Imagine that the biggest four firms in each of the sectors listed below produce the amounts defined in each cell. Compute the three-firm and four-firm concentration ratios for each sector, and rank the sectors by degree of industry concentration.
| Sector |
Firm 1 |
Firm 2 |
Firm 3 |
Firm 4 |
Total market |
| Shoes |
60 |
45 |
20 |
12 |
920 |
| Chemicals |
120 |
80 |
36 |
24 |
480 |
| Beer |
45 |
40 |
3 |
2 |
110 |
| Tobacco |
206 |
84 |
30 |
5 |
342 |
You own a company in a monopolistically competitive market. Your marginal cost of production is $12 per unit. There are no fixed costs. The demand for your own product is given by the equation P=48–(1/2)Q.
- Plot the demand curve, the marginal revenue curve, and the marginal cost curve.
- Compute the profit-maximizing output and price combination.
- Compute total revenue and total profit [Hint: Remember AC=MC here].
- In this monopolistically competitive industry, can these profits continue indefinitely?
Two firms in a particular industry face a market demand curve given by the equation P=100–(1/3)Q. The marginal cost is $40 per unit and the marginal revenue is MR=100–(2/3)Q. The quantity intercepts for demand and MR are 300 and 150.
- Draw the demand curve and MR curve to scale on a diagram. Then insert the MC curve.
- If these firms got together to form a cartel, what output would they produce and what price would they charge?
- Assuming they each produce half of the total what is their individual profit?
The classic game theory problem is the "prisoners' dilemma." In this game, two criminals are apprehended, but the police have only got circumstantial evidence to prosecute them for a small crime, without having the evidence to prosecute them for the major crime of which they are suspected. The interrogators then pose incentives to the crooks-incentives to talk. The crooks are put in separate jail cells and have the option to confess or deny. Their payoff depends upon what course of action each adopts. The payoff matrix is given below. The first element in each box is the payoff (years in jail) to the player in the left column, and the second element is the payoff to the player in the top row.
| |
|
B's strategy |
| |
|
Confess |
Deny |
| A's strategy |
Confess |
6,6 |
0,10 |
| Deny |
10,0 |
1,1 |
- Does a "dominant strategy" present itself for each or both of the crooks?
- What is the Nash equilibrium to this game?
- Is the Nash equilibrium unique?
- Was it important for the police to place the crooks in separate cells?
Taylormade and Titlelist are considering a production strategy for their new golf drivers. If they each produce a small output, they can price the product higher and make more profit than if they each produce a large output. Their payoff/profit matrix is given below.
| |
|
Taylormade strategy |
| |
|
Low output |
High output |
| Titleist strategy |
Low output |
50,50 |
20,70 |
| High output |
70,20 |
40,40 |
- Does either player have a dominant strategy here?
- What is the Nash equilibrium to the game?
- Do you think that a cartel arrangement would be sustainable?
Ronnie's Wraps is the only supplier of sandwich food and makes a healthy profit. It currently charges a high price and makes a profit of six units. However, Flash Salads is considering entering the same market. The payoff matrix below defines the profit outcomes for different possibilities. The first entry in each cell is the payoff/profit to Flash Salads and the second to Ronnie's Wraps.
| |
|
Ronnie's Wraps |
| |
|
High price |
Low price |
| Flash Salads |
Enter the market |
2,3 |
-1,1 |
| Stay out of market |
0,6 |
0,4 |
- If Ronnie's Wraps threatens to lower its price in response to the entry of a new competitor, should Flash Salads stay away or enter?
- Explain the importance of threat credibility here.
Optional: Consider the market demand curve for appliances: P=3,200–(1/4)Q. There are no fixed production costs, and the marginal cost of each appliance is 
. As usual, the MR curve has a slope that is twice as great as the slope of the demand curve.
- Illustrate this market geometrically.
- Determine the output that will be produced in a 'perfectly competitive' market structure where no profits accrue in equilibrium.
- If this market is supplied by a monopolist, illustrate the choice of output.
Optional: Consider the outputs you have obtained in Exercise 11.7.
- Can you figure out how many firms would produce at the perfectly competitive output? If not, can you think of a reason?
- If, in contrast, each firm in that market had to cover some fixed costs, in addition to the variable costs defined by the MC value, would that put a limit on the number of firms that could produce in this market?
