Chapter Summary

Of all the topics covered in an intermediate microeconomics text, students usually find the material on cost curves by far the most difficult to digest. And for good reason, since the sheer volume of specific concepts can easily seem overwhelming at first encounter. It is important to bear in mind, therefore, that all the various cost curves can be derived from the underlying production relationships in a very simple and straightforward manner.

Short-run cost curves, for example, all follow directly from the short-run production function. All short-run production functions we have discussed involved one fixed factor and one variable factor, but the theory would be exactly the same in the case of more than one fixed or variable input. Short-run total costs are decomposed into fixed and variable costs, which correspond, respectively, to payments to the fixed and variable factors of production. Because of the law of diminishing returns, beyond some point we require ever larger increments of the variable input to produce an extra unit of output. The result is that short-run marginal cost, which is the slope of the short-run total cost curve, is increasing with output in the region of diminishing returns. Diminishing returns are also responsible for the fact that short-run average total and average variable cost curves-which are, respectively, the slopes of the rays to the short-run total and variable cost curves-eventually rise with output. Average fixed costs always take the form of a rectangular hyperbola, approaching infinity as output shrinks toward zero, and falling toward zero as output grows increasingly large.

The problem of allocating a given production quota to two different production facilities is similar to the problem of allocating an available input across two different facilities. In the latter case, the goal is to maximize the amount of output that can be produced with a given amount of input. In the former, it is to produce a given level of output at the lowest total cost. The solution is to allocate the production quota so that the marginal cost is the same in each production process. This solution does not require that average costs be the same in each process, and in practice, they often differ substantially.

The optimal input bundle for producing a given output level in the long run will depend on the relative prices of the factors of production. These relative prices determine the slope of the isocost line, which is the locus of input bundles that can be purchased for a given total cost. The optimal input bundle will be the one that lies at the point of tangency between an isocost line and the desired isoquant. At the cost-minimizing point, with perfectly divisible inputs and no corner solutions, the ratio of the marginal product of an input to its price will be the same for every input. Put another way, the extra output obtained from the last dollar spent on one input must be the same as the extra output obtained from the last dollar spent on any other input. Still another way of stating the minimum-cost condition is that the marginal rate of technical substitution at the optimizing bundle must be the same as the absolute value of the slope of the isocost line.

These properties of production at minimum cost help us understand why methods of production often differ sharply when relative factor prices differ sharply. We saw, for example, that it helps explain why developing countries often use labour-intensive techniques while their industrial counterparts choose much more capital-intensive ones, and why labour unions might lobby on behalf of increased minimum wages, even though virtually all of their members earn more than the minimum wage to begin with.

For a given level of output, long-run total costs can never be larger than short-run total costs for the simple reason that we have the opportunity to adjust all of our inputs in the long run, only some of them in the short run. The slope of the long-run average cost curve is a direct reflection of the degree of returns to scale in production. With constant input prices, when there are increasing returns, LAC declines with output. With decreasing returns, in contrast, LAC rises with output. And finally, constant returns in production give rise to a horizontal LAC function. A U-shaped LAC curve is one that corresponds to a production process that exhibits first increasing, then constant, and finally decreasing returns to scale. No matter what its shape, the LAC curve will always be an envelope of the corresponding family of SAC curves, each of which will be tangent to the LAC at one and only one point. At the output levels that correspond to these points of tangency, LMC and the corresponding SMC will be the same.

The relationship between market structure and long-run costs derives from the fact that survival in the marketplace requires firms to have the lowest costs possible with available production technologies. If the LAC curve is downward sloping, lowest costs occur when only one firm serves the market. If the LAC curve is U-shaped and its minimum point occurs at a quantity that corresponds to a substantial share of total market output, the lowest costs will occur when only a few firms serve the market. In contrast, if the minimum point on a U-shaped LAC curve corresponds to only a small fraction of total industry output, the market is likely to be served by many competing firms. The same will be true when the LAC curve is either horizontal or upward sloping.

The appendix to this chapter considers the relationship between long-run and short-run costs in greater detail. It also develops the calculus approach to cost minimization.