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Law of Variable Proportions in Production Functions

Understand the Law of Variable Proportions in production functions, exploring the relationship between input factors in short and long runs. Learn about total product, average product, marginal product dynamics, and the rational choices for producers based on different production stages.

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Law of Variable Proportions in Production Functions

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  1. LAW OF VARIABLE PROPORTIONS FOR DEGREE SEMESTER II STUDENTS Prepared by : Pheba Ann Zachariah

  2. PRODUCTION FUNCTION Production means transformation of physical inputs into physical outputs Production function thus explains the functional relationship between inputs and output

  3. Production function takes the form of Q = f(L,K) where Q represents the output, L and K stands for factors Labour and Capital respectively

  4. Types of Production functions • Short run Production function- The producer will keep all fixed factors(Capital) as constant and changes only a few variable factors(Labour) • Long Run Production function- The producer will vary the quantities of all factor inputs

  5. The Law of variable proportions comes under the Short Run Production function and it examines the production function with one factor variable(Labour) and other factor constant (capital)

  6. The Law States that when the quantity of one input(labour) is increased keeping other inputs(capital) constant, the proportion between factors changes. When the proportion of variable factor increases, the total output does not always increase in the same proportion but in varying proportion

  7. Assumptions of the Law • Only one factor is variable while others are constant • All units of the variable factor are homogenous • There is no change in technology • It is possible to vary the proportions in which different inputs are combined • The products are measured in physical units

  8. Concepts of Productivity Total Product(TP)- refers to the total volume of goods produced during a specified period of time. Total Product can be raised only by increasing the variable factors Average product(AP)- refers to total product divided by the total number of units of the variable factor. TP/Q Marginal Product(MP)- refers to addition to the total product resulting from a unit increase in the quantity of the variable factor

  9. Three stages of law of variable proportions • Stage 1- The law of increasing returns • TP increases at an increasing rate up to point F (point of inflexion) • MP also rises and becomes maximum at point F • After point F, TP rises but at a diminishing rate and MP falls but positive • Stage 1 ends when AP reaches its maximum

  10. Stage 2- law of diminishing returns • TP continues to increase at a diminishing rate until it reaches the maximum point H • MP and AP falls during this time • Stage end when TP reaches its maximum and MP reaches zero

  11. Stage 3- law of negative returns • TP Declines • MP Negative • AP is diminishing

  12. Relationship between AP and MP • AP and MP rises but MP is greater than AP • When AP reaches maximum, MP=AP. MP curve cuts the AP curve at its maximum • AP and MP falls but AP is greater than MP

  13. The Choice of a rational producer • A rational producer will never produce in stage 3 because MP of variable factor(Labour) is negative. • A rational producer will never produce in stage 1 because the MP of fixed factor(capital) is negative • A rational producer will produce in stage 2 where both AP and MP of variable factor is diminishing but positive.

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