### ATC, AVC and MC

```ECON111
Tutorial 9 Week 10
Question 1.a
• Two firms have exactly the same MC curve, but their
AFC is not the same.
i.
Will their AVC cost curve be the same or different?
Their AVC cost will be the same because if they have
the same MC curve, then they must have the same
TC curve, with intercept zero and slope equals MC.
ii. Will their ATC curve be the same or different? Their
ATC will be different because ATC = AFC + AVC and we
don’t know whether their AFC is not the same.
Question 1.b
• What shape does the AFC curve take?
120
100
80
Cost
Q
TFC
TVC
TC
0
2
5
9
12
14
15
\$200
200
200
200
200
200
200
\$0
100
200
300
400
500
600
\$200
300
400
500
600
700
800
AFC
100
40
22.222
16.667
14.286
13.333
AVC
50
40
33.333
33.333
35.714
40
ATC
MC
150
80
55.556
50
50
53.333
\$50.00
33.33
25
33.33
50
100
60
TFCs do not vary with Q
Hence, as Q increases AFC = TFC/Q
falls continuously and approaches the
horizontal axis as Q expands.
40
20
AFC
0
0
5
10
Q
15
20
Question 1.b
• Why do the AVC and MC curves maintain a set
relationship to each other?
• AVC = TVC/Q
• MC = ∆TC/∆Q = ∆TVC/∆Q
• MC and AVC are both derive from TVC, hence
they are related to each other.
Question 1.c
• Explain why the MC curve must intersect the
ATC and the AVC curves at their minimum
point?
ATC, AVC and MC
 When MC is above
AVC and ATC, AVC
and ATC is increasing
 When MC is below AVC
MC
(ATC), the AVC and
ATC is falling
 When MC = AVC
(ATC), AVC (ATC) is at
ATC
its minimum.
Cost (\$)
\$150
125
100
75
AVC
50
25
0
5
10
15
Q
6
Question 2.a
• How is the law of diminishing marginal returns
related to the shape of the short-run marginal
cost curve?
– According to that law, beyond some point the MP
decreases as more of a variable factor is added to a
fixed factor of production.
– As production increases, diminishing marginal returns
for the variable production factors mean that each
additional unit of output will require more of the
variable factors, so marginal costs go up when
diminishing returns set in.
• Suppose capital is fixed and labour is the variable
factor of production. Assuming the wage rate remains
constant (new employees earn the same wage as
existing employees), as marginal product increases,
marginal cost falls.
• When the marginal product curve is at its maximum,
the marginal cost curve is at a minimum. As
diminishing returns set in and the marginal product
curve falls, the marginal cost curve rises.
• Hence, the marginal cost curve is a u shape, which is
inversely related to the marginal product curve.
Units of the
variable factor
(Labor or L)
TP
(tons moved
per day)
MPL
(tons moved
per day)
Return
0
1
2
3
4
5
6
7
8
0
2
5
9
12
14
15
15
14
2
3
4
3
2
1
0
-1
-----Increasing
“
“
Diminishing
“
“
“
Diminishing and
Negative
TP and MPL
TP
15
Total
product
10
5
Labor
0
5
MPL
5
4
3
2
1
0
Increasing
marginal
returns
7
10
Diminishing but
positive
marginal returns
Negative
marginal
returns
Labor
5
7
10
Marginal product
10
• MP = ∆Q/∆L
• MC = ∆ATC/ ∆Q = w.∆L/∆Q
• ∆Q = MP. ∆L
• ∆Q = w. ∆L/MC
• So, MP. ∆L = w. ∆L/MC
• There is an inverse relationship b/w MP and ML
• As MP increases, MC decreases
• As MP decreases, MC increases
Costs (dollars)
Average product and
marginal product
•When marginal product is
increasing, marginal cost falls.
•When marginal product falls,
MP marginal costs increase.
Quantity of labor
MP and MC are mirror images
MC
of each other.
Quantity of output
12
Question 2.b
• Much discussion of productivity focuses on
“output per worker”. Is this an average or a
marginal productivity notion? Which of these
concepts do you think is most relevant to a firm’s
hiring decisions?
– Output per worker is an average notion. APP = Q/L
– Marginal productivity (ΔQ/ΔL) is most relevant to a
firm’s hiring decisions because firms weigh up the
additional benefits against the additional costs when
deciding whether or not to hire an extra worker.
Question 3.c
• At a management luncheon, two managers were overheard arguing
about the following statement: “A manager should never hire an
extra worker if the new person causes diminishing returns”. Is this
statement correct? If so, why? If not, explain why not.
– No – just because an extra worker may have lower marginal product
that the last unit of labour hired, does not mean that the worker
should not be hired. The decision to hire depends on marginal benefits
and marginal costs.
– The value of marginal product is the marginal product (ΔQ/ΔL)
multiplied by the price of output. A competitive profit maximising firm
hires workers up to the point where the value of marginal product of
labour equals the wage rate. Below this level of employment, the
value of marginal product exceeds the wage, so hiring another worker
would increase profit. Above this level of employment, the value of
marginal product is less than the wage, so the marginal worker is
Question 3.a
Q
0
1
2
3
4
5
6
7
8
9
10
TC
20
21
24.00
32.00
48.00
75.00
116.00
174.02
260.02
380.00
540.00
TC = TFC + TVC
ATC = TC/Q = AFC + AVC
AFC = TFC/Q
AVC = TVC/Q
TFC
20
20
20
20
20
20
20
20
20
20
20
TVC
0
1
4.00
12.00
28.00
55.00
96.00
154.02
240.02
360.00
520.00
ATC
AFC
AVC
MC
21
12
10.667
12
15
19.33
24.86
32.50
42.22
54
20
10
6.667
5
4
3.33
2.86
2.50
2.22
2
1
2
4
7
11
16
22.00
30.0025
40
52
1.00
3.00
8.00
16.00
27.00
41.00
58.02
86.00
119.98
160.00
MC = ∆TC/∆Q
MC = ∆TFC/∆Q + ∆TVC/ ∆Q
MC = ∆TVC/ ∆Q
Note: ∆TFC/ ∆Q = 0
Question 3.b
• Explain the difference between MC and AC.
– MC vs. ATC
– ATC = TC/Q = TFC/Q + TVC/Q
– MC = ∆TC/∆Q = ∆TFC/∆Q + ∆TVC/∆Q
– Since ∆TFC = 0
– MC = ∆TC/∆Q = ∆TVC/∆Q
Question 3.c
• Explain why short-run marginal cost is equal to the
slope of both the total cost and total variable cost
curves, and why can marginal cost be computed from
either total variable cost or from total cost?
– Because fixed costs do not vary as output varies (ΔTFC/ΔQ
= 0), MC can be calculated from either TC or TVC.
– The slope of the TC curve gives MC.
– Since TC = TVC+TFC where TFC is the constant fixed costs,
the TVC curve is parallel to the TC curve and hence has the
same slope.
– So MC can be calculated from either TC or TVC curve.
Question 3.c
25
20
15
ATC
AFC
AVC
10
MC
5
0
0
1
2
3
4
5
6
7
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