INPUTS AND COSTS
Profit Defined
π = TR − TC
Total Revenue
TR = P × Q
Costs
“Costs merely register competing attractions.”
Explicit versus Implicit Opportunity Costs
Page 1 of 18
Economic Profit Versus Accounting Profit
TR₀ = P₀Q = $4 × 100,000 = $400,000
Explicit Costs = $320,000
Accounting profit = 400,000 – 320,000 = $80,000
Implicit Costs = $50,000
Economic profit = 400,000 – (320,000 + 50,000) = 30,000
Page 2 of 18
Economic Profit Versus Normal Profit
TR₀ = P₀Q = $3.70 × 100,000 = $370,000
Explicit Costs = $320,000
Accounting profit = 370,000 – 320,000 = $80,000
Implicit Costs = $50,000
Economic profit = 370,000 – (320,000 + 50,000) = 0
Any return above the return on the next best alternative line of business is an economic profit. When economic profit is zero, the firm is making a normal
profit. Thus, the earnings or the return that is equal to the return on the next best alternative is a normal profit.
Short Run Versus Long Run Decisions
Tom faces two time horizons regarding his business decisions whether to expand his operations (produce more) or reduce them. These time horizons are not measured in any
specific time periods such as months or years. They are rather a time frame within which Tom is able to change the scale (or the size of physical plant) of his operations.
In the short run, responding to higher price of corn, he could increase output by using more intensive production method, use more fertilizer, and hire more workers. However,
his expansion of production is limited by the size of his farm and the size of heavy farming equipment. Simply put, in the short run, Tom can only change his variable inputs and
is forced to keep some inputs fixed (fixed inputs). In the long run, if the corn market remains robust, Tom can expand the size of his farm and buy bigger or additional heavy
equipment. So in the long run no inputs remain fixed.
Page 3 of 18
Production Function
Total Product
Q = 15L² − L³
550
0
1
2
3
4
5
6
7
8
9
10
11
Output
Q
500
0
14
52
108
176
250
324
392
448
486
500
484
450
Total product (Units of output, Q)
Variable input
L
400
350
300
250
200
150
100
50
0
0
1
2
3
4
5
6
7
Units of variable input (L)
Page 4 of 18
8
9
10
11
Marginal Product
Variable input
L
Total product
Q = 15L² − L³
0
Marginal Product
MP = ∆Q ⁄∆L
0
80
14
38
2
52
56
3
108
68
4
176
74
5
250
74
6
392
448
38
9
486
14
10
Page 5 of 18
50
40
30
20
10
500
0
0
1
2
3
4
5
6
7
Units of variable input (L)
56
8
60
324
68
7
70
14
Marginal product (Units of output, Q)
1
8
9
10
The law of diminishing returns
Alternative presentation of marginal product: marginal product of a very small Increase in the variable input
Variable input
L
0
1
2
3
4
5
6
7
8
9
10
Page 6 of 18
Total product
Q = 15L² − L³
0
14
52
108
176
250
324
392
448
486
500
Marginal Product
MP = 30L − 3L²
MP = ∆Q ⁄∆L
MP = dQ ⁄dL
0
14
27
38
48
56
63
68
72
74
75
74
72
68
63
56
48
38
27
14
0
Q
0
14
52
108
176
250
324
392
448
486
500
MP
0
27
48
63
72
75
72
63
48
27
0
550
500
450
Total product (Units of output, Q)
L
0
1
2
3
4
5
6
7
8
9
10
400
350
300
250
200
150
100
50
0
0
1
2
3
4
5
6
7
8
9
10
8
9
10
Units of variable input (L)
Marginal product (Units of output,
Q)
80
70
60
50
40
30
20
10
0
0
1
2
3
4
5
6
7
Units of variable input (L)
Page 7 of 18
Average Product
Variable input
L
0
1
2
3
4
5
6
7
8
9
10
Page 8 of 18
Total product
Q = 15L² − L³
0
14
52
108
176
250
324
392
448
486
500
Marginal Product
MP = ∆Q ⁄∆L
MP = dQ ⁄dL
0
14
27
38
48
56
63
68
72
74
75
74
72
68
63
56
48
38
27
14
0
Average Product
AP = Q ⁄ L
14
26
36
44
50
54
56
56
54
50
The Relationship Between Marginal Product and Average Product
Figure 9-5 shows the relationship between marginal product and the average product. The behavior of the AP curve follows directly from that of the MP curve. This behavior
follows simply the mathematical relationship between average and marginal values: When the marginal value is greater than the average value, then the average rises. In
Figure 9-5 up to point M marginal product is above the average product and, therefore, it pulls the average product up. After M marginal product is below the average product
and, therefore, pulls the average product down. Thus, the marginal and average products are equal when the average product reaches the maximum.
Consider the following simple example close to your own personal experience: suppose an economics course requires five tests and your average score for the first four is 80. If
you score above 80 on the 5th test (the marginal test), then your average score will rise above 80, and If the score on the fifth test is below 80, your average will fall below 80.
For example, if your score on the 5th test is 84, then your average will rise from 80 to 80.8. If, on the other hand, your score on the 4th test is 76, then the average will fall from
80 to 79.2. The same is true, therefore, of the relationship between the average product and the marginal product.
Marginal product (Units of output, Q)
80
70
60
50
40
30
20
10
0
0
1
2
3
4
5
6
Units of variable input (L)
Page 9 of 18
7
8
9
10
Short-Run Cost Functions
Fixed Costs
)
Total Fixed Cost (TFC) and Average Fixed Cost (AFC)
AFC
-
$1,100
$1,100
$1,000
$1,000
$900
$900
$800
$800
Average fixed cost
TFC
$1,000
Total fixed cost
Q
0
1
2
3
4
5
6
7
8
9
10
$700
$600
$500
$400
$600
$500
$400
$300
$300
$200
$200
$100
$100
$0
$0
0
Page 10 of 18
$700
1
2
3
4
5
6
7
Units of output (Q)
8
9
10
0
1
2
3
4
5
6
7
Units of output (Q)
8
9
10
Variable Costs
Total Variable Cost (TVC) is the firm's total cost of hiring variable inputs in producing a given level of output. Unlike the fixed cost, TVC varies with the level of output. For a
given size workshop, plant, or farm, to increase output the firm’s must hire or use more variable inputs. The opportunity cost of variable inputs, both implicit and explicit costs,
is the variable cost. The total variable cost function is denoted as,
TVC = f(Q)
which states that TVC is a function of the level of output.
The Relationship Between the Production Function and the Total Variable Cost Function
Q = f(L)
TVC = f(Q)
(1)
(2)
Production Function
L
Q = 15L2 − L3
0
0
1
14
2
52
3
108
4
176
5
250
6
324
7
392
8
448
9
486
10
500
Page 11 of 18
Total Variable Cost
Q
TVC = $400L
0
$0
14
400
52
800
108
1,200
176
1,600
250
2,000
324
2,400
392
2,800
448
3,200
486
3,600
500
4,000
550
$4,500
500
$4,000
450
$3,500
Total variable cost
Uints of output (Q)
400
350
300
250
200
$3,000
$2,500
$2,000
$1,500
150
$1,000
100
$500
50
0
$0
0
1
2
3
4
5
6
7
Units of variable input (L)
Page 12 of 18
8
9
10
0 14 52
108
176
250
324
392
Units of output (Q)
448 486
500
A different numerical example
TVC = 60Q − 12Q² + Q³
TVC
0
49
80
99
112
125
144
175
224
297
400
$450
$400
$350
$300
Cost
Q
0
1
2
3
4
5
6
7
8
9
10
$250
$200
$150
$100
$50
$0
0
1
2
3
4
5
6
Units of output (Q)
Page 13 of 18
7
8
9
10
Marginal Cost
$450
$400
$350
MC
TVC
0
49
80
99
112
125
144
175
224
297
400
∆TVC ∕ ∆Q
49
31
19
13
13
19
31
49
73
103
dTVC ∕ dQ
60
39
24
15
12
15
24
39
60
87
120
$300
Cost
Q
0
1
2
3
4
5
6
7
8
9
10
$250
$200
$150
$100
$50
$0
0
1
2
3
4
5
6
7
8
9
10
7
8
9
10
Units of output (Q)
$140
$120
Cost
$100
$80
$60
$40
$20
$0
0
1
2
3
4
5
6
Units of output (Q)
Page 14 of 18
Average Variable Cost
TVC
0
49
80
99
112
125
144
175
224
297
400
AVC =
TVC ∕ Q
$140
$120
49
40
33
28
25
24
25
28
33
40
$100
Cost
Q
0
1
2
3
4
5
6
7
8
9
10
MC =
∆TVC ∕ ∆Q dTVC ∕ dQ
60
49
39
31
24
19
15
13
12
13
15
19
24
31
39
49
60
73
87
103
120
$80
$60
$40
$20
$0
0
1
2
3
4
5
6
Units of output (Q)
Page 15 of 18
7
8
9
10
Total Cost and Average Total Cost
$600
$550
$500
TFC
200
200
200
200
200
200
200
200
200
200
200
TVC
0
49
80
99
112
125
144
175
224
297
400
TC
200
249
280
299
312
325
344
375
424
497
600
MC
49
31
19
13
13
19
31
49
73
103
MC
60
39
24
15
12
15
24
39
60
87
120
AFC
AVC
$450
ATC
$400
200.00
100.00
66.67
50.00
40.00
33.33
28.57
25.00
22.22
20.00
49 249.00
40 140.00
33
99.67
28
78.00
25
65.00
24
57.33
25
53.57
28
53.00
33
55.22
40
60.00
$350
Cost
Q
0
1
2
3
4
5
6
7
8
9
10
$300
$250
$200
$150
$100
$50
$0
0
1
2
3
4
5
6
7
8
9
10
7
8
9
10
Units of output (Q)
$250
$200
Cost
$150
$100
$50
$0
0
1
2
3
4
5
6
Units of output (Q)
Page 16 of 18
$160
$150
$140
$130
$120
$110
Cost
$100
$90
$80
$70
$60
$50
N
$40
$30
M
$20
$10
$0
0
1
2
3
4
5
6
7
8
9
Units of output (Q)
Page 17 of 18
10
11
12
13
14
15
Some important points to keep in mind about the above cost curves.
1) Why is MC U-shaped?
In the production process, initially each additional variable input improves efficiency through better division of labor and specialization of tasks.
This implies that marginal product of labor increases, production is subject to increasing returns. So each additional unit of output embodies or
incorporates smaller amount of the variable input. Therefore, cost of producing each additional unit of output first decreases. This is why MC
decreases first. But soon, as more workers and other variable inputs are put to work with a fixed input, diminishing returns sets in. Thus, each
additional unit of output incorporates increasing amount of the variable input. MC, therefore, begins to rise. This is the explanation behind the
so called “U” shape of the MC curve.
2) Why is AVC U-shaped?
The behavior of AVC follows or trails the behavior of MC. While MC is below AVC, AVC will decrease. (Recall the example of your average and
marginal test scores.) Note that, as shown in Figure 9-10, MC may be decreasing or increasing when below the AVC. MC may be increasing, but
still below the AVC. Regardless, as long as MC is below AVC, average variable cost will be falling. But once MC exceeds AVC, the latter will
begin to increase. Thus, MC must necessarily cross the U-shaped AVC at the minimum point M.
3) Why does ATC reach the minimum at a higher output level than AVC?
Note that ATC consists of two components, AFC and AVC: ATC = AFC + AVC. Up to point N on the graph of ATC, two factors cause the ATC fall.
First is the role of spreading effect attributed to average fixed cost. This effect is caused by the fact that as quantity of output increases, fixed
costs are distributed or spread over larger quantities, leading to lower AFC. Also, the AVC component decreases first due to specialization, but
soon it will rise due to diminishing returns effect. At low levels of output the spreading effect of AFC far outweighs the diminishing returns
effect, causing ATC to continue to decrease while AVC rises. But at higher levels of output, the spreading effect loses its impact and is
outweighed by the diminishing returns effect. In the graph you can clearly observe that AVC and ATC converge asymptotically (they get very
close, but don’t touch each other) at higher levels of output.
Page 18 of 18