2 and Profit
Problem 15 Suppose that any firm intending to produce SOMA must build an integer number of plants: 0, 1, 2,.... Building Q plants costs each firm 3.5 × Q dollars. Each plant produces one unit of SOMA. If firm 1 builds Q1 plants and firm 2 builds Q2 plants, the market price p for one unit of SOMA will be 9 − (Q1 + Q2). For example, if firm 1 builds 2 plants and firm 2 builds 4 plants, the market price will be 9 − (2 + 4) = 3 per unit. At this price firm 1 will make a profit of 2 × 3 − 2 × 3.5 = −1 while firm 2 will make a profit of 4×3−4×3.5 = −2. Assume, no firm will build more than 4 plants.
Cost (Q) = 3.5 * Q
Price = 9 -(Q1+Q2)
1. Set up a 4-by-4 table that records the profits of each firm for each possible choice of the number of plants to build. Then, use your table to answer the questions below.
Price Firm 2
0
1
2
3
4
0
9
8
7
6
5
Firm 1
1
8
7
6
5
4
2
7
6
5
4
3
3
6
5
4
3
2
4
5
4
3
2
1
Revenue
Firm 2
Rev 1
Rev 2
Rev 1
Rev 2
Rev 1
Rev 2
Rev 1
Rev 2
Rev 1
Rev 2
0
0
1
1
2
2
3
3
4
4
Firm 1
0
0
0
0
8
0
14
0
18
0
20
1
8
0
7
7
6
12
5
15
4
16
2
14
0
12
6
10
10
8
12
6
12
3
18
0
15
5
12
8
9
9
6
8
4
20
0
16
4
12
6
8
6
4
4
Cost
Firm 2
Cost 1
Cost 2
Cost 1
Cost 2
Cost 1
Cost 2
Cost 1
Cost 2
Cost 1
Cost 2
0
0
1
1
2
2
3
3
4
4
Firm 1
0
0.0
0.0
0.0
3.5
0.0
7.0
0.0
10.5
0.0
14.0
1
3.5
0.0
3.5
3.5
3.5
7.0
3.5
10.5
3.5
14.0
2
7.0
0.0
7.0
3.5
7.0
7.0
7.0
10.5
7.0
14.0
3
10.5
0.0
10.5
3.5
10.5
7.0
10.5
10.5
10.5
14.0
4
14.0
0.0
14.0
3.5
14.0
7.0
14.0
10.5
14.0
14.0
Profit
Firm 2
Profit 1
Profit 2
Profit 1
Profit 2
Profit 1
Profit 2
Profit 1
Profit 2
Profit 1
Profit 2
0
0
1
1
2
2
3
3
4
4
Firm 1
0
0.0
Cost (Q) = 3.5 * Q
Price = 9 -(Q1+Q2)
1. Set up a 4-by-4 table that records the profits of each firm for each possible choice of the number of plants to build. Then, use your table to answer the questions below.
Price Firm 2
0
1
2
3
4
0
9
8
7
6
5
Firm 1
1
8
7
6
5
4
2
7
6
5
4
3
3
6
5
4
3
2
4
5
4
3
2
1
Revenue
Firm 2
Rev 1
Rev 2
Rev 1
Rev 2
Rev 1
Rev 2
Rev 1
Rev 2
Rev 1
Rev 2
0
0
1
1
2
2
3
3
4
4
Firm 1
0
0
0
0
8
0
14
0
18
0
20
1
8
0
7
7
6
12
5
15
4
16
2
14
0
12
6
10
10
8
12
6
12
3
18
0
15
5
12
8
9
9
6
8
4
20
0
16
4
12
6
8
6
4
4
Cost
Firm 2
Cost 1
Cost 2
Cost 1
Cost 2
Cost 1
Cost 2
Cost 1
Cost 2
Cost 1
Cost 2
0
0
1
1
2
2
3
3
4
4
Firm 1
0
0.0
0.0
0.0
3.5
0.0
7.0
0.0
10.5
0.0
14.0
1
3.5
0.0
3.5
3.5
3.5
7.0
3.5
10.5
3.5
14.0
2
7.0
0.0
7.0
3.5
7.0
7.0
7.0
10.5
7.0
14.0
3
10.5
0.0
10.5
3.5
10.5
7.0
10.5
10.5
10.5
14.0
4
14.0
0.0
14.0
3.5
14.0
7.0
14.0
10.5
14.0
14.0
Profit
Firm 2
Profit 1
Profit 2
Profit 1
Profit 2
Profit 1
Profit 2
Profit 1
Profit 2
Profit 1
Profit 2
0
0
1
1
2
2
3
3
4
4
Firm 1
0
0.0