Theory of Cost
August 19th, 2007 | by Qurratulain |Cost Theory: fixed, variable, total, average and marginal costs
Economists try to use language precisely. The words cost and price are often confused. When we discuss costs we mean, how much did something cost to produce. This might be expressed as an opportunity cost, or in a currency such as dollars. When price is mentioned, economists mean the amount the consumer pays.
Economists also try to explain the nature of costs. Why does one thing cost more to produce than another? Why does making an airplane cost so much less in a big factory than in a small factory. To help explain, total costs are broken down into several parts and looked at in different ways. Before we start we make one basic assumption that the firm is operating in the short-run time period.
Fixed costs
If aircraft are to be made then a factory is required. The land, the factory building, the machinery and office equipment must be bought or rented. These costs are called fixed costs and must be paid even when the factory has not produced anything. Fixed costs are costs that do not change, whatever the level of output is. Assuming an airplane factory’s fixed costs is a $60 million. See below a graph of the fixed costs (FC) would look like this;
Variable costs and total variable costs
Variable costs do change as the level of output changes. These costs are costs such as raw materials in production. In our example this would be the steel, components and labour needed to make each airplane. If nothing were made the variable costs would of course be nothing. But as production rises the total variable costs (TVC) would rise. The variable cost is the cost per unit. The total variable cost is found by multiplying the variable cost (VC) by the level of output (Q), so TVC = VC x Q. Assuming that variable costs are constant at $1 million per airplane, a graph of TVC would look like this;
Total costs are simply the sum of the total variable costs and the fixed costs. Note that the TC and TVC lines are parallel. The distance between the two lines is the amount of the fixed costs.
Marginal cost
Marginal cost is the cost of producing one extra unit.
marginal cost = the change in total costs /the change in output
Using mathematical notation where the Greek letter delta is used to signify - change in.
MC = DTC/ DQ
Notice that this equation is the same as the formula for the gradients of the variable cost and the total cost lines.
When output rises from 0 to 10 the change in output is 10.The corresponding change in total cost is 70 - 60 = 10. The cost of producing 10 extra units has been $10 million. Therefore the cost of producing one extra unit is $1 million.
MC = DTC / DQ= 10/10 =1
Notice that the marginal cost in this example is the same as the variable cost. This is because we assumed that variable costs are not always the same. In the later unit on the law of diminishing returns we will see that calculating and graphing marginal cost is a little more complicated than in this example.
Average costs
Average fixed costs (AFC) are the fixed costs divided by the level of output (FC/Q). So when output is 10 the AFC is 60/10 = 6.
Average total costs (ATC) are the total costs divided by the level of output (TC/Q). So when output is 10 the average fixed cost is 70/10 = 7.
So using the costs in table 1 above
Distinction between short run and long run:
Economic models usually begin with a statement about their assumptions. One of the assumptions is usually concerned with the time period involved. We always need to know if a model is a short-run or a long-run model. What economists mean by time period is not the same as a physicist or mathematician. Time periods in economics are not measured with a stopwatch in minutes, hours or days. Rather, the short run and long run are more like philosophical concepts.
The short-run
In economics the short run is defined as a period of time when at least one of the four factors of production is fixed in supply. Remember that the four factors are, land, labour, capita and entrepreneurship.
The law of diminishing returns is one economic model that is a short-run concept. When textbooks construct examples of this model the authors usually describe land as the fixed factor. A farmer can more easily and quickly change the amounts of labour, or capital than he can buy a new piece of land. However, any other factor could be used as the fixed factor.
Thus in the above example the short-run becomes the length of time that it takes for a farmer to buy a new land. Authors almost never use entrepreneurship as an example of the fixed factor because, as we have said earlier, it is a particularly difficult factor to quantify.
Another way of expressing the short-run is to say that it is the period of time when a new firm cannot enter a market. Because a new firm would have to change one or more of its factors of production to compete in the market, this is identical to our earlier statement.
The long run
The long run is therefore the period of time when all factors of production are variable in supply.
The definitions are both elegant and frustrating. The time to construct a new football stadium can be measured in years. It takes an age to get planning permission, to clear a site and to build new stands. Here a new entrant into the football market might take two or three years. The short run is then up to three years and the long run over-three years.
Yet with a fruit stall in a market it might take only a day or so to buy the stall and the fruit. Here the long run is anything over a day. But even then we are not able to say with any precision how long the short run for football stadium or fruit stalls is, the next stadium will almost certainly take a different length of time to construct than the last one. The long run can therefore also be said to be the time taken for a new entrant to come into the market.
The short-run and the long run are important concepts in economics and high-school students and undergraduates deal with them frequently. Elasticity varies greatly with time ñ so that any economic model with a demand or supply curve needs to have a stated time period. Short run and long run costs are two very different concepts. The economic models of perfect competition, monopolistic competition, oligopoly and monopoly all need the student to have a firm grasp of the definitions of short and long run.
Source: Economics for International Students, C Rodda
