Laws of Production: Laws of Production The PF has been explained by different economists in different ways to formulate laws relating to the relationship between inputs and outputs. They are: First Type of PF has only one factor variable while other factors are kept constant . Prof Benham explained this type of PF which has been described as The Law Of Variable Proportions . Modern version of the law of diminishing returns. Second Type of PF with Two Variable Inputs and all other factors kept constant. Iso- Quants and Iso -Costs Third type of PF , the quantities of every input in the combination of inputs can be varied to produce different quantities of OP. Known as The Law Of Returns To Scale . It is associated with long period production process.
Measurements of Product: Measurements of Product TOTAL PRODUCT (TP ) = Total # of unit produced per unit of time by all the factor inputs In SR Total OP increases with an increase in the variable factor input. Thus TP= f(QVF) where QVF denotes the quantity of the variable factor. AVERAGE PRODUCT (AP) = The total product per unit of a given variable factor . AP= TP/QVF Ex: TP of a commodity is 400 units per day with 25 workers then, AP= 400/25= 16 units per worker. MARGINAL PRODUCT (MP) = owing to the addition of a unit to a variable factor , all other factors being held constant , the addition realized in the total product is technically referred to a the MP. MPn = TPn – TPn-1 where MPn = MP when n units of a variable factor are employed. TP = Total Product and refers to the # of units of variable factor employed (n= QVF). Ex: When 26 workers are employed the TP increased to 440 units from 400 units . The MP of twenty sixth worker is MP= TP26- TP25 = 440-400=40 units. MP= TP QVF
The Law of Variable Proportions: The Law of Variable Proportions Only one factor of Production is variable while other factors are fixed. As we Increase the quantity of variable factor while keeping other factors constant the OP of variable factor may increase more than proportionately in the initial stages of Production but finally it will not increase proportionately. As the proportion of one factor in a combination of factors is increased after a point, the average and marginal production of that factor will diminish . Conditions underlying the law are as follows: Only one factor is varied and all others should remain constant. The scale of OP is unchanged, and the Production plant or the size efficiency of the firm remain constant The technique of P does not change. All units of the factor input varied are homogenous, i.e. all the units have identical characteristics and equal efficiencies. Under such circumstances the physical relationship between input(variable factor proportions) and OP is described by the Law of Factor Proportions or the Law of Non-Proportional OP.
The Law of Variable Proportions: The Law of Variable Proportions Elaborately stating the Law : In the short run, as the amount of variable factors increases, other things remaining equal, OP(or the returns to the factors varied will increase more than proportionally to the a amount of the variable inputs in the beginning than it may increase in the same proportion and ultimately it will increase less proportionately. Assuming that the firm only varies the labour (L), it alters the proportion between the fixed input and the variable input. As this altering goes on, the firm experiences the Law of Diminishing Marginal Returns.
Production Schedule: Production Schedule Using the concept of MP, During the SR, under the given state of technology and other conditions remaining unchanged, with the given fixed factors, when the units of a variable factor are increased in the production function in order to increase the TP, the TP initially may rise at an increasing rate and after a point, it tends to increase at a decreasing rate because the MP of the variable factor in the beginning may tend to rise but eventually tends to diminish. Units of Variable Input (Labour) (n) Total Product (TP) Average Product (AP) ( TPn ) Marginal Product ( TPn - TPn-1) 1 20 20 20 STAGE I 2 50 25 30 3 90 30 40 4 120 30 30 STAGE II 5 135 27 15 6 144 24 9 7 147 21 3 8 148 18.5 1 9 148 16.4 0 10 145 14.5 -3 STAGE III
Slide 6: Increasing Returns Diminishing Returns Negative Returns TP
Stages: Stages Diminishing Total returns -implies reduction in total product with every additional unit of input. Diminishing Average returns -which refers to the portion of the Average Physical Product curve after its intersection with MPP curve. Diminishing Marginal returns refers to the point where the MPP curve starts to slope down and travels all the way down to the x-axis and beyond. Putting it in a chronological order, at first the marginal returns start to diminish, then the average returns, followed finally by the total returns .
Observations: Observations The L of DMR becomes evident in the marginal product column. Initially MP of Labor rises . The TP rises at an increasing rate (= MP). Average Product also rises. Stage of increasing Returns After certain point (4 th unit of Labour), the MP begins to diminish. Rate of increase in the TP slows down. Stage of diminishing returns . When AP is max, AP=MP=30 at 4 th unit of labour . AS MP diminishes, it becomes zero and negative thereafter (Stage III) When MP is zero, TP is maximum. (148 is the highest amount of TP, when MP is equal to 0 when 9 units of labour are employed. When MP becomes negative, TP also starts to diminish in the same proportion but AP declines after being positive up to a certain point.
PF Through Iso quant Curve: PF Through Iso quant Curve Equal Product Curve (Iso-Quant - meaning equal quantity) or also called as Production Iso- Quant. The firm increases its OP by using more of two inputs that are substitutes for each other say, Labour and Capital The two variable input case may be a short run or a long run based on the assumptions made Firm uses only twi inputs and both of them are variable –long run analysis If more than two inputs areused but only two of them are variable and others fixed then short run analysis
Iso quant Curve: Iso quant Curve It represents all the combinations of two factor inputs which produce a given quantity of product. Ex: 2L+9K 3L+6k 4L+4k 5L+8k EPC signifies a definite measureable quantity of OP so the units of OP can be labeled to the given iso-quant. Iso quant map represents a set of iso-quants describing production function of a firm. A higher IQ represents a larger quantity of OP than the lower one.
Equal Product Combination: Equal Product Combination Combinations Factor X Labour Factor Y Capital Total OP in Units A 12 1 100 B 8 2 100 C 5 3 100 D 3 4 100 E 2 5 100
Production Function Plot: Production Function Plot 2/17/2011 12
Isoquants: Isoquants 2/17/2011 13 An isoquant is a contour, which contains all input combinations yielding the same production output
Properties of Iso-Quant: Properties of Iso -Quant Iso- Quants have negative slope. Are convex to Origin Do not intersect and do not intercept either axis. Are oval in shape
Difference between EPC and IC: Difference between EPC and IC IC indicate higher level of satisfaction. EPC indicate the quantity of OP. IC relate to combinations of 2 commodities. EPC relate to combinations between two factors of production. Cant be labeled but EPC can be labeled numerically as physical units of OP. On Ic, between higher and lower IC, the extent of difference in the satisfaction is not quantifiable. In EPC, the size of the physica OP at various points on EPM are quantifiable and comparable.
Marginal Rate of Substitution: Marginal Rate of Substitution Marginal Rate of Substitution (MRS) is the rate at which one input can be substituted for another without changing the production output. MRTS will be diminishing and hence is known as the law of Diminishing Marginal Rate of Technical Substitution (DMRTS). Combinations Feactor X Labour Factor Y Capital MRTS of X for Y A 12 1 Nil B 8 2 4:1 C 5 3 3:1 D 3 4 2:1 E 2 5 1:1
Marginal Rate of Substitution: Marginal Rate of Substitution The MRS is related to the slope of the isoquant at any combination of inputs INCREASED QUANTITY ΔK ΔL The MRS is the negative of the slope of the isoquant
Isocost Lines: Isocost Lines An isocost line is a line containing all input combinations that result in the same cost. The cost equation is: P K = $1/unit K P L = $2/unit L Cost = $6 With constant cost: INCREASED COST
Least-Cost Production: Least-Cost Production What is least-cost production and how is it measured and achieved? Least Cost Production occurs when the inputs are combined in such a way that the cost is minimum. Marginal Product tells how much output we get from an additional unit of input. Greater marginal product means lower cost per additional unit of output. 19 NOTE: Unit cost of output varies inversely with input productivity. or
MRS related to Marginal Product: MRS related to Marginal Product If we move along an isoquant (Q is constant) then the impact of increasing one input must be offset by the decrease in the other input. therefore: Or 20 The rate at which one input can be substituted for another is inversely related to their productivities
Producers Equilibrium -Optimum factor combination or least cost combination : Producers Equilibrium -Optimum factor combination or least cost combination The optimal combination of factor inputs may help in either minimizing cost for a given level of OP or maximizing OP with a given amount of investment expenditure. For every production output quantity there is a unique combination of inputs that minimizes cost called the Least-Cost Combination of Inputs. Integration of the Iso -quant curve with that of the Iso cost line represents the position of equilibrium where the Iso cost line is tangential to the Iso quant curve. Represents minimum cost or optimum factor combination for producing a given level of OP here MRTS between two points is equal to the ration between the process of the inputs.
Test for Least-Cost Combination: Test for Least-Cost Combination With constant cost: 2/17/2011 22 With constant quantity: Therefore at the least–cost combination: Increase cost until the curves first touch this is the least-cost combination
Expansion Path: Expansion Path Given the slope of the isocost line (input price ratio), each isoquant has a unique least-cost combination point. 2/17/2011 23 A least-cost point occurs whenever an isocost line is tangent to an isoquant. These points can be connected to form an expansion path. In the long run, the firm will expand by moving out the path that connects these points.
Economic region: Economic region The economic region of the iso-quant is determined by drawing tangents to the curves parallel to the axes, and the points of tangency indicate zero marginal productivity of the abundant factors. Ridge lines are lines which connect all the points where MP K and MP L are zero. The region between the ridge lines is called the economic region of production. In the long run, a profit oriented firm will never employ input combinations outside the ridge lines. Ridge Line Ridge Line
Long Run Production Function - Law of Returns to scale: Long Run Production Function - Law of Returns to scale As the firm in the long run increases the quantities of all factors employed, other things being equal, the output may rise initially at a more rapid rate than the rate of increase in inputs, then OP may increase in the same proportion of input and ultimately, OP increases less proportionately. Three phases of Returns in Long Run: The Law of Increasing Returns The Law of constant Returns The Law of Decreasing Returns Assumptions: Technique of production is unchanged. All units of factors are homogenous. Returns measured in physical terms.
Returns to Scale: Returns to Scale Units of labour Units if capital % increase in labour and capital Total product % increase in Total Product Returns to Scale 1 100 - 100 0 Increasing 2 200 100 220 120 3 300 50 350 59 4 400 33.33 500 42.9 5 500 25 625 25 Constant 6 600 20 750 20 7 700 16.66 860 14.66 Decreasing 8 800 14.29 940 9.3 9 900 12.5 1000 6.4
Phases: Phases The Law of Increasing Returns: If PFC (Production Function Coefficient) >1, then increasing returns to scale Increased returns means increased efficiency of labour and capital in the improved organization with the expanding scale of OP and employment of factor input. Referred to as the economy of organization in the earlier stages of expansion. Q / Q > F / F = Q / Q X F/ F where Q/ Q= Proportionate change in OP F/F = Proportionate change in inputs (factors)
The Law of constant Returns: The Law of constant Returns Q / Q = F / F = Q / Q X F/ F where Q/ Q= Proportionate change in OP F/F = Proportionate change in inputs (factors) The Law of Constant Returns: The LIR is followed by the constant returns to scale because as the firm continues to expand its scale of operations, it gradually exhausts the economies of scale responsible for the increasing returns to scale. If PFC (Production Function Coefficient) =1, then constant returns to scale. The effect of internal economies emerging in certain factors is neutralized by the internal economies that my result in some other factors, so that the OP increasing in the same proportion as input. CRS are relevant only for the time periods in which the adjustment of all factors is possible.
The Law of Decreasing Returns: The Law of Decreasing Returns As the firm Expands , it may encounter growing diseconomies of the factors employed. As such when powerful diseconomies are met by feeble economies of certain factors, decreasing returns to scale set in. There are DRS when the percentage increase in OP is less than the percentage increase in input. Attributed to increased problems of organization and complexities of large scale management which may be physically very difficult to handle. PFC<1, under DRS. Q / Q < F / F = Q / Q X F/ F where Q/ Q= Proportionate change in OP F/F = Proportionate change in inputs (factors)
Reasons for DRS: Reasons for DRS Physical Factors increased proportionately but organizational and management cant be. Business risk increases with the increased scale of production as the entrepreneurial efficiency has its own physical limits. With expansion, growing diseconomies of LS production set in. Increases difficulties of managing a big enterprise. Imperfect substitutability of factor s of production causes diseconomies.