Concept explainers
a
To find:
a
Explanation of Solution
The annual capacity of plants A, B, and C are 75,000, 150,000, and 350,000 units, respectively. Production beyond annual capacities requires multiple plants of the same type. And hence, the fixed costs would increase by the same multiples too.
Unit variable costs are $9, $8 and $7 for plant A, B, and C, respectively.
The schedule below shoes the average total cost for Plant A for varying output levels.
|
Q |
VC (1) |
FC (2) |
TC (1)+(2) |
ATC |
|
25,000 |
$9(25,000) =$225,000 |
$150,000 |
$375,000 |
$15 |
|
50,000 |
$9(50,000) =$450,000 |
$150,000 |
$600,000 |
$12 |
|
75,000 |
$9(75,000) =$675,000 |
$150,000 |
$825,000 |
$11 |
|
100,000 |
$9(100,000) =$900,000 |
2($150,000) =$300,000 |
$1,200,000 |
$12 |
|
125,000 |
$9(125,000) =$1,125,000 |
2($150,000) =$300,000 |
$1,425,000 |
$11.40 |
|
150,000 |
$9(150,000) =$1,350,000 |
2($150,000) =$300,000 |
$1,650,000 |
$11 |
|
175,000 |
$9(175,000) =$1,575,000 |
3($150,000) =$450,000 |
$2,025,000 |
$11.57 |
|
200,000 |
$9(200,000) =$1,800,000 |
3($150,000) =$450,000 |
$2,025,000 |
$11.25 |
|
225,000 |
$9(225,000) =2,025,000 |
3($150,000) =$450,000 |
$2,475,000 |
$11 |
|
250,000 |
$9(250,000) =$2,250,000 |
4($150,000) =$600,000 |
$2,850,000 |
$11.40 |
|
275,000 |
$9(275,000) =$2,475,000 |
4($150,000) =$600,000 |
$3,075,000 |
$11.18 |
|
300,000 |
$9(300,000) =$2,700,000 |
4($150,000) =$600,000 |
$3,300,000 |
$11 |
|
325,000 |
$9(325,000) =$2,925,000 |
5($150,000) =$750,000 |
$3,675,000 |
$11.31 |
|
350,000 |
$9(350,000) =$3,150,000 |
5($150,000) =$750,000 |
$3,900,000 |
$11.14 |
The schedule below shows the average total cost for Plant B for varying output levels.
| Q | VC(1) | FC(2) | TC(1)+(2) | ATC |
|
25,000 |
$8(25,000) =$200,000 |
$250,000 |
$450,000 |
$18 |
|
50,000 |
$8(50,000) =$400,000 |
$250,000 |
$650,000 |
$12 |
|
75,000 |
$8(75,000) =$600,000 |
$250,000 |
$850,000 |
$11.33 |
|
100,000 |
$8(100,000) =$800,000 |
$250,000 |
$1,050,000 |
$10.50 |
|
125,000 |
$8(125,000) =$1,000,000 |
$250,000 |
$1,250,000 |
$10 |
|
150,000 |
$8(150,000) =$1,200,000 |
$250,000 |
$1,450,000 |
$9.67 |
|
175,000 |
$8(175,000) =$1,400,000 |
2($250,000) =$500,000 |
$1,900,000 |
$10.86 |
|
200,000 |
$8(200,000) =$1,600,000 |
2($250,000) =$500,000 |
$2,100,000 |
$10.50 |
|
225,000 |
$8(225,000) =$1,800,000 |
2($250,000) =$500,000 |
$2,300,000 |
$10.22 |
|
250,000 |
$8(250,000) =$2,000,000 |
2($250,000) =$500,000 |
$2,500,000 |
$10 |
|
275,000 |
$8(275,000) =$2,200,000 |
2($250,000) =$500,000 |
$2,700,000 |
$9.82 |
|
300,000 |
$8(300,000) =$2,400,000 |
2($250,000) =$500,000 |
$2,900,000 |
$9.67 |
|
325,000 |
$8(325,000) =$2,600,000 |
3($250,000) =$750,000 |
$3,350,000 |
$10.31 |
|
350,000 |
$8(350,000) =$2,800,000 |
3($250,000) =$750,000 |
$3,550,000 |
$10.14 |
The schedule below shows the average total cost for Plant C for varying output levels.
| Q | VC(1) | FC(2) | TC(1)+(2) | ATC |
|
25,000 |
$7(25,000) =$175,000 |
$450,000 |
$625,000 |
$25 |
|
50,000 |
$7(50,000) =$350,000 |
$450,000 |
$800,000 |
$16 |
|
75,000 |
$7(75,000) =$525,000 |
$2450,000 |
$975,000 |
$13 |
|
100,000 |
$7(100,000) =$700,000 |
$450,000 |
$1,150,000 |
$11.50 |
|
125,000 |
$7(125,000) =$875,000 |
$450,000 |
$1,325,000 |
$10.60 |
|
150,000 |
$7(150,000) =$1,050,000 |
$450,000 |
$1,500,000 |
$10 |
|
175,000 |
$7(175,000) =$1,225,000 |
$450,000 |
$1,675,000 |
$9.57 |
|
200,000 |
$8(200,000) =$1,600,000 |
$450,000 |
$2,850,000 |
$9.25 |
|
225,000 |
$7(225,000) =$1,575,000 |
$450,000 |
$2,025,000 |
$9 |
|
250,000 |
$7(250,000) =$1,750,000 |
$450,000 |
$2,200,000 |
$8.80 |
|
275,000 |
$7(275,000) =$1,925,000 |
$450,000 |
$2,375,000 |
$8.64 |
|
300,000 |
$8(300,000) =$2,100,000 |
$450,000 |
$2,550,000 |
$8.50 |
|
325,000 |
$7(325,000) =$2,275,000 |
$450,000 |
$3,725,000 |
$8.38 |
|
350,000 |
$7(350,000) =$2,450,000 |
$450,000 |
$3,900,000 |
$8.29 |
Introduction:
Fixed costs (FC) are the costs that the firm has to incur irrespective of the level of output.
Variable costs (VC) are the costs that vary with the level of output, that is, increase as the output level increases, and vice versa.
Total cost (TC) is the total cost incurred by the firm in the production process. It is the sum of fixed cost and variable cost.
Average total cost
b)
To ascertain:Long run average total cost schedule.
b)
Explanation of Solution
The combined long-run average cost schedule for three plants is as given below:
|
Q |
Long Run ATC |
| 25,000 | $15 |
| 50,000 | $12 |
| 75,000 | $11 |
| 100,000 | $10.50 |
| 125,000 | $10 |
| 150,000 | $9.67 |
| 175,000 | $9.57 |
| 200,000 | $9.25 |
| 225,000 | $9 |
| 250,000 | $8.80 |
| 275,000 | $8.64 |
| 300,000 | $8.50 |
| 325,000 | $8.38 |
| 350,000 | $8.29 |
For output level beyond 75,000 units (production capacity of plant A), average total cost is lower for plant B. Similarly, for output level beyond 150,000 units (production capacity of plant B), average total cost is lower for plant C.
Introduction:
Fixed costs (FC) are the costs that the firm has to incur irrespective of the level of output.
Variable costs (VC) are the costs that vary with the level of output, that is, increase as the output level increases, and vice versa.
Total cost (TC) is the total cost incurred by the firm in the production process. It is the sum of fixed cost and variable cost.
Average total cost
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