Production Function

Production Function

• Relationship between quantity of input and quantity of output.
• Functional relationship exists between physical inputs and physical output of a firm.
• Production Function includes minimum quantity of steel, color, labor, machine-time, and electricity needed to makes 50 steel chairs
• Production function consists of the maximum number of chairs that can be produced with given quantities of inputs

Technology and the Production Function

• Largely determined by technology.
• Production function changes with technology improvements which creates a new production function.

Mathematical Expression

• Q = f (Ld, L, C, O)
• Q represents output.
• Ld represents Land.
• L represents Labour.
• C represents Capital.
• O represents Organisation.

Modern Managerial Factors

• Managerial economists emphasize quality of technology and quality of management as additional factors.
• Q = f (Ld, L, C, M, T)
• M represents Management.
• T represents Technology.

Linear Homogeneous Function

• Also known as the Cobb-Douglas Function.
• Profounded by Paul H. Douglas and C.W. Cobb.
• Applies to manufacturing in the country and not to individual firms.
• Output is manufacturing production, with labor and capital being the inputs.
• Cobb-Douglas function is Q = k* La * C(1-a)
  • Q is quantity produced
  • L is Labour
  • C is Capital
  • k and a are positive constants
• The production function works out for the American economy is Q = 1.01* L75 * C25

Short Run vs. Long Run

• Short run is a brief time where at least one input is fixed, featuring both fixed and variable factors.
• Long run is is a period that is sufficient for all inputs to be variable for an individual firm.

Marginal Product

• Increase in quantity of output from one additional unit of input.
• The marginal product declines because the number of workers increases.
• This property is called diminishing marginal product

Law of Variable Proportions

• A short run function that is also called the law of non-proportional output.
• If quantity of one variable is varied and the quantities of other variable factors are kept constant, then the output would not respond in a proportionate manner.
• Production increases at an increasing rate initially, then at a diminishing rate.
• Relationship between input and output is not constant during production.

Assumptions for the Law of Variable Proportions

• Only one factor is variable while others are held constant.
• Units of the variable factor are homogeneous.
• There is no change in technology.
• Possible to vary the proportions in which different inputs are combined.
• Assumes a short-run situation since factors are variable in the long-run.
• Product is measured in physical units i.e in quintals, tonnes, etc.

Marginal, Average, and Total Product Relationships

• When marginal product increases, total product increases at an increasing rate.
• When marginal product is zero, total product is at its maximum.
• When marginal product becomes negative, total product starts falling.
• Average product rises as long as the marginal product is above it.
• Average product starts falling when marginal product is below it.
• The marginal product curve cuts the average product curve at its maximum.

Stages of Production

First Stage

• Marginal and average products are increasing.
• Stage ends when marginal product cuts average product at its maximum.
• The first stage indicates increasing returns.
• The cause of increasing returns is the indivisibility of factors of production
• Indivisibility of factors of production as factors of production are not subject to division.
• Capacity can be under-utilized

Second Stage

• Marginal product diminishes until zero.
• Happens due to diseconomies.
• Diseconomies means Under-utilization initially transitions to optimum point and output increases but at a diminishing rate.
• Example: Fishing in the sea

Third Stage

• Additional variable factors lead to a fall in total production.
• Marginal product tends to be negative.
• Excessive variable factors hurt the efficiency of a fixed factor.
• This stage is theoretical, and no producer would want to be in it.

Law of Returns to Scale

• The relationship as outputs and scale of inputs in the long-run when all the inputs are increased in the same proportion
• Returns to scale is the relationship between changes in output and proportionate changes in all factors of production
• A firm increases its scale of production (long-run change in demand) by using more space, machines, and labor.
• Assumes all inputs are variable but enterprise is fixed.
• This law assumes that a worker works with given tools and implements
• Technological changes are absent.
• There is perfect competition.
• Product is measured in quantities.

Increasing Returns to Scale

• Increase in total output > proportional increase in all inputs.
• Causes
  • Indivisibility of Factors
  • Specialization and Division of Labour
  • Internal Economies.
  • External Economies

Constant Returns to Scale

• Increase in total output = increase in inputs.
• Causes
  • Internal Economies and Diseconomies
  • External Economies and Diseconomies
  • Divisible Factors

Diminishing Returns to Scale

• Increase in output < increase in inputs
• Causes
  • Indivisible factors become inefficient. - Business becomes unwieldy.
  • Supervision/coordination problems.
  • Higher factor prices.

Concept of Cost

• Total money expenditure to pay all the factors of production for their participation.
• Production requires different factors to be hired, involving production costs.
• Cost is in terms of money for understanding and comparison.
• Interpretations of cost can be opportunity cost, real cost and money cost of production

Types of Costs

Accounting Costs

• Costs associated with producing.

Economic Costs

• The costs of producing a good along with opportunity costs.

Opportunity Costs

• Sacrifices made to obtain an item.
• If a firm is producing Computers then the Accounting costs are the costs incurred for producing the computers. Economic costs include the cost of producing the computers as well as opportunity cost. If this firm could lease its office and the plant for say Rs. 100,000 then that is the opportunity cost

Explicit costs

• Input costs requiring money outlay by firm.
• Includes all money expenditure incurred by a firm in the process of production
• Money spent on fuels, raw materials, power, advertising and transportation

Implicit costs

• Input costs not requiring money outlay by firm.
• Costs not included by accounting authority.
• e.g., opportunity cost of entrepreneur's services and/or cost of land belonging to him

Fixed costs

• Doesn't vary with output quantity.
• Incurred even if the firm produces nothing.

Variable costs

• Changes as firm alters output quantity.

Marginal cost

• Increase in total cost from extra unit of production.

Total cost

• Sum of fixed and variable costs.

Total revenue

• Amount a firm receives from selling its output.

Profit

• Total revenue - total cost.

Break-Even Point

• No-profit, no-loss point where total costs equal total revenues.