# Why is the short-run cost (SAC) curve U-shaped?

## Why is SAC U Shaped?

The nature of the SAC curve is ‘U’ shaped. The standard SAC curve is ‘U’ Shaped while the modern SAC curve is ‘⌴’ shaped. That is, the modern SAC curve is more flattened at its bottom. This means the SAC curve falls at the beginning and reaches a minimum point to rising thereafter. In the case of the modern SAC curve, the minimum point stays stable for a more extended period and then rises again, while the standard AC curve rises more quickly than the modern AC curve. Therefore, the traditional SAC curve is U-Shaped while the modern SAC curve is ‘⌴’ shaped. The SAC curve is U-Shaped because of the following four significant reasons:

a) Inclusion of AFC and AVC:

SAC includes both AFC and AVC. i.e;

SAC = (STC/ Q)

or, SAC = (TFC + TVC)/ Q

or, SAC = TFC/Q + TVC/ Q

∴ SAC = AFC + AVC

When the output increases, AFC falls continuously throughout the increment in output up to a certain level. After reaching a minimum point, AFC starts to rise. Similar nature is shown by the AVC curve, too, due to increasing returns to scale during the production process. However, the rise in AVC is more significant than the fall rate in AFC due to the operation of the law of diminishing returns. Since SAC includes both AFC and AVC, the combined effect of both costs causes SAC to rise after reaching a minimum point. So, the SAC curve is U-shaped.

b) Applicability of the law of variable proportions:

SAC is U-Shaped also because of the operation of the law of variable proportion in short-run production. The SAC curve falls at the beginning because combining a variable factor with a fixed factor causes production to increase at an increasing rate. When there are diminishing returns in production, Total Product (TP) decreases, causing SAC to rise again. Hence, SAC becomes ‘U’ shaped.

c) Indivisibility of fixed factors:

The SAC curve takes a ‘U’ shape because of the inseparability of fixed factors of production. During the short run, a firm cannot separate or divide the fixed factors of production, which leads to a fall in AC. This is due to the operation of economies of scale. After a certain output level, SAC rises again because of internal economies of scale. Hence, SAC becomes U-Shaped.

d) Economies and Diseconomies of scale:

At the beginning of the production process, certain internal and external dis-economies of scale result in higher SAC. Gradually, the producer becomes aware as the production activities continue further. Certain economies of scale cause the cost to decline till it becomes minimum. This motivates the producer to increase the level of output. However, it becomes too large for the producer to handle the output after a point. The reduced costs are not guaranteed due to internal and external dis-economies of scale, which push the costs up. Hence, the SAC curve is ‘U’ shaped.

The ‘U’ shaped nature of SAC can also be clarified with the help of the following diagram:

The above diagram depicts the nature of the SAC curve, which is ‘U’ shaped. During the initial production phase, the output produced was OQ1 which incurred C1 level of costs due to reasons such as managerial inefficiencies, perturbed input-output ratio, management issues, etc.

Gradually the cost declines to C2 and remains minimum at the OQ2 level of output because of the optimum utilization of fixed factor, work division, specialization, and managerial abilities. However, a higher output level in OQ3 does not guarantee the same efficiencies and economies of scale as in OQ2. Therefore, the cost rises again to C3. When all these combinations of costs and outputs are joined together, we get a ‘U’ shaped SAC curve.