1. Unit -3: Production and Business Organization and Analysis
of Costs
2. Production function A production function relates physical
output of a production process to physical inputs or factors of
production. Production function The production function is the
relationship between the maximum amount of output that can be
produced and the inputs required to make that output. Put in other
way, the function gives for each set of inputs, the maximum amount
of output of a product that can be produced. It is defined for a
given state of technical knowledge (If technical knowledge changes,
the amount of output will change.)
3. A production function provides an abstract mathematical
representation of the relation between the production of a good and
the inputs used. A production function is usually expressed in this
general form: Q =f(L, K) where: Q = quantity of production or
output, L = quantity of labor input, and K = quantity of capital
input. The letter "f" indicates a generic, as of yet unspecified,
functional equation.
4. A production function can be expressed in a functional form
as the right side of where is the quantity of output and are the
quantities of factor inputs (such as capital, labour, land or raw
materials).
5. Short run and long run production function Economists define
the short run as being the time period when at least one of the
factors of production is completely fixed. so the relationship
between input and out put in short run is called short term
production function. In short run , factors of production are both
fixed and variable. Q= f(L,K) Where, q=production L= labour
(variable) K= capital (fixed) Note: here capital means
machinery
6. If the situation is like that ,to increase production(Q) we
can change only the labour(L) and the capital(K) is fixed, it will
be treated as short term production function. Example: ABC
corporation is used to export RMG products to Europe. It receives
an order for 10,000 pieces of RMG products whereby it should supply
as per order with in 2 weeks. In this situation the owner will not
establish new building or machinery. He will try to accomplish the
order by increasing the number of labour . so here we see labour is
variable and capital is fixed. The relationship between input and
output in this situation is called short term production
function.
7. Long run production function: Economists define the long-run
as being the time period when all the factors of production can be
changed. In long run all the factors of production are variable.
Q=f(L,K) Where, Q=production L= labour ,K= capital If the situation
is like that ,to increase production(q) we can change both the
labour(L) and capital(K) , it will be treated as long term
production function. Example: after the order for 10,000 piec es,
if the firm gets order on continuous basis, it will establish new
building and machinery. That means in long run both the labour and
capital can be changed. So the production function is called long
run production function.
8. Law of returns or law of variable proportions Law of
returns, in economics, the quantitative change in output of a firm
or industry resulting from a proportionate increase in one input ,
where other inputs are fixed. Law of returns can be 1.Law of
increasing return 2.Law of constant return 3.Law of diminishing
return. Note: law of returns is associated with short term ,
because in short term there are some fixed factors and returns to
scale is associated with long term ,because in long run all the
factors are variable.
9. Example Look at the table below. Let us assume that the firm
in question is making computer laser printers and they have four
machines in the factory (capital = 4). Capital Labour (L) Marginal
product (MP) Total product (TP) Average product (AP) 4 0 - 0 - 4 1
5 5 5.0 4 2 8 13 6.5 4 3 10 23 7.7 4 4 11 34 8.5 4 5 10 44 8.8 4 6
7 51 8.5 4 7 4 55 7.9 4 8 1 56 7.0 4 9 -2 54 6.0
10. Law of increasing return If the output of a firm increases
at a rate higher than the rate of increase in one input while
others factors are held constant, the production is said to exhibit
increasing returns to scale. A concept in economics that if one
factor of production (number of workers, for example) is increased
while other factors (machines and workspace, for example) are held
constant, the output will rise increasingly at the primary
stage.
11. Law of constant returns: If the output of a firm increases
at a rate equal to the the rate of increase in one input while
others factors are held constant, the production is said to exhibit
constant law of returns. A concept in economics that if one factor
of production (number of workers, for example) is increased while
other factors (machines and workspace, for example) are held
constant, the output will rise proportionately at the middle
stage.
12. Law of diminishing returns A concept in economics that if
one factor of production (number of workers, for example) is
increased while other factors (machines and workspace, for example)
are held constant, the output per unit of the variable factor will
eventually diminish. The law of diminishing returns is a classic
economic concept that states that as more investment in an area is
made, overall return on that investment increases at a declining
rate, assuming that all variables remain fixed.
13. Returns to Scale returns to scale, in economics, the
quantitative change in output of a firm or industry resulting from
a proportionate increase in all inputs. If the quantity of output
rises by a greater proportion e.g., if output increases by 2.5
times in response to a doubling of all inputsthe production process
is said to exhibit increasing returns to scale. Such economies of
scale may occur because greater efficiency is obtained as the firm
moves from small- to large-scale operations. Decreasing returns to
scale occur if the production process becomes less efficient as
production is expanded, as when a firm becomes too large to be
managed effectively as a single unit
14. Returns to Scale In economics, returns to scale describes
what happens when the scale of production increases over the long
run when all input levels are variable (chosen by the firm). There
are three stages in the returns to scale: increasing returns to
scale (IRS), constant returns to scale (CRS), and diminishing
returns to scale (DRS). Returns to scale vary between industries,
but typically a firm will have increasing returns to scale at low
levels of production, decreasing returns to scale at high levels of
production, and constant returns to scale at some point in the
middle .
15. Returns to Scale (1) Increasing Returns to Scale: If the
output of a firm increases at a rate higher than the rate of
increase in all inputs, the production is said to exhibit
increasing returns to scale. For example, if the amount of inputs
are doubled and the output increases by more than double, it is
said to be an increasing returns returns to scale. When there is an
increase in the scale of production, it leads to lower average cost
per unit produced as the firm enjoys economies of scale.
16. (3) Diminishing Returns to Scale: The term 'diminishing'
returns to scale refers to scale where output increases in a
smaller proportion than the increase in all inputs. For example, if
a firm increases inputs by 100% but the output decreases by less
than 100%, the firm is said to exhibit decreasing returns to scale.
In case of decreasing returns to scale, the firm faces diseconomies
of scale. The firm's scale of production leads to higher average
cost per unit produced. Increasing, constant, and diminishing
returns to scale describe how quickly output rises as inputs
increase
17. Explanation The figure 11.6 shows that when a firm uses one
unit of labor and one unit of capital, point a, it produces 1 unit
of quantity as is shown on the q = 1 isoquant. When the firm
doubles its outputs by using 2 units of labor and 2 units of
capital, it produces more than double from q = 1 to q = 3. So the
production function has increasing returns to scale in this range.
Another output from quantity 3 to quantity 6. At the last doubling
point c to point d, the production function has decreasing returns
to scale. The doubling of output from 4 units of input, causes
output to increase from 6 to 8 units increases of two units
only.
18. Iso product curve/Iso quant curve An iso quant may be
defined as a curve showing all the various combinations of two
factors that can produce a given level of output In Latin, "iso"
means equal and "quant" refers to quantity. This translates to
"equal quantity". The isoquant curve helps firms to adjust their
inputs to maximize output and profits. A graph of all possible
combinations of inputs that result in the production of a given
level of output.
19. An isocost line is a term used in economics. It shows all
combinations of inputs which cost the same total amount. An
isoquant is a firms counterpart of the consumers indifference
curve. An isoquant is a curve that show all the combinations of
inputs that yield the same level of output. Iso means equal and
quant means quantity. Therefore, an isoquant represents a constant
quantity of output. The isoquant curve is also known as an Equal
Product Curve or Production Indifference Curve or Iso-Product
Curve.
20. The concept of isoquants can be easily explained with the
help of the table given below: Table 1: An Isoquant Schedule
Combinations of Labor and Capital Units of Labor (L) Units of
Capital (K) Output of Cloth (meters) A 5 9 100 B 10 6 100 C 15 4
100 D 20 3 100
21. The above table is based on the assumption that only two
factors of production, namely, Labor and Capital are used for
producing 100 meters of cloth. Combination A = 5L + 9K = 100 meters
of cloth Combination B = 10L + 6K = 100 meters of cloth Combination
C = 15L + 4K = 100 meters of cloth Combination D = 20L + 3K = 100
meters of cloth The combinations A, B, C and D show the possibility
of producing 100 meters of cloth by applying various combinations
of labor and capital. Thus, an isoquant schedule is a schedule of
different combinations of factors of production yielding the same
quantity of output. An iso-product curve is the graphic
representation of an iso-product schedule.
22. Thus, an iso quant is a curve showing all combinations of
labor and capital that can be used to produce a given quantity of
output.
23. Isoquant Map An isoquant map is a set of isoquants that
shows the maximum attainable output from any given combination
inputs.
24. Isoquants Vs Indifference Curves Isoquants Vs Indifference
Curves An isoquant is similar to an indifference curve in more than
one way. The properties of isoquants are similar to the properties
of indifference curves. However, some of the differences may also
be noted. Firstly, in the indifference curve technique, utility
cannot be measured. In the case of an isoquant, the product can be
precisely measured in physical units. Secondly, in the case of
indifference curves, we can talk only about higher or lower levels
of utility. In the case of isoquants , we can say by how much IQ2
actually exceeds IQ1 (figure 2).
25. Properties of isoquants: Properties of isoquants: 1. Convex
to the origin. 2. Slopes downward to the right. 3. Never parallel
to the x-axis or y-axis. 4. Never horizontal to the x-axis or
y-axis. 5. No 2 curves intersect each other. 6. Each iso quant is a
part of an oval. 7. It cannot have a positive slope. 8. It cannot
be upward sloping
26. Each iso quant is oval-shaped An important feature of an
isoquant is that it enables the firm to identify the efficient
range of production consider figure 11
27. In economics an isocost line shows all combinations of
inputs which cost the same total amount. The isocost line is an
important component when analysing producers behaviour. The isocost
line illustrates all the possible combinations of two factors that
can be used at given costs and for a given producers budget. In
simple words, an isocost line represents a combination of inputs
which all cost the same amount. Iso cost curve:
28. Now suppose that a producer has a total budget of Rs 120
and and for producing a certain level of output, he has to spend
this amount on 2 factors A and B. Price of factors A and B are Rs
15 and Rs. 10 respectively.
29. Combinations Units of Capital Units of Labour Total
expenditure Price = 150Rs Price = 100 Rs ( in Rupees) A 8 0 120 B 6
3 120 C 4 6 120 D 2 9 120 E 0 12 120
30. What is isocost line? What is isocost line? An isocost line
is also called outlay line or price line or factor cost line. An
isocost line shows all the combinations of labour and capital that
are available for a given total cost to the producer. Just as there
are infinite number of isoquants, there are infinite number of
isocost lines, one for every possible level of a given total cost.
The greater the total cost, the further from origin is the isocost
line. The isocost line can be explained easily by taking a simple
example.
31. Let us examine a firm which wishes to spend Rs.100 on a
combination of two factors labour and capital for producing a given
level of output. We suppose further that the price of one unit of
labour is Rs. 5 per day. This means that the firm can hire 20 units
of labour. On the other hand if the price of capital is Rs.10 per
unit, the firm will purchase 10 units of capital. In the fig. 12.7,
the point A shows 10 units of capital used whereas point T shows 20
units of labour are hired at the given price. If we join points A
and T, we get a line AT. This AT line is called isocost line or
outlay line. The isocost line is obtained with an outlay of
Rs.100.
32. Let us assume now that there is no change in the market
prices of the two factors labour and capital but the firm increases
the total outlay to Rs.150. The new price line BK shows that with
an outlay of Rs.150, the producer can purchase 15 units of capital
or 30 units of labour. The new price line BK shifts upward to the
right. In case the firm reduces the outlay to Rs.50 only, the
isocost line CD shifts downward to the left of original isocost
line and remains parallel to the original price line. The isocost
line plays a similar role in the firms decision making as the
budget line does in consumers decision making. The only difference
between the two is that the consumer has a single budget line which
is determined by the income of the consumer. Where as the firm
faces many isocost lines depending upon the different level of
expenditure the firm might make. A firm may incur low cost by
producing relatively lesser output or it may incur relatively high
cost by producing a relatively large quantity.
33. Iso cost curve: Although similar to the budget constraint
in consumer theory, the use of the isocost line relates to cost-
minimization in production, as opposed to utility- maximization.
For the two production inputs labour and capital, with fixed unit
costs of the inputs, the equation of the isocost line is where w
represents the wage rate of labour, r represents the rental rate of
capital, K is the amount of capital used, L is the amount of labour
used, and C is the total cost of acquiring those quantities of the
two inputs
34. Least cost combination or producers equilibrium A rational
firm combines the various factors of production in such a way that
gives maximum output from minimum input and minimum cost. Such a
combination is referred to as the least cost combination.
35. 41 0 1 2 3 4 5 6 7 8 9 10 Capital,K(machinesrented) 2 4 6 8
10 Labor, L (worker-hours employed) a equ. W = $6; R = $3;C = $30
Choose the recipe where the desired isoquant is tangent to the
lowest isocost. C = $18 12 C = $36
36. Producers equilibrium or least cost combination producers
equilibrium is achieved with isoquants and isocost curves
37. Least Cost Decision Rule The least cost combination of two
inputs (i.e., labor and capital) to produce a certain output level
Occurs where the iso-cost line is tangent to the isoquant Lowest
possible cost for producing that level of output represented by
that isoquant This tangency point implies the slope of the isoquant
= the slope of that iso-cost curve at that combination of
inputs
38. Explanation
39. In figure 2, NM is the firms isocost line. Isoquants IQ1,
IQ2 and IQ3 represent different levels of output. Equilibrium is
attained at the point where the isoquant is tangent to the isocost
line. The isocost line NM sets the upper boundary for the purchase
of the inputs when outlay and input prices are given. Outlay is not
sufficient to move to IQ3. Likewise, the segments of isoquants
falling below the isocost line indicate under-utilization of his
outlay fully. Rationality on the part of the producer requires full
utilization of resources for optimization of output.
40. Points A and B also satisfy the tangency condition and they
lie within the reach of the producer. However, at these points the
firm remains at a lower isoquant IQ1, which yields a lesser level
of output than that on IQ2. Thus, E is the point of equilibrium
from where there is no tendency on the part of the producer to move
away. The firm will get its maximum output when it employs OL0
units of labor and OK0 units of capital.
41. Cost functionCost function is the relationship between
production cost and production. Generally an increase in production
rises the production cost and an decrease in production decreases
the production cost. C=f(q)
42. Short-run and long run cost function Short run cost
function: it is the relationship between production cost and
quantity of production in short term. Fixed cost exists in short
term. In short term- Total cost= total fixed cost + total variable
cost In short run some costs are not change in response to increase
or decrease in production. Those are fixed costs. Example: abc
corporation has 10 sewing machines and 10 workers . It receives an
order for 10,000 pieces of rmg products whereby it should supply as
per order with in 2 weeks. In this situation the owner will not
establish new machine. He will try to accomplish the order by
increasing the number of labours or workers. so here we see labour
is variable and capital is fixed.
43. Long run cost function: economists define the long-run as
being the time period when all the factors of production can be
changed. In long run all the costs of production are variable.
Relationship between variable costs and production in long run is
called long run production cost function. Short-run and long run
cost function
44. Concepts of cost Total cost is the cost incurred to produce
a quantity of output. A total cost schedule shows the total cost
for various output amounts Fixed Cost Fixed cost is the cost that
does not increase with the increase in production. Firms have to
commit costs for production capacity at the start of a period and
they have to incur these costs irrespective of the production
output. Such committed capacity costs are termed fixed cost for a
period. Variable Cost Variable cost is incurred when production is
there and it varies with the level of output.
45. Marginal Cost At each output level or at any output level,
marginal cost of production is the additional cost incurred in
producing one extra unit of output. Marginal cost can be calculated
as the difference between the total costs or producing two adjacent
output levels. The difference in variable cost of two adjacent
output levels also gives marginal cost, as fixed cost is constant
for the two levels. Marginal cost is a central economic concept
with a crucial important role to play in resource allocation
decisions by organizations.
46. Average Costs or Units Costs Average cost or unit cost is
the total cost divided by number of units produced. Average fixed
cost is total fixed cost divided by number of units produced. It
keeps on decreasing as output increases. Average variable cost is
total variable cost divided by number of units produced.
47. Relationship among total , average and marginal cost
Quantity (Q) Total cost(TC) Average cost(AC) Marginal cost (MC) 1
unit 2unit 3 unit 4 unit Tk.5 Tk.8 Tk.12 Tk.20 Tk.5 Tk.4 Tk.4 Tk.5
Tk.5 Tk.3 Tk.4 Tk.8
48. 1.When the production increases total cost also increases
but average cost and marginal cost decreases. That means total cost
increases in decreasing trend. 2.Marginal cost decreases at a rate
higher than the rate of decrease in average cost. 3.When the
average cost is lowest it is equal to marginal cost at this
production level. 4.From this level of production , if we increases
the production total cost will increase In increasing trend. 5.When
average cost increases, marginal cost increases at a higher rate
than AC.
49. Relationship between production function and cost function
1. when TP rises increasingly then TC rises decreasingly. Again
,when TP rises decreasingly then TC rises increasingly.
50. 2.If AP rises, MP rises at a higher rate. If AC decreases,
MC decreases at a higher rate. 3.When AP decreases , MP decreases
at a higher rate. when AC increases, MC increases at a higher rate.
4.MP curve intersects AP curve at a point where AP is highest. MC
curve intersects ac curve when ac is lowest.
51. Short-run Economists define the short run as being the time
period when at least one of the factors of production is completely
fixed. For example, for a particular company this might mean that
they have reached full capacity in a warehouse or at a factory
site. These short-run costs consist of both fixed and variable
costs. These are both defined fully in the Key Terms section.
Long-run In contrast, economists define the long-run as being the
time period when all the factors of production can be changed. So
in the example above, the company can now look to expand its
warehouse or factory capacity without any problems. Cost in short
and long run: Long run costs have no fixed factors of production,
while short run costs have fixed factors and variables that impact
production.
53. Concepts of revenue Meaning of Revenue: The amount of money
that a producer receives in exchange for the sale proceeds is known
as revenue. For example, if a firm gets Rs. 16,000 from sale of 100
chairs, then the amount of Rs. 16,000 is known as revenue. Revenue
refers to the amount received by a firm from the sale of a given
quantity of a commodity in the market. Revenue is a very important
concept in economic analysis. It is directly influenced by sales
level, i.e., as sales increases, revenue also increases.
54. Concept of Revenue The concept of revenue consists of three
important terms; Total Revenue, Average Revenue and Marginal
Revenue.
55. Total Revenue (TR): Total Revenue refers to total receipts
from the sale of a given quantity of a commodity. It is the total
income of a firm. Total revenue is obtained by multiplying the
quantity of the commodity sold with the price of the commodity.
Total Revenue = Quantity Price For example, if a firm sells 10
chairs at a price of Rs. 160 per chair, then the total revenue will
be: 10 Chairs Rs. 160 = Rs 1,600 Average Revenue (AR): Average
revenue refers to revenue per unit of output sold. It is obtained
by dividing the total revenue by the number of units sold. Average
Revenue = Total Revenue/Quantity For example, if total revenue from
the sale of 10 chairs @ Rs. 160 per chair is Rs. 1,600, then:
Average Revenue = Total Revenue/Quantity = 1,600/10 = Rs 160
56. Marginal Revenue (MR): Marginal revenue is the additional
revenue generated from the sale of an additional unit of output. It
is the change in TR from sale of one more unit of a commodity. MRn
= TRn-TRn-1 Where: MRn = Marginal revenue of nth unit; TRn = Total
revenue from n units; TR n-1 = Total revenue from (n 1) units; n =
number of units sold For example, if the total revenue realised
from sale of 10 chairs is Rs. 1,600 and that from sale of 11 chairs
is Rs. 1,780, then MR of the 11th chair will be: MR11 = TR11 TR10
MR11 = Rs. 1,780 Rs. 1,600 = Rs. 180
57. AR and Price are the Same: We know, AR is equal to per unit
sale receipts and price is always per unit. Since sellers receive
revenue according to price, price and AR are one and the same
thing. This can be explained as under: TR = Quantity Price (1) AR =
TR/Quantity (2) Putting the value of TR from equation (1) in
equation (2), we get AR = Quantity Price / Quantity AR = Price
58. Additional data Total cost (TC) is the sum of all the
different costs they incur when producing and selling their
product. Average cost (AC) is the total cost divided by the
quantity of goods: AC = TC/q Marginal cost (MC) is the extra cost
incurred in producing one more of the product. This can be found by
measuring the slope of the TC curve: MC = (change in TC)/(change in
q)
59. Costs can also be broken down into types of costs: Total
variable costs (TVC) refers to costs which vary with the amount of
goods a firm makes and sells. An example of TVC could be the cost
of chocolate chips, if the firm makes chocolate chip cookies. Total
fixed costs (TFC) refers to costs THAT a firm has to pay, no matter
how much or how little it produces. One example might be the
monthly rent on a store.
60. Added together, TVC and TFC are equal to TC: TVC + TFC = TC
TVC and TFC, when divided by q, yield average variable cost (AVC)
and average fixed cost (AFC): AVC = TVC/q AFC = TFC/q Added
together, AVC and AFC are equal to AC: AVC + AFC = AC
61. We can also find the marginal variable cost (MVC) and the
marginal fixed cost (MFC) by taking the slopes of the two curves.
Because fixed costs don't change with quantity, however, the MFC
will be 0: MVC = (change in TVC)/(change in q) MFC = (change in
TFC)/(change in q) = 0 Added together, MVC and MFC are equal to MC,
but since MFC is 0, the marginal cost is equal to the marginal
variable cost: MVC + MFC = MC MVC + 0 = MC MVC = MC
62. If we can combine a firm's costs and revenues, we can
calculate the firm's profits. Using the variables we have been
working with, we can represent profit as: Profit = TR - TC TR - TC
= q(AR - AC) = q(P - AC) Profit = q(P - AC)