Transcript Concept Explorer 8.2

8.
Production Function and
Cost
1
Chapter 8 : main menu
8.1
Fixed and variable factors
8.2
Short run and long run
Progress Checkpoint 1
8.3
Input-output relationship in short
run
Concept Explorer 8.1
Concept Explorer 8.2
Concept Explorer 8.3
Theory in Life 8.1
Progress Checkpoint 2
8.4
Cost-output relationship in short
run
Theory in Life 8.2
Concept Explorer 8.4
8.5
Cost-output relationship in long run
Concept Explorer 8.5
Progress Checkpoint 3
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Progress Checkpoint 1
Statement 1 : If there is at least one variable
factor, it is a short-run period
Statement 2 : If there is at least one variable
factor, it is a long-run period.
Which statement is correct? Are both correct?
3
Progress Checkpoint 1
Statement 1 is incorrect. In short run, there is
at least one fixed factor. It is possible that all
factors may be fixed.
Statement 2 is incorrect. In long run, all
factors are variable. If there is a variable
factor with a fixed factor, it is still a short run.
4
Progress Checkpoint 1
Sam operates a photocopying shop. He is
considering two plans in expanding his shop :
Plan 1 : Use more photocopying papers, employ more
workers but keep the number of photocopying
machines unchanged.
Plan 2 : Use more of all factors of production.
Which is a short run and which is a long run
expansion plan?
How will the scale of production be affected by
EACH plan?
5
Progress Checkpoint 1
Plan 1 is a short run expansion plan, because
a fixed factor (the photocopying machines)
exists. The scale of production will not
change.
Plan 2 is a long run plan, because all factors
are variable. The scale of production will be
enlarged.
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Concept Explorer 8.1
L
MP
0
-
1
3
2
6
3
12
4
10
5
7
6
4
7
0
What are the values of TP and AP of each
unit of labour?
After which unit of labour does diminishing
(marginal) returns set in?
At which unit of labour is average product at
its maximum?
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Concept Explorer 8.1
L
MP
TP
AP
0
-
1
3
2
6
3
12
4
10
5
7
6
4
7
0
0
3
9
21
31
38
42
42
-
3
4.5
7
7.75
7.6
7
6
Diminishing returns sets in after the 3rd
unit of
labour is employed, as MP begins to
diminish thereafter.
The average product is at its maximum (=7.75)
4th unit of labour is employed.
when the
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Concept Explorer 8.2
Reasons for diminishing (marginal)
returns
Why does diminishing (marginal) returns
happen in reality?
Why does it happen only in the short run?
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Concept Explorer 8.2
Reasons for diminishing (marginal)
returns



In short run, initially when a few labour is
employed, the fixed factor is not fully utilized.
When more labour is employed, division of
labour can be adopted, cooperation among
workers is possible, and workers also learn from
experience.
This will increase marginal product.
10
Concept Explorer 8.2
Reasons for diminishing (marginal)
returns



However, when more labour is continuously
added, coordination among factors of production
becomes difficult.
Also, the fixed factor may be insufficient for the
increasing number of workers to use.
Hence, marginal product will eventually diminish.
11
Concept Explorer 8.3
Is the law of diminishing (marginal) returns
illustrated?
Mr. Chan is the owner of a DVD player producing firm.
The number of machines used in his firm is fixed.
He observes the following decrease in daily output when
some workers are absent from work due to sickness :
Number of sick workers
absent from work
1
2
3
4
5
Decrease in daily output
(units of DVD player)
4
16
33
53
74

Is the law of diminishing (marginal) returns illustrated in Mr.
Chan’s firm?
12
Concept Explorer 8.3
We can transform the above table into the following
by assuming that :
Mr. Chan’s firm normally employs 10 workers, and
the daily output of his firm is 100 units of DVD player.
Number of
workers employed
Total product
(units)
Marginal product
(units)
5
6
7
8
9
10
(5 absentees)
(4 absentees)
(3 absentees)
(2 absentees)
(1 absentee)
(assumed)
26
47
67
84
96
100
(= 100 - 74)
(= 100 - 53)
(= 100 - 33)
(= 100 - 16)
(= 100 - 4)
(assumed)
-
21
20
17
12
4
(= 47 - 26)
(= 67 - 47)
(= 84 - 67)
(= 96 - 84)
(= 100 - 96)
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Concept Explorer 8.3
Mr. Chan’s firm is in short run because
machines are a fixed factor.
We can see that when more and more
workers are added, the marginal
product diminishes.
Thus the law of diminishing (marginal)
returns is illustrated in his firm.
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Theory in Life 8.1
Famine and the law of
diminishing (marginal)
returns
It is said that if the law
of diminishing (marginal)
returns did not hold,
there would not be
famine anymore. Why?
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Theory in Life 8.1
If the law of diminishing (marginal) returns did not
hold, then when more and more farmers (a variable
factor) worked on a farmland (a fixed factor),
marginal product (in terms of agricultural product)
would not fall.
This implied that the total product would be ever
increasing.
There would be no limit to the amount of
agricultural product grown from a piece of land.
Famine could be avoided.
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Theory in Life 8.1
However, it is observed that many countries
in the world suffer from famine.
This implies that the amount of food grown
on farmland is not sufficient to avoid famine,
and there is a limit on the total product of a
piece of farmland.
The law of diminishing (marginal) returns is
empirically confirmed.
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Progress Checkpoint 2
Consider the following input-output relationship of a
firm :
L
MP
0
-
1
9
2
15
3
18
4
20
5
18
6
13
7
5
(a) What are the values of AP and TP of EACH unit
of labour?
(b) After which unit of labour does diminishing
returns set in?
(c) At which unit of labour is average product at its
maximum?
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Progress Checkpoint 2
(a)
L
MP
TP
AP
0
-
1
9
2
15
3
18
4
20
5
18
6
13
7
5
0
9
24
42
62
80
93
98
-
9
12
14
15.5
16
15.5
14
b) Diminishing (marginal) returns begins to set in after
the 4th unit of labour is employed
c) Average product is at its maximum at 16 when the
5th unit of labour is employed.
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Theory in Life 8.2
Fixed and variable costs of a fast food shop
Raymond operates a fast food shop in a shopping
centre. The following list shows some of the cost
items of his shop :
•
•
•
•
•
•
Rent of the shop
Water charges
Labour cost
Expenses on food
Management fee of the shopping centre
Fire insurance payment
Which of the above are fixed costs?
Which are variable costs?
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Theory in Life 8.2
Fixed and variable costs of a fast food shop
Raymond operates a fast food shop in a shopping
centre. The following list shows some of the cost
items of his shop :
•
•
•
•
•
•
Fixed costs  they remain constant
no matter whether more output is produced.
Rent of the shop
Water charges
Variable costs  they increase when more
Labour cost
output is produced.
Expenses on food
Management fee of the shopping centre
Fire insurance payment
Which of the above are fixed costs?
Which are variable costs?
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Concept Explorer 8.4
Calculation of total, average and marginal costs
What are the values of the unknowns in the following table?
What is the amount of fixed cost?
At which unit of output does diminishing returns set in?
At which unit of output is average cost at its minimum?
Q
TC ($)
AC ($)
0
3
-
1
10
10
2
?
7.5
3
18
?
4
23
5.75
5
34
6.8
6
54
9
MC
-
7
5
3
?
11
20
($)
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Concept Explorer 8.4
At 2 units of output,
TC = AC x Q
=
$7.5 x 2
= $15, or
TC = TC(Q = 1) + MC(Q = 2) = $10 + $5 = $15
At 3 units of output,
AC =
TC
=
Q

$18
= $6
3
At 4 units of output,
 MC
= TC (Q = 4) - TC (Q = 3) = $23 - $18 = $5
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Concept Explorer 8.4
When Q = 0, VC = $0 and TC = $3. Therefore,
TC
$3
$3
=
=
=
FC + VC
FC + $0
FC
The amount of fixed cost is $3.
Marginal cost and marginal product are inversely related.
As marginal cost starts to increase after 3 units of output
are produced, marginal product starts to decrease.
Diminishing returns set in after 3 units of output are
produced.
Average cost is at its minimum at $5.75 when 4 units of
output are produced.
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Concept Explorer 8.5
Suppose labour is the only factor required in the
production process of a firm. The following shows
some information of the firm in two months :


January 2004
February 2004
Labour cost
$20
$18
Labour employed (units)
10
20
Output produced (units)
50
100
If the market price of the firm’s product is fixed at $5,
what are the values of total revenue, total cost, average
cost and profit for the firm in each month?
How does average cost change in the period?
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Concept Explorer 8.5
January 2004
February 2004
Total revenue
$250 ( = $5 x 50)
$500 ( = $5 x 100)
Total cost
$200 ( = $20 x 10)
$360 ( = $18 x 20)
$200
Average cost
$4
=
Profit
$50
( = $250 - $200) $140
50
$3.6
=
$360
100
( = $500 - $360)
We can observe that when the firm doubles its output
by doubling its labour employed, the profit increases by
more / less than double.
This is because the average cost is higher / lower.
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Progress Checkpoint 3
Consider the following cost-output relationship of a firm :




Q
0
1
2
3
4
5
6
7
TC
??
22
29
33
35
39
48
63
AC
0
22
14.5
11
??
7.8
8
9
MC
-
12
7
4
2
??
9
15
Complete the above table.
What is the amount of fixed cost?
At which unit of output does diminishing returns set in?
At which unit of output is average cost at its minimum?
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Progress Checkpoint 3
At 1 unit of output, TC = $22 and MC = $12.
Therefore the total cost at 0 unit of output is $10
(= $22 - $12).
At 4 units of output, AC =
At 5 units of output, MC =

TC
Q
=
TC
Q
$35
=
4
= $8.75
$39 - $35
5-4
= $4
The amount of fixed cost is $10.
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Progress Checkpoint 3
Marginal cost and marginal product are
inversely related to each other.
As marginal cost starts to increase after 4
units of output are produced, marginal
product starts to fall.
Diminishing returns set in after 4 units of
output are produced.
Average cost is at its minimum at $7.8 when
5 units of output are produced.
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End of Chapter 8
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