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The Theory and Estimation of Production

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1 The Theory and Estimation of Production
Chapter 6 The Theory and Estimation of Production Chapter Six AGW614 Dr. Chu

2 Chapter Six AGW614 Dr. Chu

3 Chapter Six AGW614 Dr. Chu

4 Chapter Six AGW614 Dr. Chu

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 AGW614 Dr. Chu

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 AGW614 Dr. Chu

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 AGW614 Dr. Chu

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 AGW614 Dr. Chu

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 AGW614 Dr. Chu

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 AGW614 Dr. Chu

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 AGW614 Dr. Chu

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 AGW614 Dr. Chu

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 AGW614 Dr. Chu

14 Which is short run? Chapter Six AGW614 Dr. Chu

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 AGW614 Dr. Chu

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 AGW614 Dr. Chu

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 AGW614 Dr. Chu

18 Chapter Six AGW614 Dr. Chu

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 AGW614 Dr. Chu

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 AGW614 Dr. Chu

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 AGW614 Dr. Chu

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 AGW614 Dr. Chu

23 Explanation of Production Stages
Chapter Six AGW614 Dr. Chu

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 AGW614 Dr. Chu

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 AGW614 Dr. Chu

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 AGW614 Dr. Chu

28 Chapter Six AGW614 Dr. Chu

29 Chapter Six AGW614 Dr. Chu

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 AGW614 Dr. Chu

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 AGW614 Dr. Chu

32 Malaysia 678 corporation Cost of Goods Sold and ROA
Chapter Six AGW614 Dr. Chu

33 MRP = MLC????? Chapter Six AGW614 Dr. Chu

34 Chapter Six AGW614 Dr. Chu

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 AGW614 Dr. Chu

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 AGW614 Dr. Chu

37 Long Run Production Funtion
Chapter Six AGW614 Dr. Chu

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 AGW614 Dr. Chu

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 AGW614 Dr. Chu

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 AGW614 Dr. Chu

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 AGW614 Dr. Chu

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 AGW614 Dr. Chu

43 Q = a + bL + cL2 – dL3 Q = a + bL - cL2 Only stage 2 of production AP
MP

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 AGW614 Dr. Chu

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 AGW614 Dr. Chu

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 AGW614 Dr. Chu

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 AGW614 Dr. Chu

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 AGW614 Dr. Chu

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 AGW614 Dr. Chu

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 AGW614 Dr. Chu

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 AGW614 Dr. Chu

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 AGW614 Dr. Chu

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 AGW614 Dr. Chu

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 AGW614 Dr. Chu


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