In a well labelled diagram distinguish between short run cost and the long run cost

Here's a distinction between short-run and long-run costs, illustrated with a diagram.

Short-Run Costs

In the short run, at least one factor of production is fixed. This means a firm can only change its output by altering its variable inputs. Short-run cost curves are typically U-shaped due to the law of diminishing marginal returns.

• Total Cost (TC): The sum of total fixed costs (TFC) and total variable costs (TVC).
• Total Fixed Cost (TFC): Costs that do not change with output (e.g., rent).
• Total Variable Cost (TVC): Costs that vary directly with output (e.g., labor, raw materials).
• Average Fixed Cost (AFC): TFC divided by output (Q). It declines continuously as output increases.
• Average Variable Cost (AVC): TVC divided by Q. It is typically U-shaped.
• Average Total Cost (ATC): TC divided by Q, or AFC + AVC. It is also U-shaped.
• Marginal Cost (MC): The change in TC resulting from producing one more unit of output. It is also U-shaped and intersects AVC and ATC at their minimum points.

Long-Run Costs

In the long run, all factors of production are variable. A firm can adjust its scale of operations. The long-run cost curve represents the lowest cost of producing any given output level, assuming the firm can choose the optimal plant size.

• Long-Run Average Cost (LRAC): This curve is typically U-shaped, but the shape is due to economies and diseconomies of scale, not diminishing marginal returns.
  • Economies of scale occur when LRAC falls as output increases (e.g., specialization, bulk buying).
  • Diseconomies of scale occur when LRAC rises as output increases (e.g., management difficulties, coordination problems).
• Long-Run Marginal Cost (LRMC): The change in total long-run cost from producing one more unit of output.

Diagram

Imagine a graph with Output (Q) on the horizontal axis and Cost ($) on the vertical axis.

1. Short-Run Curves: Draw several U-shaped Average Total Cost (ATC) curves, each representing a different fixed plant size. Label them ATC₁, ATC₂, ATC₃. ATC₁ is for a small plant, ATC₂ for a medium plant, and ATC₃ for a large plant. The Marginal Cost (MC) curve for each plant size will intersect its respective ATC at the minimum point.
2. Long-Run Average Cost (LRAC): The LRAC curve is the lower envelope of all the short-run ATC curves. It is tangent to each ATC curve at its minimum point (or at a point on the downward-sloping portion of ATC if the firm is expanding to a larger plant size). The LRAC curve will initially slope downwards (economies of scale) and then slope upwards (diseconomies of scale), forming a U-shape.

[Diagram Description: A graph with Output on the x-axis and Cost on the y-axis. Several U-shaped short-run Average Total Cost (ATC) curves are shown. A smooth, U-shaped Long-Run Average Cost (LRAC) curve is drawn below and tangent to the lowest points of the short-run ATC curves. The LRAC curve slopes down initially and then slopes up.]

The key difference is that short-run costs are influenced by fixed factors and diminishing returns, while long-run costs are determined by the ability to change all factors and the presence of economies and diseconomies of scale.