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Theory of production

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Theory of production

- 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 down

2.How much output to produce

3.What input combination to use

4.What type of technology to use

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

- 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

When a firm makes choices, it faces many constraints:

- Constraints imposed by the firms customers
- Constraints imposed by the firms competitors
- Constraints imposed by nature
Nature imposes constraints that there are only certain kinds of technological choices that are possible

- The Production Process
- Combining inputs or factors of production to achieve an output

- Categories of Inputs (factors of production)
- Labor
- Materials
- Capital

- Inputs
- Labor, Capital, Land

- Fixed Inputs
- Variable Inputs
- Short Run
- At least one input is fixed

- Long Run
- All inputs are variable

- 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

- 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.

TPL

MPL =

TP L

APL =

MPLAPL

EL =

Total Product

TP = Q = f(L)

Marginal Product

Average Product

Production orOutput Elasticity

TCL

Marginal RevenueProduct of Labor

MRPL = (MPL)(MR)

Marginal ResourceCost of Labor

MRCL =

MRPL = MRCL

Optimal Use of Labor

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.

A

B

C

Q1

Q2

Q3

Capital

per

month

Labor

per month

Perfect Substitutes

- Observations when inputs are perfectly substitutable:
1)The MRTS is constant at all points on the isoquant.

Perfect Substitutes

- 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)

Q3

C

Q2

B

Q1

K1

A

L1

Capital

per

month

Labor

per month

Fixed-Proportions Production Function

- 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 Function

- 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).

Marginal Rate of Technical Substitution

MRTS = -K/L = MPL/MPK

- 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.

Units of K

Employed

Isoquant

- 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.

Production and Costs

Optimal combination of multiple inputs

Shift

Slope

Isocost curves.

All combinations of products

that can be purchased for a fixed

dollar amount

Units of

Y

12

10

Downward sloping curve.

8

B

= $1,000

1

B

= $2,000

2

6

B

= $3,000

3

4

2

Units of

X

0

2

4

6

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

Production and Costs

Optimal combination of multiple inputs

Optimal combination corresponds to the point of tangency of the isoquant and isocost.

Y

Units of

B

3

B

2

B

1

Expansion path

Y

3

C

Y

2

B

Y

1

A

Q

3

Q

2

Q

1

X

X

X

1

2

3

X

Units of

Production and Costs

Optimal combination of multiple inputs

Optimal combination corresponds to the point of tangency isoquant and isocost.

- 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.

Units of

Y

B

3

B

2

B

1

Expansion path

Y

3

C

Y

2

B

Y

1

A

Q

3

Q

2

Q

1

X

X

X

1

2

3

Units of

X

Production and Costs

Optimal combination of multiple inputs

Optimal combination corresponds to the point of tangency isoquant and isocost.

- Profits are maximized when MRPX = PX for all inputs.
- Profit maximization requires optimal input proportions plus an optimal level of output.

Units of

Y

B

3

B

2

B

1

Expansion path

Y

3

C

Y

2

B

Y

1

A

Q

3

Q

2

Q

1

X

X

X

1

2

3

Units of

X

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.

- 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

Increasing Returns:

The isoquants move closer together

A

4

30

20

2

10

0

5

10

Capital

(machine

hours)

Labor (hours)

- 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

A

6

30

4

20

2

10

0

5

10

15

Capital

(machine

hours)

Constant Returns:

Isoquants are equally spaced

Labor (hours)

- 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

A

4

30

2

20

10

0

5

10

Capital

(machine

hours)

Decreasing Returns:

Isoquants get further

apart

Labor (hours)

- 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.

- 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.

Cobb-Douglas Production Function

Q = AKaLb

Estimated Using Natural Logarithms

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

- Cobb-Douglas Production Function
- Example: 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

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