The Theory of Production

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1 The Theory of Production Production: the creation of any good or service that has economic value to either consumers or other producers. Production analysis focuses on the efficient use of inputs to create outputs. The process involves all of the activities associated with providing goods and services. Managerial Questions: 1. Whether to produce or shut down 2. How much to produce 3. What input combination to use 4. What type of technology to use Examples: a. physical processing or manufacturing of material goods b. production of transportation services c. production of legal advice d. production of education e. production of invention (R & D) f. production of bank loans

2 MELed7_01: Production Theory Page: 2 Production Function: a mathematical model relating the maximum quantity of output that can be produced from given amounts of various inputs. -or- a schedule (table, equation) showing the maximum amount of output that can be produced from any specified set of inputs, given the existing technology or "state of the art." In short -- the production function is a catalog of output possibilities. Economic Efficiency: Q = f (X,Y) or (K,L) The production function incorporates the technically efficient method of production -- the latest technological processes are used. When economists use production functions they assume that the maximum level of output is obtained from any given combination of inputs; that is, they assume that production is technically efficient. When producers are faced with input prices, the problem is not technical but economic efficiency: how to produce a given amount of output at the lowest possible cost. To be economically efficient, a producer must determine the combination of inputs that solves this problem.

3 MELed7_01: Production Theory Page: 3 What then is technical inefficiency? If, for example, an alternative process can produce the same amount of output using less of one or more inputs and the same amounts of all others, then the first process is technically inefficient. If, however, the second process uses less of some inputs but more of others, the economically efficient method of producing a given level of output depends on the prices of the inputs. One might cost less but actually be less technically efficient. Effect on Production Management on Fundamental Analysis Traditional fundamental analysis involves selecting the relevant information from financial statement data and evaluating it. Traditional ratio dimensions: 1. Return on investment 2. Liquidity 3. Profitability 4. Activity 5. Financial leverage The firm operating cycle (Liquidity) It is the duration form the time cash is invested in goods and services to the time that the investment produces cash. Four phases that impact firm liquidity:

4 MELed7_01: Production Theory Page: 4 1. Purchase raw materials and produce goods, investing in inventory. 2. Sell goods, generating sales, which may or may not be for cash. 3. Extend credit, creating accounts receivable. 4. Collect accounts receivable, generating cash CGS $6,500, 000 AvgDay ' scgs $17,808 / day On average the cost of producing goods sold is $17,808. Components of Income Against Sales (Profitability) Gross profit margin is a measure of income that is the direct result of production management. GPM Sales CGS Sales GPM $10,000,000 $6,500,000 $3,500, % $10,000,000 $10,000,000 For XYZ corporation, the GPM is affected by: Changes in sales volume, which affect CGS and Sales Changes in sales price, which affects sales Changes in the cost of production which affect CGS

5 MELed7_01: Production Theory Page: 5 Any change in GPM from one-period to the next is caused by one or more of the above factors. To properly evaluate operating performance it is important to consider operating expenses in addition to the CGS. This is accomplished by removing expenses (e.g., selling and general administrative expenses) from gross profit. That produces operating profit or EBIT. Operating profit margin is defined as: OPM Sales CGS OperatingExp EBIT $2,000, % Sales Sales $10,000,000 For each dollar of sales (revenue) the XYZ corporation generated an operating income of 20-cents. OPM is affected by the same factors as GPM plus: Rent and lease expense Misc. income Adv. Expenditures Bad debt expense

6 MELed7_01: Production Theory Page: 6 Pfizer Inc: The Recent History

7 MELed7_01: Production Theory Page: 7 Pfizer, Inc. Timeline 2007: Launches Seizentry tablets. The first in a new class of oral HIV medicines 2008: Jeff Kindler, Chairman a. Smaller operating units designed to enhance innovation and accountability while drawing on scale. b. New Medicine Safety Website c. Grameen Health (Grameen Bank) pioneer micro-financing in Bangladesh to alleviate poverty looking for sustainable models for healthcare in the developing world. d. Launches Global Regenerative Medicine Unit (stem cell research). e. Agreement with Medivation to develop and commercialize an investigational medicine, Dimebon, for treating Alzheimer s disease and Huntington s disease 2009: Research Enhancement a. Acquires Wyeth, creating a company with a broad range of products and therapies. b. Creates two distinct research organizations: PharmaTherapeutics Research & Development Group (small-molecule research) and The Bio Therapeutics Research & Development Group (large-molecule research including vaccines).

8 MELed7_01: Production Theory Page: 8 Pfizer Inc. Ten Year Summary: NOTE: 1. Net income stabilized but did not appreciate appreciably after erratic results early in decade 2. Impact of Weyth acquisition in 2010 results 3. Impact of non-case expenses (depreciation) after acquisitions.

9 MELed7_01: Production Theory Page: 9 Classifying Production Inputs: Fixed: a fixed input is one that is required in the production process. The amount of the fixed input employed is constant over a given period of time regardless of the quantity of output produced. Variable Input: one whose quantity employed in the production process is varied, depending on the desired quantity of output to be produced. Time Frames: Short-Run: a period of time in which one or more of the inputs is fixed. Very Short-Run: all resources are fixed. Long Run: time period long enough that all resources can be varied.

10 MELed7_01: Production Theory Page: 10 ORE MINING EXAMPLE Output = tons or ore mined Capital (horsepower) Labor ,000 1,250 1,500 1,750 2,

11 MELed7_01: Production Theory Page: 11

12 MELed7_01: Production Theory Page: 12 Labor Output MP Q X AP (Q X) Elasticity MP AP Returns to Scale: The relation between output and variation in all inputs taken together. Returns to factor: The relation between output and variation in only one of the inputs employed. Total Product: The total output that results from employing a specific quantity of resources in a production system.

13 MELed7_01: Production Theory Page: 13 Marginal Product: the incremental change in total output that can be produced by the use of one more unit of the variable input in the production process. -or- The change in output associated with a unit change in one input factor, holding other inputs constant. Q change brought about by a change in X units of the variable input Y remains fixed MP x = Q X -or, in continuous terms: MP x = Q X Average Product AP x = Q X the ratio to total output to the amount of the variable input used in producing the output.

14 MELed7_01: Production Theory Page: 14 Production Elasticity: The percentage change in output resulting from a given percentage change in the amount of the variable input X employed in the production process with Y remaining constant. -or- The percentage change in output associated with a 1 (one) percent change in all inputs. E x = % Q % X = Q/Q X/X Rearranging Terms -- = Q/ X Q/X = MP x AP x

15 MELed7_01: Production Theory Page: 15 Law of Diminishing Marginal Returns: The use of increasing amounts of a variable factor in a production process beyond some point, given the amount of all other production factors remains unchanged, will eventually result in diminishing marginal returns in total output. This observation is easily verified by reviewing the slope of the marginal product curve. As the number of units of the variable input increases, other inputs held constant, there exists a point beyond which the marginal product of the variable input declines. NOTE: a) not a mathematical theorem b) empirical assertion The concepts of total and marginal product and the law of diminishing returns to a factor are important in identifying efficient as opposed to inefficient input combinations. Summary: The Three Stages of Production Stage 1: the range of X over which the average product is increasing. Stage 2: the range of X from the point at which the average product is a maximum to the point of where MP declines to zero

16 MELed7_01: Production Theory Page: 16 (0.0). The endpoint of stage 2 corresponds to the point of maximum output on the TP curve. Stage 3: encompasses the range of X over which the TP is declining or, equivalently, the MP is negative.

17 MELed7_01: Production Theory Page: 17 DETERMINING THE OPTIMAL USE OF THE VARIABLE INPUT With one of the inputs (Y) fixed in the short run, the producer must determine the optimal quantity of the variable input (X) to employ in the production process. This is a study of Marginal Revenue Product (MRP) and Marginal Factor Cost (MFC). That is, this is a study about the role of revenue and cost in the production system. MRP The conversion from physical to economic relations is accomplished by multiplying the MP of input factors by the MR resulting from the sale of goods or services produced to obtain a quantity known as the Marginal Revenue Product of input: Def: the amount that an additional unit of the variable input adds to total revenue, -or- MRP is the economic value of a marginal unit of a particular input factor when used in the production of a specific product. MRP = TR X

18 MELed7_01: Production Theory Page: 18 where TR is the change in total revenue associated with the given change ( X) in the variable input. MRP x is equal to the marginal product of X (MP x ) times the marginal revenue (MR Q ) resulting form the increase in output obtained: Example MRP = MP x. MR Q Units TP MP MR at $ $ If the addition of one more laborer to a work force would result in the production of two incremental units of a product than can be sold for $5, the MP of labor is 2, and its MRP is $10 (2 x $5).

19 MELed7_01: Production Theory Page: 19 Marginal Factor Cost Def: MFC is the amount that an additional unit of the variable input adds to total cost MFC = TC X Optimal Input Level Given the marginal revenue product and marginal factor cost, we can compute the optimal amount of the variable input to use in the production process. Recall that prior discussions on optimality and marginal analysis suggest that an economic activity should be expanded as long as the marginal benefits exceed the marginal costs. The optimal point occurs at the point where the marginal benefits are equal to the marginal costs. MRP x = MFC x Single Input System Profit maximization requires production at a level such that marginal revenue equals marginal cost. Because the only variable in the system is input L, the marginal cost of production is:

20 MELed7_01: Production Theory Page: 20 MC = TC Output MC = P L MP L Since marginal revenue must equal marginal cost at the profitmaximizing level, MR Q can be substituted for MC Q MR Q = P L MP L solving for P L yields: P L = MR Q x MP L -or- P L = MRP L The profit maximizing firm will always employ an input up to the point where its marginal revenue product equals its cost. NOTE: if MRP L > P L the expand labor usage. if MRP L < P L the cutback labor usage.

21 MELed7_01: Production Theory Page: 21 The Ore-Mining Example Revisited 1. Firm can employ as much labor as it needs by paying workers $50 per period (the labor market is considered perfectly competitive). 2. Firm can sell all the ore it can produce at a price of $10 per ton. MRP = MFC = $50 3. At less than 6 workers, MRP > MFC and the addition of more workers will increase revenues. Beyond 6, the opposite is true. Labor Input Total Prod. Tons of Ore MP of Labor TR or P Q MR TR Q MRP MP MR MFC

22 MELed7_01: Production Theory Page: 22 PRODUCTION FUNCTIONS WITH 2 VARIABLE INPUTS Using the Ore Mining example, assumed that both capital and labor are now variable. Production Isoquant A production isoquant is either a geometric curve or an algebraic function representing all the various combinations of the two inputs that can be used in producing a given level of output, -or- An isoquant is a curve (a locus of points) showing all possible combinations of inputs physically capable of producing a given fixed level of output.

23 MELed7_01: Production Theory Page: 23 MARGINAL RATE OF TECHNICAL SUBSTITUTION Def: the rate at which one input may be substituted for another input in the production process, -or- the rate at which one input is substituted for another along an isoquant. The rate of change of one variable with respect to another variable is given by the slope of the curve relating the two variables. Thus, the rate of change of input Y with respect to X --- that is, the rate at which Y may be substituted for X in the production process --- is given by the slope of the curve relating Y to X. This is the slope of the isoquant. Since the slope is negative and one wishes to express the substitution rate as a positive quantity, a negative sign is attached to the slope. MRTS = Y 1 - Y 2 X 1 - X 2 = Y X For example, in the Ore Mining problem, a targeted ouptup (Q) of producing 29 tons of ore can be achieved by different combinations of the two inputs (L and K). For example, moving from 3 to 4 workers yields an MRTS of 250 (horsepower). MRTS = = 250

24 MELed7_01: Production Theory Page: 24 Stated differently, for every unit of labor added 250 horsepower may be discharged without changing total output. Note that we can show the MRTS to equal the ratio of the marginal products of X and Y; remember: and, Y = X = Q MP Y Q MP X substituting these in above yields, MRTS = MP X MP Y

25 MELed7_01: Production Theory Page: 25 THE OPTIMAL COMBINATION OF INPUTS The firm must make two input choice decisions: 1. Choose the input combination that yields the maximum level of output possible with a given level of expenditure. 2. Choose the input combination that leads to the lowest cost of producing a given level of output. This occurs when, in any constrained optimization problem, we choose the level of each activity whereby the marginal benefits from the last unit of each activity per dollar cost of the activity are equal. This is known as the equimarginal criterion. MP X C X = MP Y C Y -or- MP X P X = MP Y P Y The optimal combination of inputs in either the costminimization or output-maximization problem is a function of the relative prices of the inputs.

26 MELed7_01: Production Theory Page: 26 CHANGES IN INPUT PRICES Assume that a firm is producing with the most cost minimizing combination of labor and capital. This is an efficient operation. From our development above, we know that: MP X C X = MP Y C Y Now suppose that the price of input X rises while the price of input Y is unchanged and the original combination of inputs MP X and MP Y are unchanged. At the original combinations, the increase in C X makes: MP X C X < MP Y C Y Substitution Effect: If the firm wishes to produce the same level of output, it will increase Y and decrease X as it moves along the isoquant. If the input-price ratio changes, firms substitute toward the input that becomes relatively less expensive and away form the input that becomes relatively more expensive. In the case of labor and capital, if wages/interest increases (decreases), K/L increases (decreases) at each level of output. This change in the K/L ratio is called the substitution effect.

27 MELed7_01: Production Theory Page: 27 Isoquant and Isocost Combinations Optimal input proportions can be found graphically for a twoinput, single-output system by adding a budget line or isocost curve (a line of constant costs) to the diagram of production isoquants. Each point on a budget line represents some combination of inputs (X and Y) whose cost equals constant expenditure. The expansion path is the optimal input combinations for increasing output. Note that the proportions in which the inputs are combined need not be the same for all levels of outputs. Stated differently, the expansion path shows how factor proportions change when output changes, with the factor-price ratio held constant.

28 MELed7_01: Production Theory Page: 28 The Decision Making Principle: To minimize the cost (expenditure) of producing a given level of output with fixed input prices, the producer must combine inputs in such quantities that the marginal rate of technical substitution of capital and labor is equal to the input ratio (the price of labor to the price of capital). RETURNS TO SCALE Production theory also offers a means for analysis of the effects on output of changes in the scale of production. An increase in the scale of production consists of a simultaneous proportionate increase in all the inputs used in the production process. The proportionate increase in the output of the production process that results from the given proportionate increase in all the inputs is defined as the physical returns to scale. Q = % Q % X = Q X X Q Q > 1 increasing Q = 1 constant Q < 1 diminishing

29 MELed7_01: Production Theory Page: Increasing: Output goes up proportionately more than the increase in input usage. 2. Constant: Output goes up by the same proportion as the increase in input usage. 3. Decreasing: Output goes up proportionately less than the increase in input usage. ESTIMATION OF PRODUCTION FUNCTIONS One of the more common approaches utilizes the Cobb Douglas production function method. Q = L 1K 2 1. Both inputs are required to create output. 2. MRTS will diminish as required by production theory Logarithmic Specification Ln Q = Ln + 1 LnL + 2 LnK Elasticity of Production where; E L = MP L AP L

30 MELed7_01: Production Theory Page: 30 MP L = 1L 1-1 K 2 and, APL = L 1K 2 L = L 1-1 K 2 thus: E L = 1 L 1-1 K 2 L 1-1 K 2 = 1 The Exponents - Returns to Scale 1. Increasing: > 1 2. Constant: = 1 3. Decreasing: < 1 Example Q = K 0.25 Q was an index of physical volume of manufacturing; L was an index of the average number of employed wage earners only (that is, salaried employees, officials, and working proprietors were excluded); and K was an index of the value of plants, buildings, tools and machinery reduced to dollars of constant purchasing power. The sums of the exponents were restricted to one (constant returns to scale).

31 MELed7_01: Production Theory Page: 31 Later Studies by Cobb and Douglas Q =.84 L 0.63 K 0.30 A one (1) percent increase in labor input results in about a 2/3 percent increase in output, and a one (1) percent increase in capital input results in approximately a 1/3 percent increase in output. The sum of the exponents is slightly less than one (1). Seems to indicate the presence of decreasing returns to scale, however, the sum is not significantly different from 1.0; hence, it really confirms constant returns to scale. A Three Variable Model Q = L p 1 L n 2 K 3 Q is the value added by production plants over 18 industries L n is non-production work-years L p is production work-hours K is gross book values of depreciable and depletable assets

32 MELed7_01: Production Theory Page: 32 Empirical Estimation of a Production Function for: Major League Baseball by CE. Zech as published in the American Economist In an attempt to quantify the factors that contribute to the team s success, a Cobb-Douglas production function was developed using data from the 26 major league baseball teams in Output (Q) was measured by team victories. Inputs from five different categories were included in the model: Hitting: batting average and power (home runs) Running: stolen base record Defense: fielding percentage and total chances accepted Pitching: earned run average (ERA) and strikeouts-to-walks ratio. Coaching: Lifetime won-lost record and number of years spent managing in the major leagues. Dummy: NL = 0, AL = 1

33 MELed7_01: Production Theory Page: 33 Variable Eq. 1 Eq. 2 Eq. 3 Eq. 4 Problems Constant Anova? Dummy B avg Constant Variance? HomeRuns Stolen Bases Normality? Strikeouts/Walks TotField Chances Field % Mngr.W/L Mngr. Years R Findings: 1. Hitting average contributes almost six times as much as pitching to a team s success. Contradict traditional wisdom? 2. Home runs contribute about twice as much as stolen bases to a team s success. 3. Coaching skills are not significant in any of the regression equations. 4. Defensive skills are not significant in any of the regression equations. 5. The sums of the statistically significant variables in each of the four equations range from to Because these

34 MELed7_01: Production Theory Page: 34 are all greater than 1.0, the baseball production functions exhibit increasing returns to scale.

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