Cost curves can be combined to provide information about firms. In this diagram for example, firms are assumed to be in a perfectly competitive market. In a perfectly competitive market the price that firms are faced with in the long run would be the price at which the marginal cost curve cuts the average cost curve, since any price above or below that would result in entry to or exit from the industry, driving the market-determined price to the level that gives zero economic profit.
Assuming that factor prices are constant, the production function determines all cost functions. The variable cost curve is the constant price of the variable input times the inverted short-run production function or total product curve, and its behavior and properties are determined by the production function. Because the production function determines the variable cost function it necessarily determines the shape and properties of marginal cost curve and the average cost curves.
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If the firm is a perfect competitor in all input markets, and thus the per-unit prices of all its inputs are unaffected by how much of the inputs the firm purchases, then it can be shown that at a particular level of output, the firm has economies of scale (i.e., is operating in a downward sloping region of the long-run average cost curve) if and only if it has increasing returns to scale. Likewise, it has diseconomies of scale (is operating in an upward sloping region of the long-run average cost curve) if and only if it has decreasing returns to scale, and has neither economies nor diseconomies of scale if it has constant returns to scale. In this case, with perfect competition in the output market the long-run market equilibrium will involve all firms operating at the minimum point of their long-run average cost curves (i.e., at the borderline between economies and diseconomies of scale).
However, the shapes of the curves are not due to the same factors. For the short run curve the initial downward slope is largely due to declining average fixed costs.Increasing returns to the variable input at low levels of production also play a role, while the upward slope is due to diminishing marginal returns to the variable input. With the long run curve the shape by definition reflects economies and diseconomies of scale. At low levels of production long run production functions generally exhibit increasing returns to scale, which, for firms that are perfect competitors in input markets, means that the long run average cost is falling;the upward slope of the long run average cost function at higher levels of output is due to decreasing returns to scale at those output levels.
