THEORY OF PRODUCTION & COST

The Production FunctionThe production function refers to the physical relationship between the inputs or resources of a firm and their output of goods and services at a given period of time, ceteris paribus.

The production function is dependent on different time frames. Firms can produce for a brief or lengthy period of time.

Firms InputsInputs - are resources that contribute in the production of a commodity. Most resources fall into three categories: Land, Labor,Capital.

Fixed vs. Variable InputsFixed inputs -resources used at a constant amount in the production of a commodity. Variable inputs - resources that can change in quantity depending on the level of output being produced. The longer planning the period, the distinction between fixed and variable inputs disappears, i.e., all inputs are variable in the long run.

Production Analysis with One Variable InputTotal product (Q) refers to the total amount of output produced in physical units (may refer to, kilograms of sugar, sacks of rice produced, etc)The marginal product (MP) refers to the rate of change in output as an input is changed by one unit, holding all other inputs constant.

Total vs. Marginal ProductTotal Product (TPx) = total amount of output produced at different levels of inputsMarginal Product (MPx) = rate of change in output as input X is increased by one unit, ceteris paribus.

Production Function of a Rice Farmer

Units of LTotal Product (QL or TPL)Marginal Product (MPL)00-122264312642085266630473228320930-21026-4

FIGURE 5.1. Total product curve. The total product curve shows the behavior of total product vis-a-vis an input (e.g., labor) used in production assuming a certain technological level.LQLQL261220263032LaborTotal product024681097531

Marginal ProductObserve that the marginal product initially increases, reaches a maximum level, and beyond this point, the marginal product declines, reaches zero, and subsequently becomes negative.

The law of diminishing returns states that "as the use of an input increases (with other inputs fixed), a point will eventually be reached at which the resulting additions to output decrease"

Total and Marginal ProductTPLMPL

Law of Diminishing ReturnsAs more and more of an input is added (given a fixed amount of other inputs), total output may increase; however, as the additions to total output will tend to diminish.

Counter-intuitive proof: if the law of diminishing returns does not hold, the worlds supply of food can be produced in a hectare of land.

Average Product (AP)Average product is a concept commonly associated with efficiency. The average product measures the total output per unit of input used. The "productivity" of an input is usually expressed in terms of its average product. The greater the value of average product, the higher the efficiency in physical terms. Formula:

Rise = YRun = L0LYThe slope of the line from the origin is a measure of the AVERAGEYL1L2ab

LQTPL Highest Slope of Line from OriginMax APL Inflection pointMax MPL 0 L1L2L3

Relationship between Average and Marginal Curves: Rule of ThumbWhen the marginal is less than the average, the average decreases.When the marginal is equal to the average, the average does not change (it is either at maximum or minimum)When the marginal is greater than the average, the average increases

LAP,MPMax APL Max MPL 0 L1L2L3MPLAPLAt Max AP, MP=AP

LAP,MP0 L1L2L3MPLAPLStage IMP>APAP increasingStage IIMP

Three Stages of ProductionIn Stage I APL is increasing so MP>AP.All the product curves are increasingStage I stops where APL reaches its maximumMP peaks and then declines, so the law of diminishing returns begins to manifest at this stage

Three Stages of ProductionStage IIstarts where the APL of the input begins to decline. QL still continues to increase, although at a decreasing rate, and in fact reaches a maximumMarginal product is continuously declining and reaches zero, as additional labor inputs are employed.

Three Stages of ProductionStage III starts where the MPL has turned negative. all product curves are decreasing. total output starts falling even as the input is increased

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

Production with TwoVariable InputsIsoquants 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.

Production with TwoVariable InputsMarginal Rate of Technical SubstitutionMRTS = -K/L = MPL/MPK

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

Returns to ScaleProduction 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, then f has decreasing returns to scale.

COSTS OF PRODUCTIONOpportunity Cost Principle - the economic cost of an input used in a production process is the value of output sacrificed elsewhere. The opportunity cost of an input is the value of foregone income in best alternative employment.Implicit vs. Explicit CostsExplicit costs costs paid in cashImplicit cost imputed cost of self-owned or self employed resources based on their opportunity costs.

7 Cost Concepts (Short-run)Total Fixed Cost (TFC)Total Variable Cost (TVC)Total Cost (TC=TVC+TFC)Average Fixed Cost (AFC=TFC/Q)Average Variable Cost (AVC=TVC/Q)Average Total Cost (AC=AFC+AVC)Marginal Cost (MC= TVC/Q

Short Run AnalysisTotal fixed cost (TFC) is the cost which is not changed with the level of production." Examples: include the payment or rent for land, buildings and machinery.Graphically, depicted as a horizontal line It can be eliminated only by shutting down.

Short Run AnalysisTotal variable cost (TVC) refers to the cost that changes as the amount of output produced is changed. Examples - purchases of raw materials, payments to workers, electricity bills, fuel and power costs. Total variable cost increases as the amount of output increases. If no output is produced, then total variable cost is zero;the larger the output, the greater the total variable cost.

Short Run AnalysisTotal cost (TC) is the sum of total fixed cost and total variable cost TC=TFC+TVC As the level of output increases, total cost of the firm also increases.

Q0TFC (Total Fixed Cost)INRTVC (Total Variable Cost)TC (Total Cost)TOTAL COST CURVES

Q0AFC (Average Fixed Cost)INRAFC=TFC/Q. As more output is produced, the Average Fixed Cost decreases.

Q0TVC (Total Variable Cost)q1The Average Variable Cost at a point on the TVC curve is measured by the slope of the line from the origin to that point.AVC=TVC/QMinimum AVCINR

Q0MCq1Inflection pointTVC (Total Variable Cost)q1AVCINR

Q0AVC(Average Variable Cost)q1The Average Variable Cost is U shaped. First it decreases, reaches a minimum and then increases.Minimum AVCINR

Q0AVC(Average Variable Cost)q1The Marginal Cost curve passes through the minimum point of the AVC curve. It is also U-shaped. First it decreases, reaches a minimum and then increases.Minimum AVCMC (Marginal Cost)INR

Q0AVCq1MCAFCACThe PER UNIT COST CURVESINR

Table 5.4 Average Cost of Production

(Q)(TC)(AC)0100-1130130.00215075.00316053.33416541.25517535.00619532.50722532.14826533.13931535.001037537.50

Table 5.5 Average Variable Costs of Production

Total Product (Q)Total Variable Cost (TVC)Average Variable Cost (AVC)00013030.025025.036020.046516.357515.069515.8712517.9816520.6921523.91027527.5

Long Run Total CostLTCLTCQTotal ProductAll inputs are variable in the long run. There are no fixed costs.LONG-RUN TOTAL COST CURVE

The LACThe LAC curve is an envelop curve of all possible plant sizes. Also known as planning curveIt traces the lowest average cost of producing each level of output.It is U-shaped because of Economies of ScaleDiseconomies of Scale

LACSAC1Q0COSTSAC2LONG-RUN AVERAGE COST CURVE

LACQ0COSTSAC1q0

LACQ0COSTSAC1q0SAC2Building a larger sized plant (size 2) will result in a lower average cost of producing q0

LACQ0COSTSAC1q0SAC2Likewise, a larger sized plant (size 3) will result to a lower average cost of producing q1q1SAC3

Economies and Diseconomies of ScaleEconomies of Scale- long run average cost decreases as output increases.Technological factorsSpecialization Diseconomies of Scale: - long run average cost increases as output increases.Problems with management becomes costly, unwieldy

LACSAC1Q0COSTSAC2LONG-RUN AVERAGE COST CURVEQ1Economies of ScaleDiseconomies of Scale

LACSAC1Q0COSTLONG-RUN AVERAGE and MARGINAL COST CURVESQ1LMCSMC1SMC2SAC2

LAC and LMCLong-run Average Cost (LAC) curve is U-shaped. the envelope of all the short-run average cost curves; driven by economies and diseconomies of size.Long-run Marginal Cost (LMC) curve Also U-shaped; intersects LAC at LACs minimum point.

Economies and Diseconomies of Scaleeconomies of scale Situation in which output can be doubled for less than a doubling of cost.diseconomies of scale Situation in which a doubling of output requires more than a doubling of cost.Increasing Returns to Scale: Output more than doubles when the quantities of all inputs are doubled.

Economies of Scale: A doubling of output requires less than a doubling of cost.

Economies and Diseconomies of ScaleAs output increases, the firms average cost of producing that output is likely to decline, at least to a point.

This can happen for the following reasons:

If the firm operates on a larger scale, workers can specialize in the activities at which they are most productive.

Scale can provide flexibility. By varying the combination of inputs utilized to produce the firms output, managers can organize the production process more effectively.

The firm may be able to acquire some production inputs at lower cost because it is buying them in large quantities and can therefore negotiate better prices. The mix of inputs might change with the scale of the firms operation if managers take advantage of lower-cost inputs.

Economies and Diseconomies of ScaleAt some point, however, it is likely that the average cost of production will begin to increase with output.

There are three reasons for this shift:

At least in the short run, factory space and machinery may make it more difficult for workers to do their jobs effectively.

Managing a larger firm may become more complex and inefficient as the number of tasks increases.

The advantages of buying in bulk may have disappeared once certain quantities are reached. At some point, available supplies of key inputs may be limited, pushing their costs up.

Economies of scale are often measured in terms of a cost-output elasticity, EC. EC is the percentage change in the cost of production resulting from a 1-percent increase in output:

EC = (C/C)/ q/q)To see how EC relates to our traditional measures of cost, rewrite the equation as follows:EC = (C/ q C)/ C/q) = MC/AC

Economies and Diseconomies of Scale

Economies and Diseconomies of ScopeEconomies of scope: Situation in which joint output of a single firm is greater than output that could be achieved by two different firms when each produces a single product.Diseconomies of scope: Situation in which joint output of a single firm is less than could be achieved by separate firms when each produces a single product.

The Degree of Economies of Scopedegree of economies of scope (SC) Percentage of cost savings resulting when two or more products are produced jointly rather than Individually.To measure the degree to which there are economies of scope, we should ask what percentage of the cost of production is saved when two (or more) products are produced jointly rather than individually.

As management and labor gain experience with production, the firms marginal and average costs of producing a given level of output fall for four reasons:

Workers often take longer to accomplish a given task the first few times they do it. As they become more adept, their speed increases.

Managers learn to schedule the production process more effectively, from the flow of materials to the organization of the manufacturing itself.

Engineers who are initially cautious in their product designs may gain enough experience to be able to allow for tolerances in design that save costs without increasing defects. Better and more specialized tools and plant organization may also lower cost.

Suppliers may learn how to process required materials more effectively and pass on some of this advantage in the form of lower costs.THE LEARNING CURVE

The Learning CurveThe learning curve shows the extent to which hours of labor needed per unit of output fall as the cumulative output increases.learning curve Graph relating amount of inputs needed by a firm to produce each unit of output to its cumulative output.

A firms average cost of production can decline over time because of growth of sales when increasing returns are present (a move from A to B on curve AC1), or it can decline because there is a learning curve (a move from A on curve AC1 to C on curve AC2).

Cost-Volume-Profit AnalysisTotal Revenue = TR = (P)(Q)Total Cost = TC = TFC + (AVC)(Q)Breakeven Volume TR = TC(P)(Q) = TFC + (AVC)(Q)QBE = TFC/(P - AVC)

Operating LeverageOperating Leverage = TFC/TVCDegree of Operating Leverage = DOL

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