Long-run cost curves show the least-cost input combination for producing output assuming an ideal input selection. As in the case of short-run cost curves, wage rates, interest rates, plant configuration, and all other operating conditions are held constant. Any change in the operating environment leads to a shift in long-run cost curves. For example, product inventions and process improvements that occur over time cause a downward shift in long-run cost curves. Such changes must not be confused with movements along a given long-run cost curve caused by changes in the output level. Long-run cost curves reveal the nature of economies or diseconomies of scale and optimal plant sizes. They are a helpful guide to planning decisions.
If input prices are not affected by the amount purchased, a direct relation exists between longrun total cost and production functions. A production function that exhibits constant returns to scale is linear, and doubling inputs leads to doubled output. With constant input prices, doubling inputs doubles total cost and results in a linear total cost function. If increasing returns to scale are present, output doubles with less than a doubling of inputs and total cost. If production is subject to decreasing returns to scale, inputs and total cost must more than double to cause a twofold increase in output. A production function exhibiting first increasing and then decreasing returns to scale is illustrated, along with its implied cubic cost function, in Figure 8.2. Here, costs increase less than proportionately with output over the range in which returns to scale are increasing but at more than a proportionate rate after decreasing returns set in.
A direct relation between production and cost functions requires constant input prices. If input prices are a function of output, cost functions will reflect this relationship. Large-volume discounts can lower unit costs as output rises, just as costs can rise with the need to pay higher wages to attract additional workers at high output levels. The cost function for a firm facing constant returns to scale but rising input prices as output expands takes the shape shown in Figure 8.2. Costs rise more than proportionately as output increases. Quantity discounts produce a cost function that increases at a decreasing rate, as in the increasing returns section of Figure 8.2.
economies of scale
Decreasing long-run average costs
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