Chapter 4 2024 The theory about Production and cost.pdf

Economics studies how people use resources, make decisions, and respond to incentives, focusing on production, distribution, and consumption of goods and services.

1. Chapter Four
The Theory of Production and Cost

2. Production

•Production is the process of transforming inputs into
outputs / an act of creating value or utility.

•The end products of the production process are
outputs.

•The outputs could be
–tangible (goods) or
–intangible (services).

3. Production function
•Production function is a technical relationship
between inputs and outputs.
•A general equation for production function can be
given as:
�=�??????
�,??????
�,??????
�,…??????
�
where : � is output and
??????
1,??????
2,??????
3,…??????
?????? are different types of inputs.
•It shows the maximum output that can be produced
with fixed amount of inputs and the existing
technology.

4. Inputs
•Inputs are commonly classified as fixed or variable.
•Fixed inputs: are those inputs whose quantity
cannot readily be changed when market conditions
indicate that an immediate adjustment in output is
required.
Examples: buildings, land and machineries etc.
•Variable inputs: are those inputs whose quantity
can be altered almost instantaneously in response to
desired changes in output.
Example: Unskilled labor.

5. Short run and Long run
•Short run: refers to a period of time in which
the quantity of at least one input is fixed.
–It is a time period which is not sufficient to change the
quantities of all inputs so that at least one input
remains fixed.
–Short run periods of different firms have different
durations.
–The short run period vary across firms, industries or
economic variables being studied.

6. Theory of production in the short run

•Long run: is that time period (planning
horizon) which is sufficient to change the
quantities of all inputs.

–Thus there is no fixed input in the long-run.

7. Theory of production in the short run

Assumptions:
1.Perfect divisibility of inputs and outputs
2.Limited substitution between inputs
3.Constant technology
4.Production that uses two inputs , one variable input, and one
fixed input
�=��,� =f(�), K being constant
Where:
–� is the output level
–� is the quantity of Labor used (variable input)
–� is the quantity of Capital (fixed input)
•The firm can increase output only by increasing the
amount of labor it uses.

8. Total, Average, and Marginal Product

•Total product (TP): is total amount of output that can
be produced by efficiently utilizing specific
combinations of the L (variable input) and K (fixed
input.)

•The total product curve: represents various levels of
output that can be obtained from efficient utilization
of various combinations of the variable input, and
the fixed input.

9. Total, Average, and Marginal Product

•Initially, as we combine more and more units of the
variable input with the fixed input, output continues
to increase.

•But, eventually if we employ more and more unit of
the variable input beyond the carrying capacity of the
fixed input, output tends to decline.

10. Total, Average, and Marginal Product

•In general, the TP function in the short-run follows a
certain trend:
–It initially increases at an increasing rate,
–then increases at a decreasing rate, reaches a
maximum point and
–eventually falls as the quantity of the variable input
rises.
•This tells us what shape a total product curve
assumes.
•TP curve is nearly S-shape.

11. Total, Average, and Marginal Product

Marginal Product (MP):
•is the change in output attributed to the addition of
one unit of the variable input to the production
process, other inputs being constant.
•In our case, the Marginal product of labor
(��
�)=
���
��
=
∆��
∆�

•MPL measures the slope of the TP curve at a given
point.

12. Total, Average, and Marginal Product

•In the short run, the MP of the variable input
–first increases, reaches its maximum and
– then decreases to the extent of being negative.
Average Product (AP):
• is the level of output that each unit of input produces,
on average.
??????�
�=
����� �������
������ �� ����� �����
=
��
�
=
�
�

•The average product of labor(??????�
�) first increases with the
number of labor (i.e. TP increases faster than the increase in
labor), and eventually it declines.

13. TP, AP and MP
.
��
�
??????�
�
��
�(??????��??????��??????� ??????����)
��� ���
�(??????��??????��??????� ??????����
��
�,??????�
�
�
� �
�
��
�
��
�
��
�
�
�
�

14. Relation Ship between ��
� ????????????� ??????�
�
��=��, � ����� ��������.
��
??????=
??????????????????
??????�
=
????????????(�)
??????�
and ��
??????=
????????????
�
=
??????(??????)
??????

Slope of ��
??????=
??????(????????????
�
)
??????�
=
??????
??????(�)
�
??????�
=
????????????(??????)
????????????
∗
1
�
+��∗
??????(�
−1
)
??????�

=
��(�)
��
∗
1
??????
−
????????????
??????
2=
���
��
∗
1
??????
−
????????????
??????
∗
1
??????

=
1
�
���
��
−
????????????
??????
∗ but
���
��
=��
?????? ���
��
�
=��
??????
Slope of ��
?????? =
1
??????
��
??????−��
??????=
�??????
�
−????????????
�
�

15. Relation Ship between ��
� ????????????� ??????�
�
Slope of ��
?????? =
1
??????
��
??????−��
??????=
�??????
�
−????????????
�
�

•This shows:
–When ��
�>??????�
�, Slope of ??????�
� is positive (��
?????? rises)
–When ��
�=??????�
�, Slope of ??????�
� is zero (��
?????? is at its
maximum).
–When ��
&#3627408499;<??????&#3627408503;
&#3627408499;, Slope of ??????&#3627408503;
&#3627408499; is negative (&#3627408436;&#3627408451;
?????? falls)

•Thus, the &#3627408448;&#3627408451;
?????? curve passes through the maximum of the &#3627408436;&#3627408451;
??????
curve from above.
Generally,
–When APL is increasing, MPL > APL.
–When APL is at its maximum, MPL = APL.
–When APL is decreasing, MPL < APL.

16. Examples
Example 1: Suppose that the short-run production
function of certain cut-flower firm is given by:
&#3627408504;=&#3627409362;&#3627408498;&#3627408499; −&#3627409358;.&#3627409364;&#3627408498;
&#3627409360;
−&#3627409358;.&#3627409359;&#3627408499;
&#3627409360;

Where: Q is quantity of cut-flower produced,
L is labor input & K is fixed capital input (K=5).

a)Determine the average product of labor (APL) function.
b)At what level of labor does the total output of cut-flower
reach the maximum?
c)What will be the maximum achievable amount of cut-
flower production?

17. Examples
Example 2: The production function for a firm is
given by
&#3627408452;=6&#3627408447;
2
−0.4&#3627408447;
3
.
a)At what units of labor is output maximum?
b)At what units of labor is the AP
L maximum?
c)At what unit of labor is MP
L maximum?

18. Exercise
Suppose that the short-run production function for a
firm during a particular period is represented by a
certain cut-flower firm is given by:
&#3627408504;=&#3627408519;&#3627408498;,&#3627408499;=&#3627409364;&#3627409358;&#3627409358;&#3627408498;
&#3627409360;
&#3627408499;
&#3627409360;
−&#3627408498;
&#3627409361;
&#3627408499;
&#3627409361;

where Q is quantity produced, L is labor input and K is
fixed capital input (K=10).
a) Determine the MPL, and APL functions.
b) At what units of labor is output maximum?
b) At what units of labor is the AP
L maximum?
C) At what unit of labor is MP
L maximum?

19. The Law of Variable Proportions
(Law of Diminishing Returns(LDR)
Assuming :
•Fixed technology, thus the techniques of production do not
change.
•All units of the variable input (labor in our case) has the equal
quality
–(same innate ability, education, training, and work
experience)

•The law states that as successive units of a variable input (say
labor) are added to a fixed input (capital or land), beyond some
point, the extra or marginal product that can be attributed to each
additional unit of the variable resource will decline.
–This law is a short run law of production
–The law starts to operate after the MP curve reaches its maximum.

20. Stages of Production
.
&#3627408500;&#3627408503;
&#3627408499;
??????&#3627408503;
&#3627408499;
&#3627408507;&#3627408503;
&#3627408447;(??????&#3627408462;&#3627408479;??????&#3627408462;&#3627408463;??????&#3627408466; ??????&#3627408475;&#3627408477;&#3627408482;&#3627408481;)
&#3627408502;&#3627408534;&#3627408533; &#3627408529;&#3627408534;&#3627408533;
&#3627408447;(??????&#3627408462;&#3627408479;??????&#3627408462;&#3627408463;??????&#3627408466; ??????&#3627408475;&#3627408477;&#3627408482;&#3627408481;
&#3627408500;&#3627408503;
&#3627408499;,??????&#3627408503;
&#3627408499;
&#3627408499;
&#3627409359; &#3627408499;
&#3627409361;
&#3627408507;&#3627408503;
&#3627409361;
&#3627408507;&#3627408503;
&#3627409360;
&#3627408507;&#3627408503;
&#3627409359;
&#3627408514;
&#3627408499;
&#3627409360;
?????? ????????????I ????????????

21. Stages of Production
&#3627408506;&#3627408533;&#3627408514;&#3627408520;&#3627408518;−??????: ranges from the origin to the point of equality
of the &#3627408436;&#3627408451;
?????? and &#3627408448;&#3627408451;
??????.

&#3627408506;&#3627408533;&#3627408514;&#3627408520;&#3627408518;−????????????: starts from the point of equality of &#3627408436;&#3627408451;
?????? and
&#3627408448;&#3627408451;
?????? and ends at a point where &#3627408448;&#3627408451;
?????? is equal
to zero.
&#3627408506;&#3627408533;&#3627408514;&#3627408520;&#3627408518;−??????????????????: covers the range of labor over which the MPL
is negative.
•Now, which stage of production is efficient and preferable?
•The efficient region of production is Stage - II.

22. Theory of costs in the short run
Basic Concepts:

•To produce goods and services, firms need factors of production or
simply inputs.
Cost: is the monetary value of inputs used in the production of
an item.
•We can identify two types of cost of production:
1.Social Cost : is the cost of producing an item to the society.
2.Private Cost: This refers to the cost of producing an item to the
individual producer.

•Private cost of production can be measured in two ways:
1.Accounting Cost
2.Economic Cost

23. Theory of costs in the short run
1.Accounting cost: is the monetary value of all
purchased inputs used in production.
•It ignores the cost of non-purchased (self-owned)
inputs.
•It considers only direct expenses such as:
–wages/salaries,
–cost of raw materials,
–depreciation allowances,
– interest on borrowed funds and
–utility expenses (electricity, water, telephone, etc.).
•These costs are said to be explicit costs.
•Explicit costs are out of pocket expenses for the
purchased inputs.

24. Theory of costs in the short run
2.Economic cost: is the monetary value of all inputs
used in production.
•It considers the monetary value of all inputs (purchased
and non-purchased).
•Calculating economic costs will be difficult since there are
no direct monetary expenses for non-purchased inputs.
•The monetary value of non-purchased inputs is obtained
by estimating their opportunity costs in monetary terms.
•The estimated monetary cost for non-purchased inputs is
known as implicit cost.
•Therefore, economic cost is given by the sum of implicit
cost and explicit cost.

25. Theory of costs in the short run
Profit:
•Economists use the term “profit”‖ differently from
the way accountants use it.

For the Accountant:
Accounting Profit = Total Revenue – Accounting Cost
= Total Revenue – Explicit Cost

For the Economist:
Economic Profit = Total Revenue – Economic cost
= Total Revenue – (Explicit cost + Implicit cost )

26. Total Costs in the Short Run
•Cost function shows the algebraically relation between
the cost of production and various factors which
determine it.
•Among others, the cost of production depends on
–the level of output produced
–technology of production
–prices of factors, etc. Symbolically,
??????=&#3627408519;(&#3627408504;,&#3627408507;,&#3627408503;
&#3627408522;)
-Where: ??????- is total cost of production
&#3627408452;- is the amount of output and
&#3627408455; – is the technology of production.
&#3627408503;
&#3627408522; – is the price of input ??????

27. Total Costs in the Short Run
•Ceteris paribus, the Cost function can be written as
?????? = &#3627408519; (&#3627408504;)
•In the short run, total costs (TC) can be broken down
into two:
–Total fixed costs (TFC) and
–Total variable cost (TVC).

Thus, &#3627408507;?????? = &#3627408507;???????????? + &#3627408507;????????????

28. Total Costs in the Short Run
•TFC: Costs associated with fixed factors such as cost
of acquiring a plant (building), cost of machineries
and provision for depreciation of machineries.
–are costs which don’t vary with the level of output.

•TVC: Costs associated with the variable factors such
as cost of raw materials and cost of labor.
–include all costs which directly vary with the level of
output.

29. Total Cost Curves in the Short Run
.

&#3627408455;&#3627408438;
&#3627408455;??????&#3627408438;
&#3627408455;??????&#3627408438; &#3627408455;??????&#3627408438;
&#3627408452; &#3627408452; &#3627408452;
&#3627408438;
&#3627408438;
&#3627408438;
&#3627408455;??????&#3627408438;
????????????&#3627408468;.&#3627408436;
????????????&#3627408468;.&#3627408437;
????????????&#3627408468;.&#3627408438;

30. Total Cost Curves in the Short Run
•TFC curve:
–TFC is denoted by a straight line parallel to the output axis.
–This is because such costs do not vary with the level of
output.
•TVC curve:
–The total variable cost of a firm has an inverse S-shape due
to the law of variable proportions in production.
•TC curve:
–is obtained by vertically adding TFC and TVC at each
–level of output. When the level of output is zero, TVC is
also zero which implies TC = TFC.

31. Per Unit Costs in the Short Run
•From total costs functions we can derive per-unit costs.
•The per-unit costs are even more important in the short
run analysis of the firm.
Average Fixed Cost (AFC) :
–AFC is total fixed cost per unit of output.
–AFC is found by dividing the TFC by the level of output.
&#3627408436;??????&#3627408438;=&#3627408455;??????&#3627408438;/&#3627408452;
–Graphically the AFC is a rectangular hyperbola, showing at all its
points the same magnitude, that is, the level of TFC .
–The AFC curve is continuously decreasing curve, decreases at a
decreasing rate but can never be zero.
–Thus, AFC gets closer and closer to zero as the level of output
increases, because a fixed amount of cost is being divided by
increasing level of output.

32. $/&#3627408528;&#3627408534;&#3627408533;&#3627408529;&#3627408534;&#3627408533; &#3627408534;&#3627408527;&#3627408522;&#3627408533;
&#3627408436;??????&#3627408438;(&#3627408504;)
&#3627408504; 0
&#3627408436;??????&#3627408438;(&#3627408504;)  0 &#3627408462;&#3627408480; &#3627408504; 
??????????????????=
&#3627408507;????????????
&#3627408504;

??????&#3627408522;&#3627408520;. AFC graph

33. Per Unit Costs in the Short Run
Average Variable Cost( AVC):
–Average variable cost is total variable cost per unit of output.
–AVC is obtained by dividing the TVC with the corresponding level
of output:
??????????????????=&#3627408507;????????????/&#3627408504;
–Graphically, the AVC at each level of output is derived from the
slope of a line drawn from the origin to the point on the TVC
curve corresponding to the particular level of output.
–The short run AVC falls initially, reaches its minimum, and then
starts to increase.
–Hence, the AVC curve has U-shape and the reason behind is the
law of variable proportions.

34. Derivation of SAVC from TVC




&#3627408438;
????????????&#3627408468;.&#3627408455;??????&#3627408438;
&#3627408452;
&#3627408438;
????????????&#3627408468;. &#3627408454;&#3627408436;??????&#3627408438;.
&#3627408455;??????&#3627408438;
a
b c
d
a
b
c d
&#3627408454;&#3627408436;??????&#3627408438;
&#3627408504;
&#3627409359; &#3627408504;
&#3627409360; &#3627408504;
&#3627409361; &#3627408504;
&#3627409362; &#3627408504;
&#3627409359; &#3627408504;
&#3627409360; &#3627408504;
&#3627409361; &#3627408504;
&#3627409362; &#3627408452;

35. Per Unit Costs in the Short Run
Average Total Cost( ATC or AC):
–ATC is the total cost per unit of output.
–The ATC or AC is obtained by dividing the TC by the
corresponding level of output .
??????&#3627408507;??????=
&#3627408507;??????
&#3627408504;
=
&#3627408507;????????????+&#3627408507;????????????
&#3627408504;
=??????????????????+??????????????????
–Thus, ATC can also be given by the vertical sum of AVC and AFC.
–Alternatively, the AC curve can also be derived in the same way
as the SAVC curve.
–The AC curve is U-shaped because of the law of variable
proportions.

36. Derivation of SATC from TC




&#3627408438;
????????????&#3627408468;.&#3627408455;&#3627408438;
&#3627408452;
&#3627408438;
????????????&#3627408468;. &#3627408454;&#3627408436;&#3627408455;&#3627408438;.
&#3627408455;&#3627408438;
a
b
c
d
a
b
c d
&#3627408454;&#3627408436;&#3627408455;&#3627408438;
&#3627408504;
&#3627409359; &#3627408504;
&#3627409360; &#3627408504;
&#3627409361; &#3627408504;
&#3627409362; &#3627408504;
&#3627409359; &#3627408504;
&#3627409360; &#3627408504;
&#3627409361; &#3627408504;
&#3627409362; &#3627408452;

37. Per Unit Costs in the Short Run
Marginal Cost ( MC):
–The Marginal cost is defined as the additional cost that the
firm incurs to produce one extra unit of the output.
–In other words, it is the change in total cost which results
from a unit change in output.
&#3627408396;??????=
&#3627408517;&#3627408507;??????
&#3627408517;&#3627408504;
=
&#3627408517;(&#3627408507;????????????+&#3627408507;????????????)
&#3627408517;&#3627408504;
=
&#3627408517;&#3627408507;????????????
&#3627408517;&#3627408504;

–In fact, as can be seen from above MC is also a change in
TVC with respect to a unit change in the level of output.
–Graphically, the MC is slope of the TC curve (or equivalently
the slope of the TVC curve).

38. Per Unit Costs in the Short Run
Marginal Cost ( MC):
–Given the inverse S-shaped TC (or TVC) curve, the MC curve
will be U-shaped.
–Thus given inverse S-shaped TC or TVC curve, the slope of
the TC or TVC curve (i.e. MC) initially decreases, reaches its
minimum and then starts to rise.
–From this, we can logically infer that the reason for the U-
shapedness of MC is also the law of variable proportions.
–In summary, AVC, AC and MC curves are all U-shaped due
to the law of variable proportions.

39. Per Unit Costs in the Short Run
•The simplest total cost function which would incorporate
the law of variable proportions is the cubic polynomial of
the following form.
&#3627408507;&#3627408516;=&#3627408515;
&#3627408528;+&#3627408515;
&#3627409359;&#3627408504;−&#3627408515;
&#3627409360;&#3627408504;
&#3627409360;
+&#3627408515;
&#3627409361;&#3627408504;
&#3627409361;


–where &#3627408452; - is the level of output and &#3627408463;0,&#3627408463;1,&#3627408463;2 &&#3627408463;3 –
are none zero constants.
&#3627408507;????????????=&#3627408515;
&#3627408528;, ??????????????????=
&#3627408515;&#3627408528;
&#3627408504;

&#3627408507;????????????=&#3627408515;
&#3627409359;&#3627408504;−&#3627408515;
&#3627409360;&#3627408504;
&#3627409360;
+&#3627408515;
&#3627409361;&#3627408504;
&#3627409361;

??????????????????=&#3627408515;
&#3627409359;−&#3627408515;
&#3627409360;&#3627408504;+&#3627408515;
&#3627409361;&#3627408504;
&#3627409360;

??????&#3627408507;??????=??????????????????+??????????????????=
&#3627408515;
&#3627408528;
&#3627408504;
+&#3627408515;
&#3627409359;−&#3627408515;
&#3627409360;&#3627408504;+&#3627408515;
&#3627409361;&#3627408504;
&#3627409360;

40. The Relationship between AVC, ATC and MC
•Given &#3627408436;&#3627408455;&#3627408438; = &#3627408436;??????&#3627408438; + &#3627408436;??????&#3627408438;, AVC is part of the ATC.
• Both AVC and ATC are U– shaped however, the minimum
point of ATC occurs to the right of the minimum point of
the AVC. Why?
•This is due to the fact that ATC includes AFC which
continuously decreases as the level of output increases.
•The AVC approaches the ATC asymptotically as output
increases.
•The MC curve passes through the minimum points of
both ATC and AVC curves.

41. The Relationship between AVC, ATC and MC


&#3627408448;&#3627408438;
????????????
????????????&#3627408438;
●
●
&#3627408504;
&#3627409359; &#3627408504;
&#3627409360;
&#3627408452;(&#3627408476;&#3627408482;&#3627408481;&#3627408477;&#3627408482;&#3627408481;)
&#3627408438;&#3627408476;&#3627408480;&#3627408481;

42. The Relationship between AVC, ATC and MC
The relationship between AC and MC
&#3627408454;??????&#3627408476;&#3627408477;&#3627408466; &#3627408476;&#3627408467; ????????????=
&#3627409359;
&#3627408504;
&#3627408500;??????−???????????? , how?
Derivation: ????????????=
&#3627408507;??????
&#3627408504;
=
&#3627408507;????????????
&#3627408504;
+
&#3627408507;????????????
&#3627408504;
,
??????????????????
??????&#3627408504;
=&#3627408454;??????&#3627408476;&#3627408477;&#3627408466; &#3627408476;&#3627408467; &#3627408436;&#3627408438;

&#3627408465;????????????
&#3627408465;&#3627408504;
=−
&#3627408507;????????????
&#3627408504;
&#3627409360;
−
&#3627408507;????????????
&#3627408504;
&#3627409360;
+
&#3627409359;
&#3627408504;
∗
&#3627408517;(&#3627408507;????????????)
&#3627408517;&#3627408504;


&#3627408465;????????????
&#3627408465;&#3627408504;
=−
&#3627409359;
&#3627408504;
&#3627408507;????????????
&#3627408504;
−
&#3627409359;
&#3627408504;
&#3627408507;????????????
&#3627408504;
+
&#3627408500;??????
&#3627408504;


&#3627408465;????????????
&#3627408465;&#3627408504;
=
&#3627409359;
&#3627408504;
&#3627408500;??????−
&#3627408507;????????????
&#3627408504;
+
&#3627408507;????????????
&#3627408504;

43. The Relationship between AVC, ATC and MC
&#3627408465;????????????
&#3627408465;&#3627408504;
=
&#3627409359;
&#3627408504;
&#3627408500;??????−
&#3627408507;????????????
&#3627408504;
+
&#3627408507;????????????
&#3627408504;



&#3627408507;&#3627408521;&#3627408534;&#3627408532;,&#3627408506;&#3627408525;&#3627408528;&#3627408529;&#3627408518; &#3627408528;&#3627408519; ????????????=
&#3627409359;
&#3627408504;
&#3627408500;??????−????????????

•In a similar fashion, We can also show that
&#3627408506;&#3627408525;&#3627408528;&#3627408529;&#3627408518; &#3627408528;&#3627408519; ??????????????????=
&#3627408465;??????????????????
&#3627408465;&#3627408504;
=
&#3627409359;
&#3627408504;
&#3627408500;??????−??????????????????

????????????

44. The Relationship between AVC, ATC and MC
&#3627408507;&#3627408521;&#3627408534;&#3627408532;, &#3627408506;&#3627408525;&#3627408528;&#3627408529;&#3627408518; &#3627408528;&#3627408519; ????????????=
&#3627409359;
&#3627408504;
&#3627408500;??????−????????????
Therefore,
•when &#3627408500;??????<????????????, the slope of &#3627408436;&#3627408438; is negative, i.e. &#3627408436;&#3627408438; curve is
decreasing (initial stage of production).
•When &#3627408500;?????? = ????????????, the slope of AC is zero, i.e. the AC curve is at
its minimum point. It means, MC curve passes through the
minimum of the AC curve
•When &#3627408500;?????? >????????????, the slope of &#3627408436;&#3627408438; is positive, i.e. the AC curve
is increasing (after optimal combination of fixed and variable
inputs).

45. The Relationship between AVC, ATC and MC
&#3627408506;&#3627408522;&#3627408526;&#3627408522;&#3627408525;&#3627408514;&#3627408531;&#3627408525;??????, &#3627408506;&#3627408525;&#3627408528;&#3627408529;&#3627408518; &#3627408528;&#3627408519; ??????????????????=
&#3627409359;
&#3627408504;
&#3627408500;??????−??????????????????

Therefore,
•when &#3627408500;??????<??????????????????, the slope of &#3627408436;??????&#3627408438; is negative, i.e. &#3627408436;??????&#3627408438; curve
is decreasing.
•When &#3627408500;?????? = ??????????????????, the slope of AVC is zero, i.e. the AVC curve
is at its minimum point. It means, MC curve passes through the
minimum of the AVC curve.
•When &#3627408500;?????? >??????????????????, the slope of &#3627408436;??????&#3627408438; is positive, i.e. the AVC
curve is increasing.

46. Examples
Example 1: Suppose the short run cost function of a firm is given
by:
&#3627408507;?????? = &#3627409359;&#3627409358;&#3627409358; + &#3627409363;&#3627409358;&#3627408504; − &#3627409363;&#3627408504;
&#3627409360;
+ &#3627409358;.&#3627409360;&#3627408504;
&#3627409361;


a)Find the expression of &#3627408507;???????????? & &#3627408507;????????????
b)Derive the expressions of ??????????????????,??????????????????,???????????? &#3627408462;&#3627408475;&#3627408465; &#3627408500;??????
c)Find the levels of output that minimize &#3627408500;?????? and
?????????????????? and then find the minimum values of &#3627408448;&#3627408438;
and &#3627408436;??????&#3627408438;

47. Examples
Example 2: Suppose the short run cost function of a firm is
given by: &#3627408455;&#3627408438;=2&#3627408452;
3
−2&#3627408452;
2
+&#3627408452;+10.
a)Find the expression of TFC & TVC
b)Derive the expressions of AFC, AVC, AC and MC
c)Find the levels of output that minimize MC and AVC and
then find the minimum values of MC and AVC

Example 3: TC = 50 + 2Q – 3Q
2
+ Q
3
a)Find the expression of TFC, TVC, AFC, AVC, ATC and MC.
b)At what level of output does AVC and MC reache their
respective minimum.

48. The Relationship b/n Short run Production
and Cost curves
•Cost function is derived from production function.
•Now, lets see the important relation that per unit
production curves (i.e. AP and MP of the variable
input) and per unit cost curves (i.e. AVC and MC)
have.
•The relationship is that the short run per unit costs
are the mirror reflection (about the x-axis) of the
short run production curves.
•That is, the short run AVC curve is the mirror
reflection of the short run AP curve of the variable
input.

49. The Relationship b/n Short run Production
and Cost curves
•When AP of the variable input increases, AVC
decreases; when AP reaches its maximum, the AVC
reaches its minimum point, and finally when AP starts
to fall, the AVC curve starts to rise.
• The same relationship exists between the short run
MP of variable input curve and the MC curve.
•Let &#3627408504;=&#3627408519;(&#3627408498; ,&#3627408499;), Where K is fixed input and L is
Variable Input. And let &#3627408531; is Price of K and ?????? is price
of L, which is constant.
• So, Total cost &#3627408507;??????= &#3627408531;&#3627408498; +??????&#3627408499;

50. The Relationship Between ??????&#3627408503; and ?????????????????? ??????&#3627408430;&#3627408427;&#3627408431;&#3627408414;&#3627408428;
•Total cost &#3627408507;??????= &#3627408531;&#3627408498; +??????&#3627408499;,
where &#3627408507;????????????=??????&#3627408499;
&#3627408436;??????&#3627408438;=
&#3627408507;????????????
&#3627408504;
=
??????&#3627408499;
&#3627408504;
=
??????
&#3627408504;
&#3627408499;

but,
&#3627408504;
&#3627408499;
=??????&#3627408503;
&#3627408499;
•Thus, ??????????????????=
??????
??????&#3627408503;&#3627408499;

Hence, AVC and AP
L are inversely related.

51. The Relationship Between M&#3627408503; and M?????? ??????&#3627408430;&#3627408427;&#3627408431;&#3627408414;&#3627408428;
•Total cost &#3627408507;??????= &#3627408531;&#3627408498; +??????&#3627408499;,
where &#3627408507;????????????=??????&#3627408499;
&#3627408396;??????=
&#3627408517;&#3627408507;??????
&#3627408517;&#3627408504;
=
&#3627408517;&#3627408507;????????????
&#3627408517;&#3627408504;
=
&#3627408517;(??????&#3627408499;)
&#3627408517;&#3627408504;
=??????
&#3627408517;&#3627408499;
&#3627408517;&#3627408504;
=
??????
&#3627408517;&#3627408504;
&#3627408517;&#3627408499;


&#3627408396;??????=
??????
&#3627408517;&#3627408504;
&#3627408517;&#3627408499;

, but
&#3627408517;&#3627408504;
&#3627408517;&#3627408499;
=&#3627408500;&#3627408503;
&#3627408499;
Thus, &#3627408396;&#3627408438;=
??????
&#3627408500;&#3627408503;
&#3627408499;

Hence, &#3627408500;?????? and &#3627408500;&#3627408503;
&#3627408499; are inversely related.

52. The Relationship Between Production & Cost ??????&#3627408430;&#3627408427;&#3627408431;&#3627408414;&#3627408428;


&#3627408500;&#3627408503;
&#3627408499;
??????&#3627408503;
&#3627408499;
&#3627408447;(??????&#3627408462;&#3627408479;??????&#3627408462;&#3627408463;??????&#3627408466; ??????&#3627408475;&#3627408477;&#3627408482;&#3627408481;)
&#3627408500;&#3627408503;
&#3627408499;,??????&#3627408503;
&#3627408499;
&#3627408499;
&#3627409359; &#3627408499;
&#3627409360; &#3627408499;
&#3627409361;
&#3627408448;&#3627408438;
&#3627408436;??????&#3627408438;
&#3627408504;(&#3627408502;&#3627408534;&#3627408533;&#3627408529;&#3627408534;&#3627408533;)
&#3627408504;
&#3627409359; &#3627408504;
&#3627409360; &#3627408504;
&#3627409361;
&#3627408500;??????, &#3627408436;??????&#3627408438;

53. Examples
Example 1: Given that the MP
L = 5, wage rate is
20 and AP
L is maximum at the point MP
L = 5,
find the AVC and MC.

Example 2: Given that the MP
L = 10 and AP
L = 5
and wage rate is 100
a) Find MC and AVC?
b)At what stage of production is the firm?

54. The Theory of Production and Cost



End of Chapter Four.