long run, firms in both perfect competitive market and monopolistic competitive market make zero profits.

4. Profit Determination in the case of Oligopoly:

D2

D1

MR2

MR1

Price

Quantity0 Q

P a b

c

d

MC0

MC1

The demand curve for the firms facing oligopoly situation changed.

The demand curve is kinked

The firms still need: MR = MC to maximize their profits.

In the short run, firm will produce at quatity Q1.

At Q1, the average cost is shown in the graph, and it is below the market price P1.

In this case, the oligopoly firm makes profit in the short run.

In the long run, the profit can be zero or greater than zero.

5. Profit Determination in the case of Monopoly:

MR = MC • The demand curve determines price, and • The average total cost (ATC) curve determines average cost. Profit is the difference between these (P–ATC), times quantity (Q).

Since there are barriers to entry, additional firms cannot enter the market.

• So there is no distinction between the short run and long run for a monopoly.

Then unlike for perfect competition and monopolistic competition, we expect monopolists to continue to earn profits in the long run.

Below is the summary chart for the different market structures:

6 Cournot Oligopoly Model

The Cournot model explains how oligopoly firms behave if they simultaneously choose how much they produce.

Four main assumptions: 1. There are two firms and no others can enter the market 2. The firms have identical costs 3. The firms sell identical products 4. The firms set their quantities simultaneously

Example: Airline market

6 Cournot Model of an Airline Market

Recall the interaction between American Airlines and United Airlines from Chapter 13.

• In normal-form game, we assumed airlines chose between two output levels.

• We generalize that example; firms choose any output level.

The Cournot equilibrium (or Nash-Cournot equilibrium) in this model is a set of quantities chosen by firms such that, holding quantities of other firms constant, no firm can obtain higher profit by choosing a different quantity.

6 Cournot Model of an Airline Market

Demand and Cost

The quantity each airline chooses depends on the residual demand curve it faces and its marginal cost.

Estimated airline market demand: • p = dollar cost of one-way flight • Q = total passengers flying one-way on both airlines (in

thousands per quarter)

Assume each airline has cost MC = $147 per passenger

How does the monopoly outcome compare to duopoly (Cournot with two firms)?

6 Cournot Model of an Airline Market

American Airlines’ choice under monopoly and duopoly.

In the duopoly model, American Airlines faces residual demand.

6 Cournot Model of an Airline Market

Residual Demand In duopoly, if United flies qU passengers, American transports residual demand.

• American’s residual demand:

What is American’s best-response, profit-maximizing output if it believes United will fly qU passengers?

• American behaves as if it has a monopoly over people who don’t fly on United (summarized by residual demand).

• American’s residual inverse demand:

Residual inverse demand function is useful for expressing revenue (and MR) in terms of rival’s quantity.

6 Cournot Model of an Airline Market Residual Demand Residual inverse demand function is useful for expressing revenue (and MR) in terms of rival’s quantity.

• Setting MR=MC yields American’s best-response function:

Given our assumptions, United’s best-response function is analogous:

6 Cournot Model of an Airline Market

The Equilibrium The Nash-Cournot equilibrium is the point where best-response functions intersect: qA = qU = 64

6 Cournot Equilibrium with Two or More Firms

With n firms, total market output is Q = q1 + q2 + … + qn Firm 1 wants to maximize profit by choosing q1:

• FOC when Firm 1 views the outputs of other firms as fixed:

Firm 1’s best-response function found via MR=MC:

Simultaneously solving for all firms’ best-response functions yields Nash-Cournot equilibrium quantities, q1 = q2 = … = qn = q

6 Cournot Equilibrium with Two or More Firms

Linear demand p=a-b(q1+…+qn) and marginal cost m Equilibrium output q=q1=q2=…=qn is

Equilibrium market output is

Equilibrium price is

( 1) a m

q n b 

 

( ) ( 1) n a m

Q nq n b 

  

1 a nm

p n 

 

6 Cournot Model with Nonidentical Firms Different Costs

Linear demand p=a-b(q1+…+qn) Firm 1’s marginal cost is m and Firm 2’s is m+x The best-response functions are

The equilibrium output is

The equilibrium profits are

  12 1 2and 2 2

a m x bqa m bq q q

b b    

 

1 2 2

and 3 3

a m x a m x q q

b b    

 

   2 2 1 2

2 9 9

a m x a m x b b

     

  

16 Cournot Model with Nonidentical Firms Different Products: Intel and AMD

Demands

Each firm’s marginal cost is 40

Best-response functions are

Equilibrium output is

Equilibrium prices per CPU are

197 15.1 0.3 and 490 10 6A A I I I Ap q q p q q     

157 0.3 450 6 and

30.2 30.2 I I

A I q q

q q  

 

5 21A Iq q  

$115.20 $250A Ip p  

7 Bertrand Oligopoly Model

What if, instead of setting quantities, firms set prices and allowed consumers to decide how much to buy?

A Bertrand equilibrium (or Nash-Bertrand equilibrium) is a set of prices such that no firm can obtain a higher profit by choosing a different price if the other firms continue to charge these prices.

The Bertrand equilibrium is different than a quantity-setting equilibrium in either the Cournot or Stackelberg models.

17 Bertrand Oligopoly Model

Assumptions of the model: • Firms have identical costs (and constant MC=$5) • Firms produce identical goods

Conditional on the price charged by Firm 2, p2, Firm 1 wants to charge slightly less in order to attract customers.

If Firm 1 undercuts its rival’s price, Firm 1 captures entire market and earns all profit.

Thus, Firm 2 also has incentive to undercut Firm 1’s price.

Bertrand equilibrium price equals marginal cost (as in competition) because of incentive to undercut.

17 Bertrand Oligopoly Model

Bertrand equilibrium price equals marginal cost (as in competition) because of incentive to undercut.

7 Nash-Bertrand Equilibrium with Differentiated Products

In many markets, firms produce differentiated goods. • Examples: automobiles, stereos, computers, toothpaste

Many economists believe that price-setting models are more plausible than quantity-setting models when goods are differentiated.

• One firm can charge a higher price for its differentiated product without losing all its sales (e.g. Coke and Pepsi).

If we relax the “identical goods” assumption, the Bertrand model predicts that firms set prices above MC.

7 Nash-Bertrand Equilibrium with Differentiated Products

Example: Cola market

Demand curve of Coke:

• qC = quantity of Coke demanded in tens of millions of cases • pC = price of 10 cases of Coke • pP = price of 10 cases of Pepsi

If Coke faces constant MC=m, its profit is

7 Nash-Bertrand Equilibrium with Differentiated Products

Coke maximizes profit by choosing price conditional on the price charged by Pepsi.

• Coke’s best-response function:

Assuming m = $5, Coke’s best-response function is simplified such that it can be graphed as a function of Pepsi’s price:

Analogous steps for Pepsi yield Pepsi’s best-response function:

7 Nash-Bertrand Equilibrium with Differentiated Products

Intersection of best-response curves is equilibrium e1.

If Coke’s MC rises, its best-response curve shifts up and results in new equilibrium e2.