study material for management students

1. Managerial Economics Unit 3
Production Function and Cost Analysis
Dr. Kanchan Kumari
Assistant Professor: International Business/ Management

2. Production Function
• The production function is a mathematical equation determining the
relationship between the factors and quantity of input for
production and the number of goods it produces most efficiently. It
answers the queries related to marginal productivity, level of
production, and cheapest mode of production of goods.
• To convert any product raw material to finished goods is production.
• Raw material = output
• It refers to transformation of input in to output.

3. Product
• Product refers to volume of goods produced by a firm during a
specified period of time.
• TP- Total Product- Total Production
• AP- Average Product- average Production= (tp/q)(50/5)
• MP- Marginal Product- additional utility( extra benefit)

4. Graph Production Function

5. Production Functions and its Managerial Uses
• The managerial uses of the production function are manifold.
• Firstly, it is used to determine the optimal level of inputs to use in
order to produce a given level of output.
• This is important for managers as it allows them to minimize their
costs of production while maximizing their output.

6. Managerial uses
1. To find the most profitable rate of operation of the firm.
•2. To determine the optimum quantity of output to be produced and supplied.
•3. To determine in advance the cost of business operations.
•4. To locate weak points in production management to minimize costs.
•5. To fix the price of the product.
•6. To decide what sales channel to use.
•7. To have a clear understanding of alternative plans and the right costs involved in them.
•8. To have clarity about the various cost concepts.

7. Cobb Douglas Production Function
• The Cobb-Douglas production function is based on the empirical
study of the American manufacturing industry made by Paul H.
Douglas and C.W. Cobb. It is a linear homogeneous production
function of degree one which takes into account two inputs, labour
and capital, for the entire output of the .manufacturing industry.
• Cobb –Douglas production function is given byCharles Cobb and Paul
Douglas in1928
• Originally CD Production Function was applied not to be production
process of an individual farm. But whole manufacturing Industry

8. The Cobb-Douglas production function
• The Cobb-Douglas production function is expressed as:
• Q = ALa Cβ
• Q- Manufacturing Output
• L- Quantity of Labour
• K- Quantity of Capital
• A alfa and beta are positive constant( alfa and beta both grater than
0)

9. The Cobb-Douglas production function
• where Q is output and L and С are inputs of labour and capital respectively.
A, a and β are positive parameters where = a > O, β > O.
• The equation tells that output depends directly on L and C, and that part of
output which cannot be explained by L and С is explained by A which is the
‘residual’, often called technical change.
• The production function solved by Cobb-Douglas had 1/4 contribution of
capital to the increase in manufacturing industry and 3/4 of labour so that
the C-D production function is
• Q = AL3/4 C1/4
• which shows constant returns to scale because the total of the values of L
and С is equal to one: (3/4 + 1/4), i.e.,(a + β = 1) . The coefficient of
labourer in the C-D function measures the percentage increase in (Q that
would result from a 1 per cent increase in L, while holding С as constant.

10. Laws of Production
• The two laws of production are the Law of return to scale and the
Law of variable proportion. The rules of production define the
technologically feasible methods of increasing output. The output can
be grown in a variety of ways.
• Therefore, it has three clear stages: I – TPP increasing at an
increasing rate. II – TPP increasing at a diminishing rate. III – TPP
declining.

11. Three steps of Laws of Production

12. Laws of Production

13. Laws of Production

14. Empirical Estimates of Production and Cost
• Production function can be used to estimate the required capital
andlabour for various levels of output. For example, the capital and
labourrequired for an output level of 100 units will be given by100 =
1.01K0.
• The empirical estimation of long-run cost curves is even more difficult
than the. estimation of short-run cost curves. The objective of
estimating the long-run curves is. to determine the best scale of
plant for the firm to build in order to minimize the cost. of
producing the anticipated level of output in the long .

15. Empirical estimation technique
• Two popular empirical estimation techniques are: Expert judgment
technique and Delphi cost estimation. Expert judgment is one of the
most widely used estimation techniques.
• The procedure for estimation of cost function involves three steps.
First, the determinants of cost are identified. Second, the functional
form of the cost function is specified. Third, the functional form is
chosen and then the basic technique of regression is applied to
estimate the chosen functional form.

16. Short run and Long run average cost curves
• Long-run cost curves show the cost that a company faces in the long
run for producing a certain amount of output. While in the short run,
some of the factors of production are fixed, meaning that the firm
isn't flexible in changing these factors, their cost is also fixed.
• Long-run average total cost curves are U-shaped mainly because of
economies of scale, constant returns to scale, and diseconomies of
scale. Economies of scale explain the falling segment, while
diseconomies of scale explain the rising segment. The minimum
segment is explained by the constant returns to scale.

17. Short run Curves average cost
• Following are the cost concepts that are taken into consideration in the
short run:
1. Total Fixed Costs (TFC):
Refer to the costs that remain fixed in the short period. These costs do not
change with the change in the level of output. For example, rents, interest,
and salaries.
2. Total Variable Costs (TVC):
Refer to costs that change with the change in the level of production. For
example, costs incurred on purchasing raw material, hiring labor, and using
electricity. According to Ferguson, “total variable cost is the sum of amounts
spent for each of the variable inputs used” If the output is zero, then the
variable cost is also zero. These costs are also called prime costs, direct costs,
and avoidable costs.

18. Long run Vs short run costs
• Short run costs are costs that vary with variation in output. Short run
costs are the same as variable costs
• Long run costs are costs that are incurred on fixed assets like plant,
machinery, etc
• It is to be noted that running costs and depreciation of capital assets
are included under short run costs.

19. Fixed Costs(FC)
• Fixed Cost denotes the costs which do not vary with the level of
production. FC is independent of
• output.
• Eg: Depreciation, Interest Rate, Rent, Taxes
• Total fixed cost (TFC):
• All costs associated with the fixed input
• Average fixed cost per unit of output:
• AFC = TFC /Output

20. Variable Costs(VC)
• Variable Costs is the rest of total cost, the part that varies as you produce
more or less. It depends on
• Output.
• Eg: Increase of output with labour.
• Total variable cost (TVC):
• All costs associated with the variable input.
• Average variable cost- cost per unit of output: AVC =TVC/ Output
• Semi fixed Vs semi variable costs
• Semi variable costs are also called semi fixed costs. Semi fixed or semi
variable costs are fixed up to a given level and beyond that they vary.
• For example electricity bill, telephone bill etc…

21. Marginal Costs
• The additional cost incurred from producing an additional unit of
output:
• MC=∆ TC /∆ Output
• MC=∆ TVC /∆ Output
• Controllable Vs non controllable costs
• Controllable costs are those costs that can be influenced by the
action or authority of a plant or
• any other official.
• Some times few costs are not controllable like direct costs. For
example cost of raw material ,wages etc..

22. Economies of scale
• Economies of scale refer to the cost advantage experienced by a firm when
it increases its level of output. The advantage arises due to the inverse
relationship between the per-unit fixed cost and the quantity produced.
The greater the quantity of output produced, the lower the per-unit fixed
cost.
• Economies of scale also result in a fall in average variable costs (average
non-fixed costs) with an increase in output. This is brought about by
operational efficiencies and synergies as a result of an increase in the scale
of production.
• Economies of scale can be realized by a firm at any stage of the production
process. In this case, production refers to the economic concept of
production and involves all activities related to the commodity, not
involving the final buyer.

23. Economies of scale

24. Economies of Scale on Production Costs

25. Effects of Economies of Scale on Production
Costs
1.It reduces the per-unit fixed cost. As a result of increased production,
the fixed cost gets spread over more output than before.
2.It reduces per-unit variable costs. This occurs as the expanded scale
of production increases the efficiency of the production process.

26. Diseconomies of scale
• Diseconomies of scale happen when a company or business grows so
large that the costs per unit increase. It takes place when economies
of scale no longer function for a firm. With this principle, rather than
experiencing continued decreasing costs and increasing output, a firm
sees an increase in costs when output is increased.

27. Diseconomies of scale

28. Fig Elaboration
• The diagram below illustrates a diseconomy of scale. At point Q*, this
firm is producing at the point of lowest average unit cost. If the firm
produces more or less output, then the average cost per unit will be
higher. To the left of Q*, the firm can reap the benefit of economies
of scale to decrease average costs by producing more. To the right of
Q*, the firm experiences diseconomies of scale and an increasing
average unit cost.

29. Thank You
Dr. Kanchan Kumari