Brunswick manufactures its Life Cycle fitness equipment at six factories in the
ID: 1166178 • 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.
a. 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?
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
b. 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?
c. 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
Quantity (bikes per hour) Total Cost of Production (dollars) Shipping Cost (dollars) Total Revenue(P*Q) Total Cost = Production cost + shipping cost Profit = Total Revenue- Total Cost 100 $40,000 $8,000 50000 $48,000 $2,000 101 40,380 8,080 50500 $48,460 $2,040 102 40,780 8,160 51000 $48,940 $2,060 103 41,200 8,240 51500 $49,440 $2,060 104 41,640 8,320 52000 $49,960 $2,040 105 42,100 8,400 52500 $50,500 $2,000 106 42,580 8,480 53000 $51,060 $1,940 107 43,080 8,560 53500 $51,640 $1,860 108 43,600 8,640 54000 $52,240 $1,760 109 44,140 8,720 54500 $52,860 $1,640 110 44,700 8,880 55000 $53,580 $1,420 P = $500 The firm maximizes profit for 103 units of output. Same profit for both level of output. Each plant profit is $2060. Total profit is 4*2060= $8240 Quantity (bikes per hour) Total Cost of Production (dollars) Shipping Cost (dollars) Total Cost = Previous cost +1000 Total Cost = Production cost+ Shipping Cost Total Revenue Profit = Revenue- Cost 100 $40,000 $8,000 $41,000 $49,000 $50,000 $1,000 101 40,380 8,080 $41,380 $49,460 $50,500 $1,040 102 40,780 8,160 $41,780 $49,940 $51,000 $1,060 103 41,200 8,240 $42,200 $50,440 $51,500 $1,060 104 41,640 8,320 $42,640 $50,960 $52,000 $1,040 105 42,100 8,400 $43,100 $51,500 $52,500 $1,000 106 42,580 8,480 $43,580 $52,060 $53,000 $940 107 43,080 8,560 $44,080 $52,640 $53,500 $860 108 43,600 8,640 $44,600 $53,240 $54,000 $760 109 44,140 8,720 $45,140 $53,860 $54,500 $640 110 44,700 8,880 $45,700 $54,580 $55,000 $420 Profit is maximam at output level 103. Output per plant is $1030. total profit is 4*1030 = $4130 ** For more answer post question again.
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