1. Production Theory and Estimation
Chapter 7

2. Managers must decide not only what to produce for the market, but also how to produce it in the most efficient or least cost manner.
Economics offers widely accepted tools for judging whether the production choices are least cost.
A production function relates the most that can be produced from a given set of inputs.
Production functions allow measures of the marginal product of each input. 1

3. Green Power Initiatives
California permitted and encouraged buying cheap power from other states.
So, PG&E and Southern Cal Edison scaled back their expansion of production facilities.
Off-Peak and Peak costs per MWh ranged from $25 to over $65, but regulators tried to keep prices low.
Resulting in PG&E bankruptcy

4. Green Power Initiatives
Carbon dioxide emission trading schemes in Europe encouraged construction of greener nuclear & wind generation.
Q: If you were asked to pay 3 times more for electricity in the day than night, would you change your usage?

5. 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

6. Production Function With Two Inputs
Q = f(L, K)

7. Production Function With One Variable Input
Total Product
TP = Q = f(L)
MPL =
TP L
Marginal Product
APL =
TP L
Average Product
EL =
MPL APL
Production or Output Elasticity

8. Production Function With One Variable Input
Total, Marginal, and Average Product of Labor, and Output Elasticity

9. Production Function With One Variable Input

10. Production Function With One Variable Input

11. Optimal Use of the Variable Input
Marginal Revenue Product of Labor
MRPL = (MPL)(MR)
Marginal Resource Cost of Labor
TC L
MRCL =
Optimal Use of Labor
MRPL = MRCL

12. Optimal Use of the Variable Input
Use of Labor is Optimal When L = 3.50

13. Optimal Use of the Variable Input

14. Production With Two Variable 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.

15. Production With Two Variable Inputs
Isoquants

16. Production With Two Variable Inputs
Economic Region of Production

17. Production With Two Variable Inputs
Marginal Rate of Technical Substitution
MRTS = -K/L = MPL/MPK

18. Production With Two Variable Inputs
MRTS = -(-2.5/1) = 2.5

19. Production With Two Variable Inputs
Perfect Substitutes
Perfect Complements

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

21. Optimal Combination of Inputs
Isocost Lines
AB C = $100, w = r = $10
A’B’ C = $140, w = r = $10
A’’B’’ C = $80, w = r = $10
AB* C = $100, w = $5, r = $10
Prepared by Robert F. Brooker, Ph.D. Copyright ©2004 by South-Western, a division of Thomson Learning. All rights reserved. Slide 21

22. Optimal Combination of Inputs
MRTS = w/r
Prepared by Robert F. Brooker, Ph.D. Copyright ©2004 by South-Western, a division of Thomson Learning. All rights reserved. Slide 22

23. Optimal Combination of Inputs
Effect of a Change in Input Prices

24. Production Function Q = f(L, K)
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, the f has decreasing returns to scale.

25. Returns to Scale Constant Returns to Scale Increasing Returns to Scale
Decreasing Returns to Scale
Prepared by Robert F. Brooker, Ph.D. Copyright ©2004 by South-Western, a division of Thomson Learning. All rights reserved. Slide 25

26. Empirical Production Functions
Cobb-Douglas Production Function
Q = AKaLb
Estimated using Natural Logarithms
ln Q = ln A + a ln K + b ln L

27. The Production Function
A Production Function is the maximum feasible quantity from any amounts of inputs
If L is labor and K is capital, one popular functional form is known as the Cobb-Douglas Production Function 2

28. The Production Function (con’t)
Q = a • K b1• L 2 is a Cobb-Douglas Production Function
The number of inputs is typically greater than just K & L. But economists simplify by suggesting some, like materials or labor, is variable, whereas plant and equipment is fairly fixed in the short run.

29. The Short Run Production Function
Short Run Production Functions:
Max output, from a n y set of inputs
Q = f ( X1, X2, X3, X4, X )
FIXED IN SR VARIABLE IN SR
_ _
Q = f ( K, L) for two input case, where K is Fixed
© 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. 2

30. The Short Run Production Function (con’t)
A Production Function with only one variable input is easily analyzed. The one variable input is labor, L. Q = f( L )

31. Marginal Product = DQ/DL =Q/L = dQ/dL
Average Product = Q / L
output per labor
Marginal Product = DQ/DL =Q/L = dQ/dL
output attributable to last unit of labor applied
Similar to profit functions, the Peak of MP occurs before the Peak of average product
When MP = AP, this is the peak of the AP curve 3

32. Law of Diminishing Returns
INCREASES IN ONE FACTOR OF PRODUCTION,
HOLDING ONE OR OTHER FACTORS FIXED,
AFTER SOME POINT,
MARGINAL PRODUCT DIMINISHES. MP
A SHORT
RUN LAW
point of
diminishing
returns
Variable input 7

33. Bottlenecks in Production Plants
Boeing found diminishing returns in ramping up production.
It sought ways to adopt lean production techniques, cut order sizes, and outsourced work at bottlenecked plants.

34. Increasing Returns and Network Effects
There are exceptions to the law of diminishing returns.
When the installed base of a network product makes efforts to acquire new customers increasing more productive, we have network effects
Outlook and Microsoft Office

35. Table 7.2: Total, Marginal & Average Products

36. Total, Marginal & Average Products
Marginal Product
Average
Product
The maximum MP occurs before the maximum AP

37. When MP > AP, then AP is RISING
IF YOUR MARGINAL GRADE IN THIS CLASS IS HIGHER THAN YOUR GRADE POINT AVERAGE, THEN YOUR G.P.A. IS RISING
When MP < AP, then AP is FALLING
IF YOUR MARGINAL BATTING AVERAGE IS LESS THAN THAT OF THE NEW YORK YANKEES, YOUR ADDITION TO THE TEAM WOULD LOWER THE YANKEE’S TEAM BATTING AVERAGE
When MP = AP, then AP is at its MAX
IF THE NEW HIRE IS JUST AS EFFICIENT AS THE AVERAGE EMPLOYEE, THEN AVERAGE PRODUCTIVITY DOESN’T CHANGE 6

38. Three stages of production

39. Three stages of production
Stage 1: average product rising.
Increasing returns
Stage 2: average product declining (but marginal product positive).
Decreasing returns
Stage 3: marginal product is negative, or total product is declining.
Negative returns 8

40. Determining the Optimal Use of the Variable Input
HIRE, IF GET MORE REVENUE THAN COST
HIRE if
TR/L > TC/L
HIRE if the marginal revenue product > marginal factor cost: MRP L > MFC L
AT OPTIMUM,
MRP L = W  MFC
MRP L  MP L • P Q = W
wage W •
W  MFC
MRPL
MPL
optimal labor L 9

41. Optimal Input Use at L = 6 Table 7.3
© 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

42. Production Functions with multiple variable inputs
Suppose several inputs are variable
greatest output from any set of inputs
Q = f( K, L ) is two input example
MP of capital and MP of labor are the derivatives of the production function
MPL = Q/L = DQ/DL
MP of labor declines as more labor is applied. Also the MP of capital declines as more capital is applied. 11

43. Isoquants & LR Production Functions
ISOQUANT MAP
In the LONG RUN, ALL factors are variable
Q = f ( K, L )
ISOQUANTS -- locus of input combinations which produces the same output
Points A & B are on the same isoquant
SLOPE of ISOQUANT from A to B is ratio of Marginal Products, called the MRTS, the marginal rate of technical substitution = -DK /DL K Q3 B C Q2 A Q1 L 16

44. Optimal Combination of Inputs
The objective is to minimize cost for a given output
ISOCOST lines are the combination of inputs for a given cost, C0
C0 = CL·L + CK·K
K = C0/CK - (CL/CK)·L
Optimal where:
MPL/MPK = CL/CK·
Rearranged, this becomes the equimarginal criterion

45. Optimal Combination of Inputs
Equimarginal Criterion: Produce where MPL/CL = MPK/CK where marginal products per dollar are equal
at D, slope of
isocost = slope
of isoquant 17

46. Use of the Equimarginal Criterion
Q: Is the following firm EFFICIENT?
Suppose that:
MP L = 30
MPK = 50
W = 10 (cost of labor)
R = 25 (cost of capital)
Labor: 30/10 = 3
Capital: 50/25 = 2
A: No!

47. Use of the Equimarginal Criterion
A dollar spent on labor produces 3, and a dollar spent on capital produces 2.
USE RELATIVELY MORE LABOR!
If spend $1 less in capital, output falls 2 units, but rises 3 units when spent on labor
Shift to more labor until the equimarginal condition holds.
That is peak efficiency. 19

48. Production Processes and Process Rays under Fixed Proportions
If a firm has five computers and just one person, typically only one computer is used at a time. You really need five people to work on the five computers.
The isoquants for processes with fixed proportions are L-shaped. Small changes in the prices of input may lead to no change in the process.
M is the process ray of one worker and one machine
people 5 4 3 2 1 M
computers

49. Allocative & Technical Efficiency
Allocative Efficiency – asks if the firm using the least cost combination of input
It satisfies: MPL/CL = MPK/CK
Technical Efficiency – asks if the firm is maximizing potential output from a given set of inputs
When a firm produces at point T rather than point D on a lower isoquant, that firm is not producing as much as is technically possible. D
Q(1) T
Q(0)

50. Overall Production Efficiency
Suppose a plant produces 93% of what the technical efficient plant (the benchmark) would produce.
Suppose a plant produces 85.7% of what an allocatively efficient plant would produce, due to a misaligning the input mix.
Overall Production Efficiency = (technical efficiency)*(allocative efficiency)
In this case: overall production efficiency = (.93)(.857) = or about 79.7%.

51. Returns to Scale
If multiplying all inputs by  (lambda) increases the dependent variable by, the firm has constant returns to scale (CRS).
Q = f ( K, L)
So, f(K,  L) =  • Q is Constant Returns to Scale
So if 10% more all inputs leads to 10% more output the firm is constant returns to scale.
Cobb-Douglas Production Functions are constant returns if  +  =1 12

52. Cobb-Douglas Production Functions
Q = A • K • L is a Cobb-Douglas Production Function
IMPLIES:
Can be CRS, DRS, or IRS
if  +  1, then constant returns to scale
if  + < 1, then decreasing returns to scale
if  + > 1, then increasing returns to scale
Suppose: Q = 1.4 K .35 L .70
Is this production function constant returns to scale?
No, it is Increasing Returns to Scale, because 1.05 > 1. 13

53. Reasons for Increasing & Decreasing Returns to Scale
Some Reasons for IRS
Some Reasons for DRS
The advantage of specialization in capital and labor – become more adept at a task
Engineering size and volume effects – doubling the size of motor more than doubles its power
Network effects
Pecuniary advantages of buying in bulk
Problems with coordination and control – as a organization gets larger, harder to get everyone to work together
Shirking increases
Bottlenecks appear – a form of the law of diminishing returns appears
CEO can’t oversee a gigantically complex operation

54. Interpreting the Exponents of the Cobb-Douglas Production Functions
The exponents a and b are elasticities
a is the capital elasticity of output
The a is [% change in Q / % change in K]
b is the labor elasticity of output
The b is a [% change in Q / % change in L]
These elasticities can be written as EK and E L
Most firms have some slight increasing returns to scale. 13

55. Empirical Production Elasticities Table 7
Empirical Production Elasticities Table 7.4: Most are statistically close to CRS or have IRS
˟ such as management or other staff personnel.