Livestock Economics, Marketing and Business Management

PRODUCTION FUNCTION, SHORT AND LONG-RUN PRODUCTION FUNCTION

• Production function is the relationship between inputs and outputs.
• Production function, which relates to factors and products where some resources are fixed can be termed as short-run production function (Regard­less of the number of fixed resources and level at which each is held fixed).
• Those input-output relations which permit variation in all inputs or all factors (none is fixed) can be termed as long run production func­tion.

Law of Variable Proportion or Law of Diminishing Return

Definition

• “If the quantity of one productive service is increased by equal increments, with the quantity of other resource services held constant, the increments to total product may increase at first but will decrease after a certain point” – E.O.Heady
• “An increase in capital and labour applied in cultivation of land causes in general, less than proportionate increase in the amount of product raised, unless it happens to coincide with an improvement in the arts of agriculture” - Marshall.
• As the amount of variable resource used in production of a product is increased, the output of the product will at first increase at an increasing rate, then increase at a decreasing rate and finally a point will be reached, where further application of the variable resource will result in a decline in the total output of production.
• In short, marginal product of variable input will first increase, then decrease and finally become negative.

Short Run and Long Run

• Short run refers to a period of time in which the supply of certain inputs (e.g. plant, building and machines, etc.) is fixed or inelastic.
• In short run, therefore, production of a commodity can be increased by increasing the use of variable inputs, like labour and raw materials.
• They do not refer to any fixed time period. While in some industries short term may be a matter of a few weeks or a few months, in some others (e.g., electric and power industry), it may mean three or more years.
• Long run refers to a period of time in which the supply of all the inputs is elastic, but not enough to permit a change in technology.
• In long run, the availability of even fixed factor increases. Therefore, in long run, production of commodity can be increased by employing more of both, variable and fixed, inputs.
• Economists use another term, i.e., very long period which refers to a period in which the technology of production is subject to change.
• In the very long run, the production function also changes. The technological advances mean that a larger output can be created with a given quantity of inputs.

Short run production with one variable input

• Laws of returns state the relationship between the variable input and the output in the short term.
• By definition, certain factors of production (viz., land and capital equipments such as plant and machinery) are available in short supply during the short run. Such factors are known as fixed factors.
• On the other hand, the factors which are available in unlimited supply even during the short periods are known as variable factors.
• In short run, therefore, the firms can employ a limited or fixed quantity of fixed factors and an unlimited quantity of the variable factor.
• In other words, firms can employ in the short run, varying quantities of variable inputs against a given quantity of fixed factors. This kind of change in input combination leads to variation in factor proportions.
• The laws which bring out the relationship between varying factor proportions and output are therefore known as the Law of Variable Proportions, or what is more popularly known as the Law of Diminishing Returns.

Long term production with two variable inputs

• We shall now discuss the relationships between inputs and output under the condition that both the inputs, capital and labour, are variable factors. This is a long run phenomenon.
• In the long run, supply of both the inputs is supposed to be elastic and firms can hire larger quantities of both labour and capital. With large employment of capital and labour, the scale of production changes.
• The technological relationship between changing scale of inputs and output is explained through the production function and isoquant curves techniques.

Production rules for the short run

• There are three rules for making production decisions in the short run. They are
  • Expected selling price is greater than minimum ATC (or TR greater than TC). A profit can be made and is maximized by producing where MR = MC.
  • Expected selling price is less than minimum ATC but greater than minimum AVC (or TR is greater than TVC but less than TC). A loss cannot be avoided but will be minimized by producing at the output level where MR=MC. The loss will be somewhere between zero and the total fixed cost.
  • Expected selling price is less than minimum AVC (or TR less than TVC). A loss can not be avoided but is minimized by not producing. The loss will be equal to TFC.
• Application of these rules is as follows. With a selling price equal to MR₁, the intersection of MR and MC is well above ATC, and a profit is being made.
• When the selling price is equal to MR_2, the income will not be sufficient to cover total costs but will cover al variable costs, with some left over to pay part of fixed costs. In this situation, the loss is minimized by producing where MR=MC, because the loss will be less than TFC.
• Selling price should be as low as MR_3, income would not even cover variable costs, and the loss would be minimized by stopping production. This would minimize the loss at an amount equal to TFC.

Production rules for the long run

• There are only two rules for making production decisions in the long run.
  • Selling price is greater than ATC (or TR greater than TC). Continue to produce, because a profit is being made. This profit is maximized by producing at the point where MR=MC.
  • Selling price is less than ATC (or TR less than TC). There will be a continuous loss. Stop production and sell the fixed asset(s), which eliminate the fixed costs. Money received should be invested in a more profitable alternative.
• This does not mean that assets should be sold the first time a loss is incurred. Short-run losses will occur when there is a temporary drop in the selling price.
• The second long-run rule should be invoked only when the drop in price is expected to be long lasting or permanent.