Ch 6 Product 1011

Production Theory and EstimationDepartment of Business AdministrationFALL 2010-11byAssoc. Prof. Sami Fethi

Ch 6 Production Theory 2010/11, Sami Fethi, EMU, All Right Reserved. 2004, Managerial Economics, Dominick Salvatore

The Production FunctionProduction refers to the transformation of inputs or resources into outputs of goods and services. In other words, production refers to all of the activities involved in the production of goods and services, from borrowing to set up or expand production facilities, to hiring workers, purchasing row materials, running quality control, cost accounting, and so on, rather than referring merely to the physical transformation of inputs into outputs of goods and services.


For exampleA computer company hires workers to use machinery, parts, and raw materials in factories to produce personal computers.The output of a firm can either be a final commodity or an intermediate product such as computer and semiconductor respectively.The output can also be a service rather than a good such as education, medicine, banking etc.


The Organization of ProductionInputsLabor, Capital, LandFixed InputsVariable InputsShort RunAt least one input is fixedLong RunAll inputs are variable


The Organization of ProductionInputs: are the sources used in the production of goods and services and can be broadly classified into labour, capital, land, natural resources, and entrepreneurial talent.Fixed input: are those that cannot be readily changed during the time period under consideration such as a firms plant and specialized equipment.


The Organization of ProductionVariables Inputs: are those can be varied easily and on very short notice such as raw materials and unskilled labour.The time period during which at least one input is fixed called the short-run and if all inputs are variable, we are in the long-run.


The Production FunctionA production function is an equation, tables, or graph showing the maximum output of a commodity that a firm can produce per period of time with each set of inputs.Both inputs and outputs are measured in physical rather than in monetary units. Here technology is assumed to remain constant during the period of the analysis.


The Production FunctionThe general equation of the production function of a firm using labour (L) and capital (K) to produce a good or service (Q) or shows the maximum amount of output (Q) that can be produced within a given time period with each combination of (L) and (K). This can be defined as follows:

Q= f (L,K)


Production Function With Two InputsQ = f(L, K)The table shows that by using 1 unit of labour (1L) and 1 unit of capital (1K), the firm would produce 3 units of o/p (3Q).


Production Function With Two InputsDiscrete Production SurfaceThe previous table are shown graphically in this figure. The height of bars refers to the max o/p that can be produced with each combination of labour and capital shown on the axes.


Production Function With Two InputsContinuous Production SurfaceIn this figure, If we assume that i/ps and o/ps are continuously divisibly, we would have the continuous production surface. This indicates that by increasing L2 with K1 of capital, the firm produces the o/p by height of cross section K1AB. Increasing L1 with K2, we have cross section K2CD.


Production Function With One Variable InputWhen discussing production in the short run, three definitions are important:Total productMarginal productAverage product


Production Function With One Variable InputTotal ProductMarginal ProductAverage ProductProduction or Output ElasticityTP = Q = f(L)


Total ProductTotal product (TP) is another name for output in the short run.

TP = Q = f (L)


Marginal ProductThe marginal product (MP) of a variable input is the change in output (or TP) resulting from a one unit change in the input.MP tells us how output changes as we change the level of the input by one unit.Consider the two input production function Q=f (L,K) in which input L is variable and input K is fixed at some level.The marginal product of input L is defined as holding input K constant.


Average ProductThe average product (AP) of an input is the total product divided by the level of the input.AP tells us, on average, how many units of output are produced per unit of input used.The average product of input L is defined as holding input K constant.


Production Function With One Variable Input-ExampleTotal, Marginal, and Average Product of Labor, and Output Elasticity


Production Function With One Variable Input


The Law of Diminishing Returns As additional units of a variable input are combined with a fixed input, after a point the additional output (marginal product) starts to diminish. This is the principle that after a point, the marginal product of a variable input declines.


The Law of Diminishing ReturnsIncreasing ReturnsDiminishing Returns BeginsMP


The Three Stages of Production


The Three Stages of ProductionStage I: The range of increasing average product of the variable input.From zero units of the variable input to where AP is maximizedStage II: The range from the point of maximum AP of the variable i/p to the point at which the MP of i/p is zero.From the maximum AP to where MP=0Stage III: The range of negative marginal product of the variable input.From where MP=0 and MP is negative.


The Three Stages of Production


The Three Stages of ProductionIn the short run, rational firms should only be operating in Stage II.Why Stage II?Why not Stage I and III?In Stage III- MPLis negativeIn Stage I- MPK is negativeIn Stage II- MPL and MPK are both positive but decline


The Three Stages of Production-ExampleStage II

Sheet1

Units of Y EmployedOutput Quantity (Q)Labor Unit (L)Total Product (Q or TP)Average Product (AP)Marginal Product (MP)

8.0037.0060.0083.0096.00107.00117.00127.00128.0000

7.0042.0064.0078.0090.00101.00110.00119.00120.00110,00010,00010,000

6.0037.0052.0064.0073.0082.0090.0097.00104.00225,00012,50015,000

5.0031.0047.0058.0067.0075.0082.0089.0095.00345,00015,00020,000

4.0024.0039.0052.0060.0067.0073.0079.0085.00460,00015,00015,000

3.0017.0029.0041.0052.0058.0064.0069.0073.00570,00014,00010,000

2.008.0018.0029.0039.0047.0052.0056.0052.00675,00012,5005,000

1.004.008.0014.0020.0027.0024.0021.0017.00778,00011,1433,000

1.002.003.004.005.006.007.008.00880,00010,0002,000

Units of X Employed

Units of Y EmployedOutput Quantity (Q)Variable Input (X)Total Product (Q or TP)Marginal Product (MP)Variable Input (X)Total Product (Q or TP)Average Product (AP)

8.0037.0060.0083.0096.00107.00117.00127.00128.000.000.000.000.00---

7.0042.0064.0078.0090.00101.00110.00119.00120.001.008.001.008.008.00

6.0037.0052.0064.0073.0082.0090.0097.00104.002.0018.002.0018.009.00

5.0031.0047.0058.0067.0075.0082.0089.0095.003.0029.003.0029.009.67

4.0024.0039.0052.0060.0067.0073.0079.0085.004.0039.004.0039.009.75

3.0017.0029.0041.0052.0058.0064.0069.0073.005.0047.005.0047.009.40

2.008.0018.0029.0039.0047.0052.0056.0052.006.0052.006.0052.008.67

1.004.008.0014.0020.0027.0024.0021.0017.007.0056.007.0056.008.00

1.002.003.004.005.006.007.008.008.0052.008.0052.006.50

Units of X Employed

Sheet2

Sheet3


The Three Stages of Production-ExampleWhat level of input usage within Stage II is best for the firm? Is there a precise point.

The answer depends upon how many units of output the firm can sell, the price of the product, and the monetary costs of employing the variable input.


Optimal Use of the Variable InputHow much labor or the variable input should the firm use in order to maximize profit. The firm should employ an additional unit of labor as long as the extra revenue genereted until the extra revenue equals the extra cost.Where MRP=MLC.


Optimal Use of the Variable InputMarginal Revenue Product of LaborMRPL = (MPL)(MR)Marginal Resource Cost of LaborMRCL =Optimal Use of LaborMRPL = MRCL


Optimal Use of the Variable Input-ExampleUse of Labor is Optimal When L = 3.50MRPL=MRxMPL--------MRC=W


Optimal Use of the Variable Input


Production With Two Variable Inputs-In the long run, all inputs are variable.Isoquants show combinations of two inputs that can produce the same level of output.-In other words, Production isoquant shows the various combination of two inputs that the firm can use to produce a specific 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 higher isoquant refers to a larger output, while a lower isoquant refers to a smaller output.


Production With Two Variable InputsIsoquants


Production IsoquantEconomic region of production: Negatively sloped portions of the isoquants within the ridge lines represents the relevant economic region of production.Ridge lines: The lines that separate the relevant (i.e., negatively sloped) from the irrelevant ( or positively sloped) portions of the isoquant.This refers to stage II where the MPLand MPK are both positive but declining and producers never want to operate outside this region.


Production With Two Variable InputsEconomic Region of Production


Production With Two Variable InputsMarginal Rate of Technical Substitution: The absolute value of the slope of the isoquant. It equals the ratio the marginal products of the two inputs. Slope of isoquant indicates the quantity of one input that can be traded for another input, while keeping output constant.

MRTS = -K/L = MPL/MPKSubstitution among inputs


Production With Two Variable InputsMRTS = -(-2.5/1) = 2.5


Production With Two Variable InputsPerfect SubstitutesPerfect ComplementsWhen an isoquant is straight line or MRTS is constant, inputs are perfect substitutes whilst an isoquant is right angled, inputs are perfect complements.


Optimal Combination of InputsTo determine the optimal combination of labor and capital, we also need an isocost line.Isocost lines represent all combinations of two inputs that a firm can purchase with the same total cost.Slope of isocostVertical intercept of isocost


Optimal Combination of Inputs


Example: Isocost LinesAB Total Cost = c = $100w=r=$10c/r = $100/$10 = $10k (vertical intercept)-w/r = -$10/$10 = -1(slope)ABTotal Cost = c = $140w=r=$10c/r = $140/$10 = $14k-w/r = -$10/$10 = -1

AB Total Cost = c = $80w=r=$10c/r = $80/$10 = $8k -w/r = -$10/$10 = -1

AB*C = $100,w = $5, r = $10c/r = $100/$10 =$10k-w/r = -$10/$5 = -1/2

MRTS = w/r; since MRTS = MPL/ MPK, condition for optimal combination of inputs as MPL/ MPK= w/r


Expansion PathExpansion path: joinning points of tangency of isoquants and isocost of optimal input combination. The optimal input combination required to minimize the cost of producing a given level of maximum output that the firm can produce at the tangency of an isoquant and an isocost.


Optimal Combination of InputsIf the price of an input declines, the firm will substitute the cheaper input for another inputs in production in order to reach a new optimal input combination.


Returns to ScaleHow does output vary with the scale of production?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.Returns to scale describes what happens to total output as all of the inputs are changed by the same proportion.


Returns to ScaleGraphically, the returns to scale concept can be illustrated using the following graphs.The long run production process is described by the concept of returns to scale.


If all inputs into the production process are doubled, three things can happen:

output can more than doubleincreasing returns to scale (IRTS)

output can exactly doubleconstant returns to scale (CRTS)

output can less than doubledecreasing returns to scale (DRTS)Returns to Scale


Constant Returns to ScaleIncreasing Returns to ScaleDecreasing Returns to ScaleReturns to Scale


Empirical Production FunctionsSeveral Useful Properties :The Marginal Product of capital and the marginal Product of labor depend on both the quantity of capital and the quantity of labor used in production, as is often the case in the real world.K and L are represents the output elasticity of labor and capital and the sum of these exponents gives the returns on scale. a + b = 1 Constant return to scale a + b > 1 Increasing return to scale a + b

Ch 6 Product 1011

Documents

Transcript of Ch 6 Product 1011