**Let us make an in-depth study of the impact of cost on output cost. **

A business that is fluctuating its operations needs to predict how costs will change as output changes Estimates of the costs can be obtained from the cost function; which relate the cost of production to the level of output and other variables.

Suppose we want to find out the short-run costs of production in the automobile industry. An empirical estimate of the VC curve can be obtained by using data for individual firms in an industry.

Fig 7.9 shows a typical pattern of cost and output data. Each point on the figure relates the output of a particular auto company to that firm’s variable cost of production. To predict cost reasonably accurately, we need to determine as accurately as possible the relationship between variable cost and output.

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Then, if a company expands its production, we can calculate what the associated cost is likely to be. The curve in the figure shows a reasonably close fit to the cost data (least-squares regression would be used to fit the curve to the data). But the most appropriate shape of curve would be represented algebraically.

**The following discussion would give us some idea: **

The linear cost function is easy as given below but it is applicable only when MC is constant: VC = α + βQ……… (1)

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For every unit increase in output, variable cost increases by β so the linear cost curve implies a constant MC of production.

If we wish to use a U-shaped AC curve and a MC that is not constant, we must use a more complex (the quadratic) cost function as given: VC = α + βQ + γQ^{2}……….. (2)

This implies a MC = β + 2 γQ. Here, the relationship between MC and output is linear – the MC is a straight line, MC increases with output if γ is positive, and decreases with output if γ is negative. AC = α/Q + β + γQ, is U-shaped when γ is positive.

**If the MC is not linear, we might use a cubic cost function: **

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VC= α + βQ + γQ^{2} + δQ^{3}…….. (3).

**It implies U-shaped MC and AC curves: **

As with production function, cost functions can be difficult to measure.

First, output data often represent an aggregate of different types of products. Total automobiles produced by a firm for example, involves different models of cars.

Second, cost data are normally obtained from accounting information which excludes opportunity costs.

Third, allocating maintenance and other costs to a particular product is difficult when the firm is a conglomerate. Problems like these can limit the accuracy of statistical cost studies.