Suppose a firm has only three possible plant-size options,...

Suppose a firm has only three possible plant-size options, represented by the ATC curves shown in the accompanying figure. What plant size will the firm choose in producing $(a) 50,(b) 130,(c) 160,$ and $(d) 250$ units of output? Draw the firm's long-run average-cost curve on the diagram and describe this curve. CAN'T COPY THE FIGURE

Key Concepts

Average Total Cost (ATC) Curve

The ATC curve represents the per-unit cost of production at different levels of output for a given plant size. It is influenced by both fixed and variable costs, and its shape can indicate whether a firm experiences economies or diseconomies of scale in the short run. In decision-making, firms compare the ATC curves of different plant sizes to determine which scale minimizes costs for a specific production level.

Long-Run Average Cost (LRAC) Curve

The LRAC curve shows the lowest possible average cost of production when a firm can vary its plant size and all inputs in the long run. It is constructed as the envelope of all short-run ATC curves corresponding to different plant sizes, indicating the optimal cost-minimizing plant size for every level of output. This concept is essential for understanding long-run planning and economies of scale.

Economies of Scale

Economies of scale refer to the cost advantages that a firm experiences as it increases its output. When firms produce larger quantities, they may benefit from spreading fixed costs over more units and achieving operational efficiencies, which in turn lower the average cost per unit. Recognizing economies of scale is crucial for firms when deciding on the optimal plant size and production levels.

Minimum Efficient Scale (MES)

The Minimum Efficient Scale is the smallest level of output at which a firm can achieve the lowest possible average cost in the long run. Beyond this point, further increases in production do not lead to significant reductions in average cost. Understanding MES helps firms determine the optimal capacity level and plant size to remain competitive over the long run.

Plant Size Optimization

Plant size optimization involves selecting the most appropriate scale of production, among discrete options, that minimizes costs for a given output level. This decision takes into account the ATC of different plant sizes, the resulting LRAC curve, and the potential economies of scale. It is critical for firms to align their production capacity with market demand to operate efficiently and profitably.

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