1. The Theory and Estimation of Production
Chapter 6
The Theory and Estimation of Production
Chapter Six
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2. Chapter Six
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3. Chapter Six
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4. Chapter Six
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5. Overview The production function
Short-run analysis of average and marginal product
Long-run production function
Importance of production function in managerial decision making
Chapter Six
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6. Learning objectives define the production function
explain the various forms of production functions
provide examples of types of inputs into a production function for a manufacturing or service company
Chapter Six
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7. Learning objectives understand the law of diminishing returns
use the Three Stages of Production to explain why a rational firm always tries to operate in Stage II
Chapter Six
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8. Production function
Production function: defines the relationship between inputs and the maximum amount that can be produced within a given period of time with a given level of technology
Q=f(X1, X2, ..., Xk)
Q = level of output
X1, X2, ..., Xk = inputs used in
production
Chapter Six
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9. Production function Key assumptions
given ‘state of the art’ production technology
whatever input or input combinations are included in a particular function, the output resulting from their utilization is at the maximum level
Chapter Six
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10. Production function
For simplicity we will often consider a production function of two inputs:
Q=f(X, Y)
Q = output
X = labor
Y = capital
Chapter Six
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11. Foxconn Workers Strike Over iPhone 5 Quality Demands October 10, 2012 7:28 PM
A labor rights group said Friday that workers on the iPhone 5 production line at Foxconn's Zhengzhou factory went on strike earlier this week amidst overly burdensome quality control demands for Apple's new smartphone
If 4,000 people go on strike at an iPhone factory in China, will anybody know it? That's the question at the heart of an ongoing puzzle over whether, in fact, iPhone 5 production was shut down by a labor action in the northern Chinese city of Zhengzhou on Friday.
For most of the world, the news broke on Oct. 5 when China Labor Watch, an influential New York-based workers' rights group issued a press release claiming a strike had occurred at a plant producing iPhone 5s that "according to workers, involved three to four thousand production workers."
News organizations worldwide, eager for anything iPhone- related, rushed to report the press release, and by the end of the weekend the event was international news, with some analysts going so far to blame the alleged strike for a 2.21 percent decline in Apple's stock price on Monday.
Chapter Six
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12. Production function
Short-run production function shows the maximum quantity of output that can be produced by a set of inputs, assuming the amount of at least one of the inputs used remains unchanged
Long-run production function shows the maximum quantity of output that can be produced by a set of inputs, assuming the firm is free to vary the amount of all the inputs being used
Chapter Six
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13. Short-run analysis of Total, Average, and Marginal product
Alternative terms in reference to inputs
‘inputs’
‘factors’
‘factors of production’
‘resources’
Alternative terms in reference to outputs
‘output’
‘quantity’ (Q)
‘total product’ (TP)
‘product’
Chapter Six
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14. Which is short run?
Chapter Six
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15. Short-run analysis of Total, Average, and Marginal product
Marginal product (MP) = change in output (Total Product) resulting from a unit change in a variable input
Average product (AP) = Total Product per unit of input used
Chapter Six
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16. Chapter Six AGW614 Dr. Chu Staff Cost Revenue Per Employee
Staff Cost
Revenue Per Employee
Revenue/$1 Wage
Revenue/$1 Wage (Globetronics Bhd )
Revenue/$1 Wage (MPI Bhd)
Revenue/$1 Wage (UNISEM Bhd)
2001
69,144,000
214,342
1.98
2002
73,217,000
285,254
3.09
2003
91,963,000
352,145
3.40
2004
101,313,000
618,652
5.64
2005
107,614,000
492,051
4.28
5.50
3.99
4.85
2006
95,911,000
513,184
5.75
6.01
4.58
4.91
2007
101,883,000
388,359
4.34
5.67
4.80
4.99
2008
124,422,000
328,721
3.41
5.04
4.71
5.21
2009
109,790,000
435,498
5.00
4.90
4.31
4.83
2010
108,922,000
450,715
5.35
4.76
4.84
5.26
2011
104,794,000
400,012
4.95
4.42
4.48
4.20
2012
99,456,000
337,006
4.22
4.18
3.98
4.19
Chapter Six
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17. Short-run analysis of Total, Average, and Marginal product
if MP > AP then AP is rising
if MP < AP then AP is falling
MP=AP when AP is maximized
Chapter Six
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18. Chapter Six
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19. With respect to labour, it is not so much the quantity of labour that affects your competitiveness in a given field, but rather it is specialisation and the quality of labour that are important. So it is crucial to recognise that the advantages arise less from inputs in the conventional sense, and more from technology and the efficiency with which those inputs are utilised.
I argue that the efficient utilisation of inputs is fundamentally affected by location and proximity. As the globalisation process evolves, what we see is more subdividing and specialisation of clusters. Ten or 20 years ago there would be a semiconductor cluster in the US and another in Japan. The one in Japan was heavily skewed towards memory chips, whereas the one in the US was skewed towards microprocessors. Now what you see is a cluster specialising in a narrow set of activities, based around manufacturing, for example. If there are 20 manufacturing plants you do not see these scattered across 20 different countries. They tend to be in a cluster in one location.
So the specialisation process is intensifying, and we find that even a small economic region can become a world player. But this cannot be done with one firm; you need the cluster - the critical mass - that gives the externalities and efficiency gains. It is much more efficient for components, machines and backup services to be all in the same location
Chapter Six
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20. Short-run analysis of Total, Average, and Marginal product
The Three Stages of Production in the short run:
Stage I: from zero units of the variable input to where AP is maximized (where MP=AP)
Stage II: from the maximum AP to where MP=0
Stage III: from where MP=0 on Quantity
Chapter Six
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21. Short-run analysis of Total, Average, and Marginal product
Law of diminishing returns: as additional units of a variable input are combined with a fixed input, after some point the additional output (i.e., marginal product) starts to diminish
nothing says when diminishing returns will start to take effect
all inputs added to the production process have the same productivity
Chapter Six
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22. Short-run analysis of Total, Average, and Marginal product
In the short run, rational firms should be operating only in Stage II
Q: Why not Stage III?  firm uses more variable inputs to produce less output
Q: Why not Stage I?  underutilizing fixed capacity, so can increase output per unit by increasing the amount of the variable input
Chapter Six
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23. Explanation of Production Stages
Chapter Six
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24. Short-run analysis of Total, Average, and Marginal product
What level of input usage within Stage II is best for the firm?
 answer depends upon:
how many units of output the firm can
sell the price of the product
the monetary costs of employing the
variable input ( bring in the concept of marginal input)
Chapter Six
AGW614 Dr. Chu

25. Short-run analysis of Total, Average, and Marginal product
Total revenue product (TRP) = market value of the firm’s output, computed by multiplying the total product by the market price
TRP = Q · P
Chapter Six
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26. Short-run analysis of Total, Average, and Marginal product When is the optimum point of production ?
Marginal revenue product (MRP) = change in the firm’s TRP resulting from a unit change in the number of inputs used
MRP = MP · P =
Chapter Six
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27. ford motor co (F:New York)
2009
2010
2011
2012
Ford Motor Company
195,310
Total Cars
70,647
Domestic Car
Import Car
...
Total Light Trucks
124,663
Domestic Truck
Import Truck
TOTAL REVENUES
116,283.00
128,954.00
136,264.00
134,252.00
Cost of Goods Sold
98,585.00
104,451.00
113,345.00
112,578.00
GROSS PROFIT
11,907.00
20,689.00
19,751.00
18,842.00
Selling General & Admin Expenses, Total
12,965.00
11,876.00
11,546.00
12,175.00
OTHER OPERATING EXPENSES, TOTAL
Cost of Goods Sold as “direct costs attributable to the production of the goods sold by a company, which includes the cost of the materials used in
creating the good along with the direct labor costs used to produce the good.”
Chapter Six
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28. Chapter Six
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29. Chapter Six
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30. Short-run analysis of Total, Average, and Marginal product When is the optimum point of production ?
Total labor cost (TLC) = total cost of using the variable input labor, computed by multiplying the wage rate by the number of variable inputs employed
TLC = w · X
Marginal labor cost (MLC) = change in total labor cost resulting from a unit change in the number of variable inputs used
MLC = w
Chapter Six
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31. Short-run analysis of Total, Average, and Marginal product
Summary of relationship between demand for output and demand for a single input:
A profit-maximizing firm operating in perfectly competitive output and input markets will be using the optimal amount of an input at the point at which the monetary value of the input’s marginal product is equal to the additional cost of using that input
 MRP = MLC
Chapter Six
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32. Malaysia 678 corporation Cost of Goods Sold and ROA
Chapter Six
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33. MRP = MLC?????
Chapter Six
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34. Chapter Six
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35. Short-run analysis of Total, Average, and Marginal product
Multiple variable inputs
Consider the relationship between the ratio of the marginal product of one input and its cost to the ratio of the marginal product of the other input(s) and their cost
We can decide which country/state for our foreign investment
Chapter Six
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36. Long-run production function
In the long run, a firm has enough time to change the amount of all its inputs
The long run production process is described by the concept of returns to scale
Returns to scale = the resulting increase
in total output as all inputs increase
Chapter Six
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37. Long Run Production Funtion
Chapter Six
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38. Long-run production function
If all inputs into the production process are doubled, three things can happen:
output can more than double
 ‘increasing returns to scale’ (IRTS)
output can exactly double
 ‘constant returns to scale’ (CRTS)
output can less than double
 ‘decreasing returns to scale’ (DRTS)
Chapter Six
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39. Long-run production function
One way to measure returns to scale is to use a coefficient of output elasticity:
if EQ > 1 then IRTS
if EQ = 1 then CRTS
if EQ < 1 then DRTS
Chapter Six
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40. Long-run production function
Returns to scale can also be described using the following equation
hQ = f(kX, kY)
h=magnitude; k=proportion
if h > k then IRTS
if h = k then CRTS
if h < k then DRTS
Eg:
Q=5X+7Y
10 units of input each var.
Q= 120 units
If input increase by
25%, Q=150
What is the magnitude (h)
of quantity of production?
Chapter Six
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41. Long-run production function
Graphically, the returns to scale concept can be illustrated using the following graphs Q
X,Y
IRTS Q
X,Y
CRTS Q
X,Y
DRTS
Chapter Six
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42. Estimation of production functions
Examples of production functions
short run: one fixed factor, one variable factor
Q = f(L)K
cubic: increasing marginal returns followed by decreasing marginal returns
Q = a + bL + cL2 – dL3
quadratic: diminishing marginal returns but no Stage I
Q = a + bL - cL2
Chapter Six
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43. Q = a + bL + cL2 – dL3 Q = a + bL - cL2 Only stage 2 of production APMP

44. Estimation of production functions
Examples of production functions
power function: exponential for one input
Q = aLb
if b > 1, MP increasing
if b = 1, MP constant
if b < 1, MP decreasing
Advantage: can be transformed into a linear
(regression) equation when expressed in log terms
Chapter Six
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45. Estimation of production functions
Examples of production functions
Cobb-Douglas function: exponential for two inputs
Q = aLbKc
if b + c > 1, IRTS
if b + c = 1, CRTS
if b + c < 1, DRTS
Chapter Six
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46. Estimation of production functions
Cobb-Douglas production function
Advantages:
can investigate MP of one factor holding others fixed
elasticities of factors are equal to their exponents
can be estimated by linear regression
can accommodate any number of independent variables
does not require constant technology
Chapter Six
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47. Estimation of production functions
Cobb-Douglas production function
Shortcomings:
cannot show MP going through all three stages in one specification
cannot show a firm or industry passing through increasing, constant, and decreasing returns to scale
specification of data to be used in empirical estimates
Chapter Six
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48. Estimation of production functions
Statistical estimation of production functions
inputs should be measured as ‘flow’ rather than ‘stock’ variables, which is not always possible
usually, the most important input is labor
most difficult input variable is capital
must choose between time series and cross-sectional analysis
Chapter Six
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49. Estimation of production functions
Aggregate production functions: whole industries or an economy
 gathering data for aggregate functions can be difficult:
for an economy … GDP could be used
for an industry … data from Census of Manufactures or production index from Federal Reserve Board
for labor … data from Bureau of Labor Statistics
Chapter Six
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50. Good capacity planning requires:
Importance of production functions in managerial decision making- so that can maintain in stage II of production
Capacity planning: planning the amount of fixed inputs that will be used along with the variable inputs
Good capacity planning requires:
accurate forecasts of demand
effective communication between the production and marketing functions II TP Qn I
III
Chapter Six
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51. Importance of production functions in managerial decision making
Example: cell phones
Asian consumers want new phone every 6 months
demand for 3G products
Nokia, Samsung, SonyEricsson must be speedy and flexible
Chapter Six
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52. Importance of production functions in managerial decision making
Example: Zara-example of lean production
Spanish fashion retailer
factories located close to stores
quick response time of 2-4 weeks
Chapter Six
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53. Importance of production functions in managerial decision making
Application: call centers
service activity
production function is
Q = f(X,Y)
where Q = number of calls
X = variable inputs
Y = fixed input
Chapter Six
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54. Importance of production functions in managerial decision making
Application: China’s workers
is China running out of workers?
industrial boom
eg bicycle factory in Guangdong Provence
Chapter Six
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