Q.What do the short run marginal cost, average variable cost and short run average cost curves look like?

The short-run marginal cost (SMC), average variable cost (AVC), and short-run average cost (SAC) curves all have a characteristic U-shape when plotted against output. This shape reflects the law of variable proportions operating in the short run, where at least one factor (typically capital) is fixed.

Initially, as output rises from zero, all three curves fall because of increasing returns to the variable factor—each additional unit of input adds more to output than the previous one, so per-unit costs decline. Beyond a certain output level, diminishing returns set in: additional units of the variable factor become less productive, causing marginal cost to rise. Once MC starts rising, it eventually pulls up AVC and SAC as well. …

The shape of these three cost curves flows directly from the law of variable proportions (also called the law of diminishing marginal returns). In the short run, at least one factor of production—typically capital—is fixed. As we add more units of the variable factor (say, labor) to this fixed capital, output initially rises at an increasing rate (increasing returns), then at a decreasing rate (diminishing returns), and may eventually fall (negative returns).

Cost curves are simply the mirror image of these productivity patterns. When marginal product is rising, marginal cost is falling; when marginal product starts diminishing, marginal cost starts rising. This fundamental inverse relationship between physical productivity and cost gives all three curves their characteristic U-shape.

The Short-Run Marginal Cost (SMC) Curve

Marginal cost measures the addition to total cost from producing one more unit of output. It is calculated as:

where TVC is total variable cost and $Q$ is output.

The SMC curve falls initially as marginal product rises (each additional worker adds more output, so the cost per extra unit falls). Once diminishing returns set in, marginal product declines and SMC begins to rise. The curve is U-shaped, reaching a minimum at the inflection point of the total cost curve—the output level where the rate of increase in total cost is slowest.

An important property: SMC depends only on variable costs. Fixed costs do not change with output, so they never affect marginal cost.

The Average Variable Cost (AVC) Curve

Average variable cost is total variable cost divided by output:

The AVC curve is also U-shaped. Initially, as output expands, variable costs spread over more units and average variable cost falls. This continues as long as the marginal cost of the next unit is below the current average—each cheaper unit pulls the average down. But once SMC rises above AVC, each additional unit costs more than the average, pulling AVC upward.

This gives us a crucial geometric relationship: the SMC curve intersects the AVC curve at the minimum point of AVC. Before this point, $\text{SMC} < \text{AVC}$ and AVC is falling; after this point, $\text{SMC} > \text{AVC}$ and AVC is rising. At the intersection itself, $\text{SMC} = \text{AVC}$ and AVC is at its lowest.

The Short-Run Average Cost (SAC) Curve

Short-run average cost (also called short-run average total cost) includes both fixed and variable costs:

where AFC is average fixed cost.

The SAC curve is U-shaped for two reasons working together. At low output levels, high average fixed costs dominate—spreading the fixed cost over just a few units makes each unit expensive. As output rises, AFC falls continuously (fixed cost divided by ever-larger output), pulling SAC down. Simultaneously, AVC is also falling initially due to increasing returns.

Eventually, though, diminishing returns cause AVC to rise. At first, the fall in AFC outweighs the rise in AVC, so SAC continues to decline. But beyond a point, the rising AVC dominates the falling AFC, and SAC begins to climb. The minimum of SAC occurs at a higher output than the minimum of AVC, because AFC is still falling when AVC starts to rise. …