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How is the long run average cost curve derived from short run

How is the Long run Average cost curve derived from Short run Average cost curves? Use suitable diagrams




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To understand how the Long-Run Average Cost (LRAC) curve is derived from Short-Run Average Cost (SRAC) curves, it's important to grasp the concepts of short-run and long-run in economics. The short run is a period where at least one factor of production is fixed, usually capital, while the long run is a period where all factors are variable.

Derivation of the LRAC Curve:

  1. Short-Run Average Cost Curves (SRACs): In the short run, a firm can operate with different sizes of plants, each having its own SRAC curve. The SRAC curves are U-shaped due to initially increasing and then decreasing marginal returns. Each SRAC curve corresponds to a specific plant size or level of fixed input.

  2. Long-Run Average Cost Curve (LRAC): The LRAC curve is derived by considering a series of SRAC curves corresponding to different plant sizes. It is essentially an 'envelope' of these SRAC curves, showing the lowest possible cost of producing any given level of output when all inputs are variable.

Steps to Derive LRAC:

  • Multiple SRAC Curves: Imagine several U-shaped SRAC curves on a graph, each representing different levels of fixed capital. The horizontal axis represents output while the vertical axis represents cost.

  • Finding the Envelope: The LRAC curve is formed by tracing the lowest points on these SRAC curves for each output level. This means that at any level of production, the firm will choose the plant size (SRAC) that allows it to produce at the lowest possible average cost.

  • Shape of the LRAC: The LRAC is typically U-shaped due to economies and diseconomies of scale. Initially, as output increases, average costs fall (economies of scale) until they reach a minimum point. Beyond this point, average costs start to rise due to diseconomies of scale.

Diagram Explanation:

  1. Construct SRAC Curves:

    • Plot several U-shaped SRAC curves representing different plant sizes on the same graph.
  2. Draw the LRAC Curve:

    • Draw a smooth curve that touches the lowest point of each SRAC curve. This curve is the LRAC and it envelopes the SRAC curves.

Key Points:

  • The LRAC curve reflects the lowest average cost of production for each quantity of output, assuming the firm has time to adjust all inputs.
  • The point of tangency between the LRAC and an SRAC shows the optimal plant size for a given level of output.
  • Economies of scale are realized when the LRAC is downward sloping, while diseconomies of scale occur when it is upward sloping.

This conceptual approach, along with illustrative diagrams in a textbook, helps visualize how the long-run cost relates to various short-run situations.


Answered By

Misty Nichols

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