Cost Function

Nisha Nagwanshi,

Hidayattullah National Law University, Raipur

ABSTRACT:

The cost function measures the minimum cost of producing a given level of output for some fixed factor prices. As such it summarizes information about the technological choices available to the firms. It turns out that the behavior of the cost function can tell us a lot about the nature of the firm's technology.

The average total cost curve: The average total cost curve is constructed to capture the relation between average total cost and the level of output. A productively efficient firm organizes its factors of production in such a way that the average cost of production is at lowest point.

A marginal cost Curve: A marginal cost Curve graphically represents the relation between marginal costs incurred by a firm and the quantity of output produced. This curve is constructed to capture the relation between marginal cost and the level of output, the marginal cost curve is U-shaped. Marginal cost is relatively high at small quantities of output, then as production increases, declines, reaches a minimum value, then rises.

Duality: Given a cost function we can "solve for" a technology that could have generated that cost function. This means that the cost unction contains essentially the same information that the production function contains. Any concept defined in terms of the properties of the production function has a "dual" definition in terms of the properties of the cost function and vice versa. This general observation is known as the principle of duality.

INTRODUCTION:

In Economics we usually talk about two different types of costs, explicit and implicit. Implicit costs incorporate all opportunity costs and rate of returns into your cost function. We have already covered these types of costs in Macroeconomics. We will come back to them later in this course, but for now we are going to focus on Explicit Costs. These are costs that must be paid; anything that you actually receive a bill for is an explicit cost. Explicit costs are broken down into two categories; all costs are either Fixed or Variable. Fixed costs are costs that must be paid regardless of production or output. These can be leases on cars, salaried employees, buildings, cell phones, copy machines… etc. More times than not, these costs are contractual obligations.

Variable costs are costs that change with the level of production, these are usually costs that are directly associated with output, such as electricity, paper, steal, packaging… etc. Adding together Fixed Costs and Variable Costs will give you Total Costs.

Fixed + Variable = Total Costs

We also want to find the Average costs; they are Average Fixed Cost, Average Variable Cost and Average Total Cost. To find the average costs, you divide Total by the quantity produced at that point.

Average Variable Cost = Total Variable Cost / Quantity

Average Fixed Cost = Total Fixed Cost / Quantity

Average Total Cost = Total Cost / Quantity.

Example: Quantity	Fixed	Variable	Total	MC	AFC	AVC	ATC
3	100	105	205	50	33.3	35	68.3
4	100	185	285	80	25	46.25	71.25

Microeconomics is the study of individual people, businesses, and markets. So it is very important in Micro to discuss and analyze individual changes. To do this we need to introduce a new concept called Marginal. We can apply the word/concept to any numeric definition. The term Marginal simply means one additional. We are now applying marginal to our cost function. Marginal Cost means the additional cost of producing the next unit of output. The Marginal Cost of output #2 would be the difference in cost of output 2 and output 1; it is the cost of producing that extra unit. Marginal Cost, just like the Supply Curve will be upward sloping.

The final categorization of costs we need to address. The final categorization of costs we need to address are Sunk Costs. Sunk Costs can be any type of cost, the distinction is that these are expenses that have already been paid or obligated to. Sunk Costs are most important in the decision making process, if you have already spent money you generally don’t want to consider that when deciding on future action.

CONCLUSION:

In the Long Run, the decision making process with respect to expansion or contraction occurs using Economies of Scale. Economies of scale tell you how much return you gain from expansion. Increasing Returns to Scale occurs when you expand production (increase output) and a lower average cost occurs. Constant Returns to Scale results when you have expansion and the average costs follows by the exact same percentage. Decreasing Returns to Scale happens when you expand and your average cost per unit increases by more than production. Negative Returns to Scale occurs when you expand production and output decreases.

To calculate the percentages few would use our elasticity set up. This is going to give us the Elasticity of Supply. Instead of measuring the Percent Change in Quantity, we can measure the Percent Change in Output. This doesn’t change anything about the way we measure elasticity, it is still a quantity measurement in the top half of our equation. The bottom half of the equation is still a monetary measurement, only know we are changing our costs instead of prices or incomes.

The Returns to Scale from increasing output from 3 units to 4 units is .29 (or 29%) versus a 55% increase in expenses (185 from 105). This gives us Decreasing Returns to Scale, because the change in cost was greater than the increases in output that resulted. If we finished our elasticity equation, this would give us a number between 0 and 1, or in this case an Elasticity of Supply of 0.53. This number should be positive because we expect output to increase when we spend more money; both measurements are moving in the same direction.

REFERENCES:

1. R.G.D. Allen (1938) Mathematical Analysis for Economists. New York: St. Martin's.

2. W.J. Baumol (1961) Economic Theory and Operations Research. 1976 edition, Englewood Cliffs, NJ: Prentice-Hall.

3. G. Cassel (1918) The Theory of Social Economy. 1932 edition, New York: Harcourt, Brace.

4. D.G. Champernowne (1953) "The Production Function and the Theory of Capital: A comment", Review of Economic Studies, Vol. 21 (1), p.112-35

Received on 15.01.2012

Revised on 22.02.2012

Accepted on 25.03.2012