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Theory of production

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• Production theory forms the foundation for the theory of supply

• Managerial decision making involves four types of production decisions:1.Whether to produce or to shut down2.How much output to produce3.What input combination to use4.What type of technology to use

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• Production involves transformation of inputs such as capital, equipment, labor, and land into output - goods and services

• In this production process, the manager is concerned with efficiency in the use of the inputs

- technical vs. economical efficiency

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Two Concepts of Efficiency

• Economic efficiency:– occurs when the cost of producing

a given output is as low as possible

• Technological efficiency:– occurs when it is not possible to

increase output without increasing inputs

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When a firm makes choices, it faces many constraints:

1. Constraints imposed by the firms customers2. Constraints imposed by the firms competitors3. Constraints imposed by nature

Nature imposes constraints that there are only certain kinds of technological choices that are possible

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The Technology of Production• The Production Process

– Combining inputs or factors of production to achieve an output

• Categories of Inputs (factors of production)– Labor– Materials– Capital

The Organization of Production

• Inputs– Labor, Capital, Land

• Fixed Inputs• Variable Inputs• Short Run– At least one input is fixed

• Long Run– All inputs are variable

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Long run and the short run

• In the short run there are some factors of production that are fixed at pre-determined levels. (farming and land)

• In the long run, all factors of production can be varied.

• There is no specific time interval implied in the definition of short and long run. It depends on what kinds of choices we are examining

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The Technology of Production• Production Function:

– Indicates the highest output that a firm can produce for every specified combination of inputs given the state of technology.

– Shows what is technically feasible when the firm operates efficiently.

Production Functionwith One Variable Input

Total Product

Marginal Product

Average Product

Production orOutput Elasticity

TP = Q = f(L)

MPL =TP L

APL =TP L

EL =MPL

APL

Optimal Use of theVariable Input

Marginal RevenueProduct of Labor MRPL = (MPL)(MR)

Marginal ResourceCost of Labor MRCL =

TC L

Optimal Use of Labor MRPL = MRCL

Production with TwoVariable Inputs

Isoquants show combinations of two inputs that can produce the same level of output.

Firms will only use combinations of two inputs that are in the economic region of production, which is defined by the portion of each isoquant that is negatively sloped.

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Isoquants When Inputs are Perfectly Substitutable

Laborper month

Capitalper

month

Q1 Q2 Q3

A

B

C

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• Observations when inputs are perfectly substitutable:

1) The MRTS is constant at all points on the isoquant.

Production withTwo Variable Inputs

Perfect SubstitutesPerfect Substitutes

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• Observations when inputs are perfectly substitutable:

2) For a given output, any combination of inputs can be chosen (A, B, or C) to

generate the same level of output (e.g. toll booths & musical instruments)

Production withTwo Variable Inputs

Perfect SubstitutesPerfect Substitutes

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Fixed-ProportionsProduction Function

Labor per month

Capitalper

month

L1

K1Q1

Q2

Q3

A

B

C

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• Observations when inputs must be in a fixed-proportion:

1) No substitution is possible.Each output requires a specific amount of each input (e.g. labor and jackhammers).

Fixed-Proportions Production FunctionFixed-Proportions Production Function

Production withTwo Variable Inputs

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• Observations when inputs must be in a fixed-proportion:

2) To increase output requires more labor and capital (i.e. moving from A

to B to C which is technically efficient).

Fixed-Proportions Production FunctionFixed-Proportions Production Function

Production withTwo Variable Inputs

Production with TwoVariable InputsMarginal Rate of Technical Substitution

MRTS = -K/L = MPL/MPK

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– Curves showing all possible combinations of inputs that yield the same output

An isoquant is a curve showing all possible combinations of inputs physically capable of producing a given fixed level of output

The isoquants emphasize how different input combinations can be used to produce the same output.This information allows the producer to respond efficiently to changes in the markets for inputs.

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Example 2 Production Table

Units of KEmployed Output Quantity (Q)

8 37 60 83 96 107 117 127 1287 42 64 78 90 101 110 119 1206 37 52 64 73 82 90 97 1045 31 47 58 67 75 82 89 954 24 39 52 60 67 73 79 853 17 29 41 52 58 64 69 732 8 18 29 39 47 52 56 521 4 8 14 20 27 24 21 17

1 2 3 4 5 6 7 8Units of K Employedof L

IsoquantUnits of KEmployed

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An IsoquantGraph of Isoquant

0

1

2

3

4

5

6

7

1 2 3 4 5 6 7 X

Y

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Isocost Line• Isocost line: shows all possible K/L combos that can be purchased for a

given TC.• TC = C = w*L + r*K ;• Rewrite as equation of a line:

K = C/r – (w/r)*L Slope = K/L = -(w/r).

• Interpret slope: * shows rate at which K and L can be traded off, keeping TC the

same.• Relate to consumer’s budget constraint:

* slope = ratio of prices with price from horizontal axis in numerator.

Vertical intercept = C/r. Horizontal intercept = C/w.

37Units of X0 2 4 6

2

4

6

8

10

12

Units of Y

B1 = $1,000

B2 = $2,000

B3 = $3,000

Production and CostsProduction and CostsOptimal combination of multiple inputsOptimal combination of multiple inputs

Isocost curves.

All combinations of products that can be purchased for a fixed

dollar amount

X YB P X P Y

X

Y Y

B PY X

P P

Downward sloping curve.

Y

B

PShift

X

Y

P

PSlope

Optimal Combination of Inputs

Isocost lines represent all combinations of two inputs that a firm can purchase with the same total cost.

C wL rK

C wK L

r r

C Total Cost

( )w WageRateof Labor L

( )r Cost of Capital K

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B1

X2

Q3

Y2Y3

B2

B3

X1

Units of Y

Units of X

Expansion path

A B C

Q2Q1

Y1

X3

Production and CostsProduction and CostsOptimal combination of multiple inputsOptimal combination of multiple inputs

Optimal combination corresponds to the point

of tangency of the isoquant and isocost.

X X

Y Y

P MP

P MP

Y X

Y X

MP MP

P P

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B1

X2

Q 3

Y2Y3

B2

B 3

X1

Units of Y

Units of X

Expansion path

A B C

Q2Q 1

Y1

X3

Production and CostsProduction and CostsOptimal combination of multiple inputsOptimal combination of multiple inputs

Optimal combination corresponds to the point of tangency isoquant and

isocost.

X X

Y Y

P MP

P MP

Y X

Y X

MP MP

P P

• Budget Lines– Least-cost production occurs

when MPX/PX = MPY/PY and PX/PY = MPX/MPY

• Expansion Path– Shows efficient input

combinations as output grows.• Illustration of Optimal Input

Proportions– Input proportions are optimal

when no additional output could be produced for the same cost.

– Optimal input proportions is a necessary but not sufficient condition for profit maximization.

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B1

X2

Q3

Y2Y3

B2

B3

X1

Units of Y

Units of X

Expansion path

A B C

Q 2Q1

Y1

X3

Production and CostsProduction and CostsOptimal combination of multiple inputsOptimal combination of multiple inputs

Optimal combination corresponds to the point of tangency isoquant and

isocost.

X X

Y Y

P MP

P MP

Y X

Y X

MP MP

P P

– Profits are maximized when MRPX = PX for all inputs.

– Profit maximization requires optimal input proportions plus an optimal level of output.

Returns to Scale

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, then f has decreasing returns to scale.

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Returns to Scale• Measuring the relationship between the scale

(size) of a firm and output

1) Increasing returns to scale: output more than doubles when all inputs are doubled

• Larger output associated with lower cost (autos)• One firm is more efficient than many (utilities)• The isoquants get closer together

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Returns to Scale

Labor (hours)

Capital(machine

hours)

10

20

30

Increasing Returns:The isoquants move closer together

5 10

2

4

0

A

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Returns to Scale• Measuring the relationship between the scale

(size) of a firm and output

2) Constant returns to scale: output doubles when all inputs are doubled

• Size does not affect productivity• May have a large number of producers• Isoquants are equidistant apart

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Returns to Scale

Labor (hours)

Capital(machine

hours)

Constant Returns:Isoquants are equally spaced

10

20

30

155 10

2

4

0

A

6

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Returns to Scale• Measuring the relationship between the scale

(size) of a firm and output

3) Decreasing returns to scale: output less than doubles when all inputs are doubled

• Decreasing efficiency with large size• Reduction of entrepreneurial abilities• Isoquants become farther apart

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Returns to Scale

Labor (hours)

Capital(machine

hours)

Decreasing Returns:Isoquants get further apart

1020

30

5 10

2

4

0

A

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• Decreasing returns to scale – If an increase in all inputs in the same proportion k leads to an increase of

output of a proportion less than k, we have decreasing returns to scale. Example: If we increase the inputs to a dairy farm (cows, land, barns, feed, labor, everything) by 50% and milk output increases by only 40%, we have decreasing returns to scale in dairy farming. This is also known as "diseconomies of scale," since production is less cheap when the scale is larger.

• Constant returns to scale – If an increase in all inputs in the same proportion k leads to an increase of

output in the same proportion k, we have constant returns to scale. Example: If we increase the number of machinists and machine tools each by 50%, and the number of standard pieces produced increases also by 50%, then we have constant returns in machinery production.

• Increasing returns to scale – If an increase in all inputs in the same proportion k leads to an increase of

output of a proportion greater than k, we have increasing returns to scale. Example: If we increase the inputs to a software engineering firm by 50% output and increases by 60%, we have increasing returns to scale in software engineering. (This might occur because in the larger work force, some programmers can concentrate more on particular kinds of programming, and get better at them). This is also known as "economies of scale," since production is cheaper when the scale is larger.

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• F (z1, 2) = [2z12 + 2z22]1/2 = (2)1/2(z12 + z22)1/2 = F (z1, z2). Thus this production function has CRTS.

• F (z1, z2) = (z1 + z2)1/2 = 1/2(z1 + z2)1/2 = 1/2F (z1, z2). Thus this production function has DRTS.

• F (z1, z2) = 1/2z11/2 + z2 < (z11/2 + z2) = F (z1, z2) for > 1. Thus this production function has DRTS

Determine the returns to scale of the following production functions: 1. F (z1, z2) = [z12 + z22]1/2.

2. F (z1, z2) = (z1 + z2)1/2. 3. F (z1, z2) = z11/2 + z2.

Empirical Production Functions

Cobb-Douglas Production Function

Q = AKaLb

Estimated Using Natural Logarithms

ln Q = ln A + a ln K + b ln L

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Cobb-Douglas Production FunctionExample: Q = F(K,L) = K.5 L.5

– K is fixed at 16 units. – Short run production function:

Q = (16).5 L.5 = 4 L.5

– Production when 100 units of labor are used?

Q = 4 (100).5 = 4(10) = 40 units

PowerPoint Slides Prepared by Robert F. Brooker, Ph.D.Slide 58

Innovations and Global Competitiveness

• Product Innovation• Process Innovation• Product Cycle Model• Just-In-Time Production System• Competitive Benchmarking• Computer-Aided Design (CAD)• Computer-Aided Manufacturing (CAM)