1. Session 5: Production and Optimal Input Combinations
Business Economics
Session 5: Production and Optimal Input Combinations
Faculty: Sunitha Raju
Session Date:

2. Economics of Production Decisions
Decision Problem
what is the most efficient and cheapest means of producing quantities of output demanded by consumers
Efficient Production Decisions
- understanding the fundamentals of Production functions and Production process
- selection of Production technique and resource inputs
- relationship between technology, inputs and output
Contd…

3. Basis for Production Decisions
Economic principles underlying input-output relationships
Conditions for achieving peak production efficiency
Optimising the mix of resource inputs in short run and long run
Provides the foundation for estimating production costs and for selecting the most
economical production technique

4. Short Run Production Function
A production function defines all technical efficient input-output combinations
Any improvement in technology results in new production function.
Q= f (Xₐ, Xb, Xc, Xd, ………. Xn )
Q = f (L, K )
Q= f (Xₐ, Xb, │Xc, Xd ,………. Xn )

5. Basic Production Concepts
Defining Production Function
Production is physical transformation of input resources into goods & services
Inputs → Process → Output
Production function defines the technical relationship between production inputs and output
Contd…

6. Basic Production Concepts
2. Defining Production Process
A product can be produced by various techniques/methods of production
A method in which various inputs are combined is defined by a ‘Process’ or ‘Technique’ (P)
P1 P2 P3 L K
Output is same but methods of input combination differs.
Contd…

7. Basic Production Concepts
Technically efficient process
P1 P2
L 2 3
K 3 3
P1 is technically efficient as less L used compared to P2
L 2 1
K 3 4
P1 and P2 are not comparable and both considered as technically efficient
Contd…

8. Basic Production Concepts
Economic Efficient process
Amongst the technically efficient processes, the least cost process is defined as Economically efficient process.
Contd…

9. Basic Production Concepts
3. Inputs
Based on relationship with output, broadly categorise all inputs into
Fixed inputs (Capital) : same level of input irrespective of
output level (eg : Machinery)
Variable input (Labour) : Varies with output level
Q= f (L, K)
how do changes in input level influence the changes in
output level
Contd…

10. Basic Production Concepts
4. Long Run vs Short Run
Short run
When Production decisions are defined by a given capacity/capital/technology
Fixed and variable inputs together production determine production.
decision relates to how much to produce under a given capacity
Contd…

11. Basic Production Concepts
Long run
When Production decisions are not constrained by a given technology/capacity
Number of technological options exist. As such, no fixed inputs
Production decision relates to identifying optimum capacity/scale of operation.

12. Short Run Production Function
A production function defines all technical efficient input-output combinations
Any improvement in technology results in new production function.
eg: better equipment, productivity enhancing training

13. Short Run Production Decisions
1. Case of one variable input
Decision on output/input level
defining technically efficient level of output
defining economically efficient level of output
Together (a), (b) & (c) will determine ‘how much’ output (Q) to produce and ‘how much’ inputs to use.
Q = f (L, K )

14. ABC Company: Average and Marginal Products of Labour
Amount of Machine Tools (Fixed) (K)
Amount of Labour (L)
Total Output 5 1 12 2 27 3 42 4 56 68 6 76 7 8 74

15. Production Function : Economic Principles
1. Production Function Characteristics
Given a fixed amount of capital and managerial capability, behaviour of output with alternate amounts of variable input
Technically most feasible output
Operating below the production function-what does it mean?
Nature of production function defined by nature of change in output to changes in variable input
Alternate types of production function
General type of Production function (S shaped)
Total output and relationship with Average Product (APL) and Marginal Product (MPL)of Variable input
Principle of Diminishing Marginal returns

16. ABC Company: Average and Marginal Products of Labour
Amount of Machine Tools (Fixed)
Amount of Labour
Total Output
Average Products of Labour
Marginal Product of Labour 5 - 1 12
12.0 2 27
13.5 15 3 42
14.0 4 56 14 68
13.6 6 76
12.7 8 7
10.9 74
9.2 -2
Increasing returns to variable input
More than proportional increase to variable input
MP > AP
Decreasing returns to Variable input
Less than proportional increase to variable input
MP<AP
Maximum Output level
MP=0
Declining AP

17. Production Efficiency and Production Costs
Stages of Production
Stage I (Rising APL)
Increasing returns to variable input
Efficiency of input use rising (Fixed vs Variable input)
Efficiency of additional use of variable input positive
Stage II ( Declining APL, MPL Max Q )
Decreasing return to variable input (greater than zero)
Efficiency of fixed input rises (Output continues to rise)
Additional units of variable input adds to efficiency of fixed input but diminish the efficiency of variable input
Stage III (Declining Q)
Efficiency of fixed input reaches peak
More variable input leads to fall in Q
MPL negative

18. Production Efficiency and Production Costs
Optimum Stage of Production
From standpoint of Efficiency and Cost, Stage II is Optimum
Rate of variable input and fixed input use depends on prices
Profit maximising output in Stage II, assuming no change in output prices
In Stage I unit costs are declining. Hence, more inputs to produce output
Profit max output can occur in this stage when output prices are falling (Recession)
In Stage III, Output is declining. Hence irrational to operate

19. Total Marginal and Average Product Curves

20. P Q TR = D . Decision on how much Q to produce
As long as MPL is positive
Marginal Revenue Product (MRPL)
→ MRPL ≥ = PL
= MRPL =
= MRL . MPL = PL
Corresponds to
Q = 68 and L = 5 L P Q TR = D .

21. ABC Company: Average and Marginal Products of Labour
Assume MR = 5
PL = 60
Amount of Machine Tools (Fixed)
Amount of Labour
Total Output
Average Products of Labour
Marginal Product of Labour
MRPL 5 - 1 12
12.0 60 2 27
13.5 15 75 3 42
14.0 4 56 14 70 68
13.6 6 76
12.7 8 40 7
10.9 74
9.2 -2

22. Problem Solving 1
Tax Advisors Inc. has an office for processing tax returns in Pennsylvania. The following table shows how many tax returns are processed per hour as the number of CPA (Certified Public Accountants) employed increases
CPAs (L)
Tax returns processed / hour 1
0.2 2
1.0 3
2.4 4
2.8 5
3.0 6
2.7
1. Should the firm engage the 4th CPA? What should be the optimum number of CPAs to be engaged?
2. If the CPA’s earn $35 per hour and the revenue for each tax return processed is $100, should the firm employ the 4th CPA.

23. Production Decisions : Dimensions
1. Given a production function
Under conditions of recession (output prices are falling), a firm decides to produce where APL max
Under conditions of boom (output prices are rising), a firm produces until MRPL ≥ PL
Conceptualize the rising managerial salaries
Contd…

24. Production Decisions : Dimensions
2. Case of more than one variable input
Efficient combination of inputs
Methodology used is Isoquant

25. Short run Production Function : Efficient Combination of Inputs
Isoquants L1 6 10 24 31 42 39 5 12 28 36 40 40 4 12 28 36 40 36 3 10 23 33 36 33 2 7 18 28 30 28 1 3 8 12 14 12 L2 1 2 3 4 5 6
Isoquants show combination of two inputs that can produce
same level of outputs

26. Isoquants L1 6 10 24 31 42 39 5 12 40 40 28 36 4 12 40 36 28 36 3 10 23 33 33 36 2 7 18 28 30 28 1 3 8 12 14 12 L2 1 2 3 4 5
Isoquants show combinations of two inputs that can produce
same level of outputs

27. L1
Substitution between L1 and L2 is determined by marginal productivities of L1 and L2
Marginal rate of technical substitution
(MRTS) = =
The rate of substitutability between inputs is defined by the shape of Isoquant (ratio of MPL) Q3 Q2 Q1 L2

28. Isoquant L1 L1 L1 L2 L2 L2 L1 and L2 are not perfect substitutes
L1 and L2 are perfect substitutes
L1 and L2 are complementary

29. Isocost
Isocost show the different combinations of inputs (at given prices) For the same cost outlay. L1 L2
Any point on Isocost reflects the price ratio of L1 and L2

30. Efficient Combination of Inputs.

31. Efficient Combination of inputs
Effect of a change in Input Price L1 L1 L1 Q2 L2 L2 L2

32. Problem Solving
Medical Testing Labs, Inc., provides routine testing services for
blood banks in the Los Angeles area. Tests are supervised by skilled
technicians using equipment produced by two leading competitors in
the medical equipment industry. Records for the current year show
an average of 27 tests per hour being performed on the Test logic-1
and 48 tests per hour on a new machine, the Accutest-3. The
Testlogic-1 is leased for $18,000 per month and the Accutest-3 is
leased at $32,000 per month. On average, each Machine is operated
25 days of 8 hours each.
Does the Lab usage reflect optimal mix of Testlogic-1 and Accutest-3.
2. If the price of tests conducted at the Lab is $6, should the company lease more machines.

33. Long Run Production Function
Scale of operation is another source for cost minimization
Identifying optimal scale of operation for a given demand conditions

34. Long Run Production Function
Q = f (L, K)
Where scale increases, then
output increases (Increasing Returns to Scale)
by a greater proportion
output increases (Constant Returns to Scale)
by the same proportion
output increases (Decreasing Returns to Scale)
by a lesser proportion

35. Long Run Production Function
Production Function Q = f(L, K)
Q = f (hL, hK)
If  = h, then f has constant returns to scale.
If  > h, then f has increasing returns to scale.
If  < h, the f has decreasing returns to scale.