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Economics of Pricing Strategies
Faculty:Prof. Sunitha Raju
Production Analysis - I
Session Date:13.01.2013
PGDIBS 2012-13
Economics of Pricing Strategies1. 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
Basic Production Concepts
Contd…
PGDIBS 2012-13
Economics of Pricing Strategies
2.2. InputsInputs
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
Basic Production Concepts
Contd…
PGDIBS 2012-13
Economics of Pricing Strategies
3. 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…
Basic Production Concepts
PGDIBS 2012-13
Economics of Pricing Strategies
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.
Basic Production Concepts
PGDIBS 2012-13
Economics of Pricing Strategies
4. 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 P3L 2 3 5
K 3 2 4Output is same but methods of input combination
differs.
Basic Production Concepts
Contd…
PGDIBS 2012-13
Economics of Pricing Strategies Technically efficient process
P1 P2L 2 3
K 3 3
P1 is technically efficient as less L used compared to P2
P1 P2L 2 1
K 3 4
P1 and P2 are not comparable and both considered as technically efficient
Contd…
Basic Production Concepts
PGDIBS 2012-13
Economics of Pricing Strategies
Efficient processAmongst the technically efficient processes, the least cost process is defined as Economically efficient process.
Contd…
Basic Production Concepts
PGDIBS 2012-13
Economics of Pricing Strategies
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
PGDIBS 2012-13
Economics of Pricing Strategies
Short Run Production Decisions Run Production Decisions
1. Case of one variable inputQ = f (L, K )
a) Decision on output/input levelb) defining technically efficient level of outputc) defining economically efficient level of output
Together (a), (b) & (c) will determine ‘how much’ output (Q) to produce and ‘how much’ inputs to use.
PGDIBS 2012-13
Economics of Pricing Strategies
ABC Company: Total Output and ABC Company: Total Output and Input RelationsInput Relations
Amount of Machine Tools (Fixed)
Amount of Labour Total Output
5 0 0
5 1 12
5 2 27
5 3 42
5 4 56
5 5 68
5 6 76
5 7 76
5 8 74
PGDIBS 2012-13
Economics of Pricing Strategies
ABC Company: Average and ABC Company: Average and Marginal Marginal Products of Labour of Labour
Amount of Machine Tools
(Fixed)
Amount of Labour
Total Output Average Products of Labour
5 0 0 -
5 1 12 12.0
5 2 27 13.5
5 3 42 14.0
5 4 56 14.0
5 5 68 13.6
5 6 76 12.7
5 7 76 10.9
5 8 74 9.2
PGDIBS 2012-13
Economics of Pricing Strategies
ABC Company: Average and ABC Company: Average and Marginal Marginal Products of Labour of Labour
Amount of Machine Tools (Fixed)
Amount of Labour
Total Output
Average Products of
Labour
Marginal Product of
Labour
5 0 0 - -
5 1 12 12.0 12
5 2 27 13.5 15
5 3 42 14.0 15
5 4 56 14.0 14
5 5 68 13.6 12
5 6 76 12.7 8
5 7 76 10.9 0
5 8 74 9.2 -2
PGDIBS 2012-13
Economics of Pricing Strategies
ABC Company: Average and ABC Company: Average and Marginal Marginal Products of Labour of Labour
Amount of Machine Tools
(Fixed)
Amount of Labour
Total Output
Average Products of
Labour
Marginal Product of
Labour
MRPL
5 0 0 - - -
5 1 12 12.0 12 60
5 2 27 13.5 15 75
5 3 42 14.0 15 75
5 4 56 14.0 14 70
5 5 68 13.6 12 60
5 6 76 12.7 8 40
5 7 76 10.9 0
5 8 74 9.2 -2
Assume MR = 5 PL = 60
PGDIBS 2012-13
Economics of Pricing Strategies
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
LPLQ
QTR
.
PGDIBS 2012-13
Economics of Pricing Strategies
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 / hour1 0.22 1.03 2.44 2.85 3.06 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.
PGDIBS 2012-13
Economics of Pricing Strategies
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
Production Decisions : Dimensions
Contd…
PGDIBS 2012-13
Economics of Pricing Strategies
2. Case of more than one variable input
Efficient combination of inputs
Methodology used is Isoquant
Production Decisions : Dimensions
PGDIBS 2012-13
Economics of Pricing StrategiesIsoquants
2 3 4 5 6
12345
L1
L2
3
1
7
10
12
61210
8
18
23
28
2824
12
28
33
36
3631
14
30
36
40
4042
12
28
33
36
4039
Isoquants show combination of two inputs that can produce same level of outputs
Short run Production Function : Efficient Combination of Inputs
PGDIBS 2012-13
Economics of Pricing Strategies
Isoquants
2 3 4 5
12345
L1
L2
3
1
7
10
12
61210
8
18
23
24
12
33
31
14
30
40
4042
12
33
36
4039
2828
28 28
3636
36
Isoquants show combinations of two inputs that can produce same level of outputs
PGDIBS 2012-13
Economics of Pricing Strategies
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)
L1
L2
Q1
Q2
Q3
2
1
LL
1
2
MPLMPL
PGDIBS 2012-13
Economics of Pricing Strategies
Isoquant
L1 L1 L1
L1 and L2 are not perfect substitutes
L2 L2 L2L1 and L2 are perfect substitutes
L1 and L2 are complementary
PGDIBS 2012-13
Economics of Pricing Strategies
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
PGDIBS 2012-13
Economics of Pricing Strategies
Efficient Combination of Inputs
.
1
2
L
L
PP
MRTS
1
1
1
12
1
2
1 L
L
L
L
L
L
L
L
PMP
PMP
PP
MPMP
PGDIBS 2012-13
Economics of Pricing Strategies
Efficient Combination of inputs
Effect of a change in Input Price
Q2
L1
L2L2L2
L1L1
PGDIBS 2012-13
Economics of Pricing Strategies
Problem Solving
Medical Testing Labs, Inc., provides routine testing services forblood banks in the Los Angeles area. Tests are supervised by skilledtechnicians using equipment produced by two leading competitors inthe medical equipment industry. Records for the current year showan average of 27 tests per hour being performed on the Test logic-1and 48 tests per hour on a new machine, the Accutest-3. TheTestlogic-1 is leased for $18,000 per month and the Accutest-3 isleased at $32,000 per month. On average, each Machine is operated25 days of 8 hours each.
1. 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.
PGDIBS 2012-13
Economics of Pricing Strategies
Long Run Production Function
Scale of operation is another source for cost minimization
Identifying optimal scale of operation for a given demand conditions
PGDIBS 2012-13
Economics of Pricing Strategies
Long run Production FunctionQ = 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
PGDIBS 2012-13
Economics of Pricing Strategies
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.