Production.pdf

Session 11-12
PRODUCTION BASIC
CONCEPTS

 Production refers to the transformation of inputs or resources into
outputs of goods and services.
 Inputs are the resources used in the production of goods and services.
 Fixed inputs are those that cannot be readily changed during the time
period under considerations, except perhaps at greater expense.
 Variable inputs are those that can be varied easily and on very short
notice.
 The time period during which at least one input is fixed is called the
short run, while the time period when all inputs are variable is called
long run.
 The length of the long run (i.e., the time period required for all inputs to
be variable) depends on the industry.
BASIC CONCEPTS

 A production function is an equation, graph or table showing the
maximum output of a commodity that a firm can produce per
period of time with each set of inputs.
 Technology is assumed to be constant during the period of the
analysis.
 For simplicity, we assume that a firm produces only one type of
output(good or service) with two inputs, labour (L) and Capital
(K).
 The general equation of simple production function is
Q = f(L,K)
PRODUCTION FUNCTION

 By holding the quantity of one input constant and changing
the quantity used of the other input, we derive the Total
Product (TP) of the variable input.
 The marginal product (MP) of labour (MPL) is the change in
total product or extra output per unit change in labour used.
 MPL =∆TP/ ∆L
 Average product(AP) of labour (APL) equals total product
divided by the quantity of labour used.
 APL = TP/L
TOTAL, AVERAGE AND MARGINAL
PRODUCT

 The key to understanding the pattern of change in Q, AP, and MP
is the phenomenon known as the law of diminishing returns.
 This law states: As additional units of a variable input are
combined with a fixed input, at some point the additional output
(i.e., marginal product) starts to diminish.
 As the firm uses more and more units of the variable input with
the same amount of the fixed input, each additional unit of the
variable input has less and less of the fixed inputs to work with
and, after a point, the marginal product of the variable input
declines.
LAW OF DIMINISHING MARGINAL
RETURNS

 First Stage of Production – The range from the origin to the
point where APL is maximum.
 Second stage of Production – It extends from the point where
APL is maximum to the point where MPL is zero.
 Third stage of Production –The range over which MPL is
negative.
 A rational producer will operate in stage II where MP of both
factors is positive but declining.
 The precise point within stage II at which the rational
producer operates will depends on the prices of inputs and
outputs.
STAGES OF PRODUCTION

 Production function with two variable inputs can be
represented graphically by isoquants.
 An isoquant shows the various combinations of two inputs
(labour and capital) that the firm can use to produce a
specific level of output.
 A higher isoquant refers to a larger output, while a lower
isoquant refers to a smaller output.
 Ridge lines separates the relevant from the irrelevant portions
of the isoquants.
 Negatively sloped portion of the isoquants within the ridge
lines represents the relevant economic region of production.
 If the firm wants to reduce the quantity of capital that it uses
in production, it must increase the quantity of labour in order
to remain on the same isoquant.
PRODUCTION FUNCTION WITH TWO
VARIABLE INPUTS

 Isoquants are negatively sloped which means that if the firm
wants to reduce the quantity of capital it uses in production, it
must increase the quantity of labour in order to remain on the
same isoquant (i.e. to produce same level of output).
 The absolute value of slope of isoquant is called the marginal
rate of Technical substitution(MRTS).
 For any downward movement along the isoquant the MRTS is
given by -∆K/∆L
 The MRTS of labour is also given by MPL/MPk
 For any downward movement on a given isoquant, the loss in
output resulting from the use of less capital must be equal to
gain in resulting from the use of more labour in order to have
level of output.
 (∆L)*MPL = - (∆K)*(MPk)
 MPL/MPk = -∆K/∆L = MRTS
MARGINAL RATE OF TECHNICAL
SUBSTITUTION

 The isoquants are convex to the origin because as the firm
move down an isoquant and uses more labour and less
capital, the MPL declines and MPk increases (as the firm is in
second stage of production).
 With the MPL declining and the MPk rising as we down along
an isoquant, the MPL/MPk = MRTS will fall and thus isoquant
is convex to the origin.
CONT’D………

 An isocost lines shows the various combination of inputs that
a firm can purchase or hire at a given cost.
 Suppose that a firm uses only labour and capital in
production.
 The total cost or expenditure of the firm can be represented
by C = PL* L + Pk * K
 The slope of Budget line is represented by PL / Pk
 A different total cost by the firm would define a different but
parallel isocost line, while different relative input prices
would define an isocost line with a different slope.
OPTIMAL COMBINATION OF INPUTS

 The optimal combination of inputs needed for a firm to
minimize the cost of producing a given level of output or
maximize output for a given cost is at the tangency point of
an isoquant and an isocost.
OPTIMAL INPUT COMBINATION

 Returns to scale refers to the degree by which output changes
as a result of a given change in the quantity of all inputs used
in production.
 There are three types of returns to scale: constant, increasing
and decreasing.
 If the quantity of all inputs used in production is increased by
a given proportion, increasing returns to the scale if output
increases by a greater proportion; and decreasing returns to
scale if output increases by a smaller proportion.
 The production function = Q= f(L,K)
 If we multiply L and K by h and Q increases by λ
 λQ = f(hL, hK), we have constant, increasing or decreasing
depending upon λ= h, λ>h and λ<h respectively.
RETURNS TO SCALE

 Economies of scale (EOS) can be defined as aspects of
increasing scale that lead to falling long-run unit costs.
 Managers must understand their cost relationships to
recognize where to best exploit scale economies. As we have
seen, scale economies are not confined to production; they
are found in distribution, raising capital, advertising, and
most business processes.
ECONOMIES OF SCALE

 Technical Economies - These arise mainly from increased
specialization and indivisibilities. Larger firms can make use
of more specialized equipment and labour in the production
process.
 Managerial economies - Large firms find it easier to attract
and use more specialized managers, who are more skilled and
productive at performing specific managerial functions. large
firm may employ various managers within the marketing
department, for example in purchasing, advertising, sales,
public relations and market research.
SOURCES OF ECONOMIES OF SCALE

 Marketing economies - These relate mainly to obtaining bulk
discounts; by buying in bulk larger firms can often enable
their suppliers to obtain the technical economies of scale
above. These discounts can be related to buying raw
materials, components and for advertising. For example, if a
firm buys twice as much advertising space or time, the total
cost will usually less than double, thus, unit costs will fall
(assuming the firm sells twice as much).
 Financial economies - large firms can often borrow at a lower
interest rate, because they have a better credit rating,
representing a lower default premium. They have more
sources of finance; they can use the capital markets, for
example by issuing commercial paper, bonds and shares.
These forms of raising finance often involve a lower cost of
capital.
CONT’D…..

 Diseconomies of scale (DOS) are aspects of increasing scale
that lead to rising long-run unit costs.
 However, bigger is not always better. As plants, distribution
networks, or cruise ships get bigger, at some point managing
them gets harder. Increasing size eventually causes
diseconomies of scale: Average costs per unit of output
increase, usually because of the complexity of managing and
coordinating all the necessary activities.
 Technical diseconomies - Increased specialization can lead to
problems as well as benefits. Workers doing repetitive jobs
can suffer from low motivation, which reduces productivity
and increases the chance of industrial unrest.
DISECONOMIES OF SCALE

 Managerial diseconomies - Large firms are more difficult to
manage because communications tend to break down, both
vertically and horizontally. This creates inefficiencies as
cooperation and co-ordination within the firm suffer.
 Marketing diseconomies - Although larger firms can often gain
discounts in buying raw materials in bulk, there may be
offsetting disadvantages of buying inputs in large quantities. If
the firm is relying on local sources that are in limited supply,
the high demand may drive up the price of such inputs.
 Transportation diseconomies -Larger firms, particularly if they
only use one plant, may face additional transportation costs as
they try to increase the size of their market; the average
transportation distance of goods to customers will increase
CONT’D…….

 A production process exhibits economies of scope when the
cost of producing multiple goods is less than the aggregate
cost of producing each item separately.
 A convenient measure of such economies is
 Here, C(Q1, Q2) denotes the firm’s cost of jointly producing
the goods in the respective quantities; C(Q1) denotes the cost
of producing good 1 alone and similarly for C(Q2).
ECONOMIES OF SCOPE

 The products may use common processing facilities; for
example, different car models being produced at same plant.
 There may be cost complementarity, especially when there
are joint products or by-products.
 A single production process yields multiple outputs. For
example petrochemicals.
 Production of a principal good is accompanied by the
generation of unavoidable by-products. Often these by-
products can be fashioned into marketable products.
Sawdust is a valuable by-product of timber Production.
 Another source of economies is underutilization of inputs. An
airline that carries passengers may find itself with unused
cargo space; thus, it contracts to carry cargo as well as
passengers. In recent years, many public school systems
have made their classrooms available after hours for day-
care, after-school, and community programs.
SOURCES FOR ECONOMIES OF SCOPE

 An important source of economies of scope is transferable
know-how. Soft drink companies produce many types of
carbonated drinks, fruit juices, sparkling waters etc.
Presumably, experience producing carbonated beverages
confers cost advantages for the production of related drinks.
Insurance companies provide both insurance and investment
vehicles. In fact, whole-life insurance is a clever combination
of these two services in an attractive package.
 Scope economies also may be demand related. The
consumption of many clusters of goods and services is
complementary. Many large hospitals provide care in all major
medical specialties as well as in the related areas of
emergency medicine, mental-health care, geriatrics, and
rehabilitative therapy.
CONT’D…….

 It is also possible for a firm to experience diseconomies of
scope if it sells products that ‘clash’ with each other in some
way. An example would be EMI Records in the late 1970s
when they signed the punk rock band, who openly advocated
the use of violence. Since EMI was also marketing hospital
equipment at the time, it faced considerable criticism and
decided to drop the recording contract, at considerable cost.
 Many experts argue that relying on economies of scale—
producing dedicated systems that are economical but
inflexible—is no longer enough. The most successful firms in
the future will also exploit the flexibility provided by
economies of scope.
DISECONOMIES OF SCOPE

Q1 - In the Elwyn Company, the relationship between output (Q)
and the number of hours of skilled labor (S) and unskilled labor
(U) is
Q = 300S + 200U - 0.2S2 - 0.3U2
The hourly wage of skilled labor is $10, and the hourly wage of
unskilled labor is $5. The firm can hire as much labor as it
wants at these wage rates.
a. Elwyn’s chief engineer recommends that the firm hire 400
hours of skilled labor and 100 hours of unskilled labor. Evaluate
this recommendation.
b. If the Elwyn Company decides to spend a total of $5,000 on
skilled and unskilled labor, how many hours of each type of
labor should it hire?
DISCUSSION QUESTION

A consulting firm specializing in agriculture determines that the following combinations of hay
and grain consumption per lamb will result in a 25-pound gain for a lamb:
Pounds of Hay Pounds of Grain
40 130.9
50 125.1
60 120.1
70 115.7
80 111.8
90 108.3
110 102.3
130 97.4
150 93.8
a. The firm’s president wants to estimate the marginal product of a pound of grain in producing
lamb. Can he do so on the basis of these data ?
b. The firm’s president is convinced that constant returns to scale prevail in lamb production. If
this is true and hay and grain consumption per lamb are the only inputs, how much gain
accrues if the hay consumption per lamb is 100 pounds and the grain consumption per lamb
is 250.2 pounds?
QUESTION 2

c. What is the marginal rate of technical substitution of hay for
grain when between 40 and 50 pounds of hay (and between
130.9 and 125.1 pounds of grain) are consumed per lamb?
d. A major advance in technology occurs that allows farmers to
produce a 25-pound gain per lamb with less hay and grain than
the preceding table indicates. If the marginal rate of technical
substitution (at each rate of consumption of each input) is the
same after the technological advance as before, can you draw
the new isoquant corresponding to a 25-pound gain per lamb?
CONT’D……

PRACTICE QUESTIONS
1. According to data obtained by the U.S. Department of Agriculture, the
relationship between a cow’s total output of milk and the amount of
grain it is fed is as follows:
Amount of Grain Amount of Milk
(Pounds) (Pounds)
1,200 5,917
1,800 7,250
2,400 8,379
3,000 9,371
(This relationship assumes that forage input is fixed at 6,500 pounds of
hay.)
a. Calculate the average product of grain when each amount is used.
b. Estimate the marginal product of grain when between 1,200 and 1,800
pounds are fed, when between 1,800 and 2,400 pounds are fed, and
when between 2,400 and 3,000 pounds are fed.
c. Does this production function exhibit diminishing marginal returns?

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