Brunswick manufactures its Life Cycle fitness equipment at six factories in the
ID: 1166204 • Letter: B
Question
Brunswick manufactures its Life Cycle fitness equipment at six factories in the United States. Say that you are a manager at a company like Brunswick. For simplicity, assume that your firm produces only one style of fitness equipment, an exercise bike, and that you produce it at three plants, all of which have identical costs. The table presents the costs at one of the plants. The second column includes all of the costs except the cost of transporting the bikes to the purchasers, which the table presents in the third column as the shipping costs. Suppose that your firm is a perfect competitor and the market price is $500 per bike after delivery.
Accompanies problem 3.5.
What quantity of exercise bikes maximizes your firm’s profit? At this quantity, what is the profit per plant, and what is your firm’s total profit?
Total Cost of Production (dollars)
Shipping Cost (dollars)
100
$40,000
$8,000
101
40,380
8,080
102
40,780
8,160
103
41,200
8,240
104
41,640
8,320
105
42,100
8,400
106
42,580
8,480
107
43,080
8,560
108
43,600
8,640
109
44,140
8,720
110
44,700
8,880
You are deciding whether to build a fourth plant. A fourth plant has no effect on the shipping costs, and once the new plant is built, all four plants will have identical costs. Adding a fourth plant creates managerial diseconomies that raise the costs of production by $1,000 at each quantity in the table at all four plants. If your firm adds a fourth plant, what quantity of exercise bikes maximizes profit? What is the profit for each of the four plants, and what is the firm’s total profit? Should you approve building the plant? Why or why not?
Now assume that, as in part b., building the fourth plant creates managerial diseconomies that raise the costs of production by $1,000 at each quantity in the table at all four plants. However, also suppose that the fourth plant cuts the cost of shipping in half at all four plants. What quantity of exercise bikes now maximizes your firm’s profit? What is the profit per plant and your firm’s total profit? With this revised scenario, should you approve building the fourth plant? Why or why not
Quantity (bikes per hour)Total Cost of Production (dollars)
Shipping Cost (dollars)
100
$40,000
$8,000
101
40,380
8,080
102
40,780
8,160
103
41,200
8,240
104
41,640
8,320
105
42,100
8,400
106
42,580
8,480
107
43,080
8,560
108
43,600
8,640
109
44,140
8,720
110
44,700
8,880
Explanation / Answer
It has been mentioned that the firm is perfectly competitive. This means that in equilibrium, the profit maximizing condition requires Price (P) = Marginal Cost (MC). Since P = $500 with delivery, the MC that has to be compared with P also has to include the delivery or shipping costs. The required calculations are done in tables which represents the costs and profits for 1 plant. Since costs are identical and the price is constant, the outcome of the 4 plants in total can be found out by the summation of outcome of each plant.
For the first case, the table can be summarized as follows:
Quantity (Q)
(bikes per hour)
TC of Production ($)
Shipping Cost ($)
Total Cost ($)
Marginal Cost ($)
Total Revenue (TR) ($) = P*Q
Profit ($)
100
40,000
8,000
48,000
0
50000
2,000
101
40,380
8,080
48,460
460
50500
2,040
102
40,780
8,160
48,940
480
51000
2,060
103
41,200
8,240
49,440
500
51500
2,060
104
41,640
8,320
49,960
520
52000
2,040
105
42,100
8,400
50,500
540
52500
2,000
106
42,580
8,480
51,060
560
53000
1,940
107
43,080
8,560
51,640
580
53500
1,860
108
43,600
8,640
52,240
600
54000
1,760
109
44,140
8,720
52,860
620
54500
1,640
110
44,700
8,880
53,580
720
55000
1,420
In the first case, P = $500 including delivery and MC = $500 with delivery at 103 units of output.
In the second case, the price and shipping charges remain the same. However the cost of production rises by $1000. The table changes as follows:
Quantity (Q)
(bikes per hour)
TC of Production ($)
Shipping Cost ($)
Total Cost ($)
Marginal Cost ($)
Total Revenue (TR) ($) = P*Q
Profit ($)
100
41,000
8,000
49,000
0
50000
1,000
101
41,380
8,080
49,460
460
50500
1,040
102
41,780
8,160
49,940
480
51000
1,060
103
42,200
8,240
50,440
500
51500
1,060
104
42,640
8,320
50,960
520
52000
1,040
105
43,100
8,400
51,500
540
52500
1,000
106
43,580
8,480
52,060
560
53000
940
107
44,080
8,560
52,640
580
53500
860
108
44,600
8,640
53,240
600
54000
760
109
45,140
8,720
53,860
620
54500
640
110
45,700
8,880
54,580
720
55000
420
In the second case too, P = $500 including delivery and MC = $500 with delivery at 103 units of output.
In the third case, the price remains the same. However the cost of production rises by $1000 and the shipping cost halves. The table changes as follows:
Quantity (Q)
(bikes per hour)
TC of Production ($)
Shipping Cost ($)
Total Cost ($)
Marginal Cost ($)
Total Revenue (TR) ($) = P*Q
Profit ($)
100
41,000
4000
45,000
0
50000
5,000
101
41,380
4040
45,420
420
50500
5,080
102
41,780
4080
45,860
440
51000
5,140
103
42,200
4120
46,320
460
51500
5,180
104
42,640
4160
46,800
480
52000
5,200
105
43,100
4200
47,300
500
52500
5,200
106
43,580
4240
47,820
520
53000
5,180
107
44,080
4280
48,360
540
53500
5,140
108
44,600
4320
48,920
560
54000
5,080
109
45,140
4360
49,500
580
54500
5,000
110
45,700
4440
50,140
640
55000
4,860
In the third case too, P = $500 including delivery and MC = $500 with delivery at 105 units of output.
Quantity (Q)
(bikes per hour)
TC of Production ($)
Shipping Cost ($)
Total Cost ($)
Marginal Cost ($)
Total Revenue (TR) ($) = P*Q
Profit ($)
100
40,000
8,000
48,000
0
50000
2,000
101
40,380
8,080
48,460
460
50500
2,040
102
40,780
8,160
48,940
480
51000
2,060
103
41,200
8,240
49,440
500
51500
2,060
104
41,640
8,320
49,960
520
52000
2,040
105
42,100
8,400
50,500
540
52500
2,000
106
42,580
8,480
51,060
560
53000
1,940
107
43,080
8,560
51,640
580
53500
1,860
108
43,600
8,640
52,240
600
54000
1,760
109
44,140
8,720
52,860
620
54500
1,640
110
44,700
8,880
53,580
720
55000
1,420
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