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1.4.4a Types of cost

Total Cost Splits into Fixed and Variable Costs

Definition

Fixed cost: a cost of production that does not change as output changes in the short run.

Variable cost: a cost of production that rises and falls with the level of output.

  1. Total cost is fixed cost plus variable cost, so TC=TFC+TVC\text{TC} = \text{TFC} + \text{TVC}TC=TFC+TVC.
  2. Total fixed cost stays the same at every level of output, whereas total variable cost rises as output rises.
  3. So as the firm produces more, the whole increase in total cost comes from the rise in variable cost.
Note
  • Whether a cost is fixed or variable depends on the time period.
  • In the long run, all costs are variable.

Recognising Fixed and Variable Costs

  1. Fixed costs
    1. Rent and insurance, which must be paid whatever the output.
  2. Variable costs
    1. Raw materials and the wages of extra staff, which grow with output.
Example
  • A bakery pays the same rent whether it bakes 10 or 1,000 loaves.
  • Its flour bill rises directly with the number of loaves.

Average and Marginal Cost: Per Unit and the Next Unit

  1. Average cost is total cost divided by output, the cost per unit, and it splits into average fixed cost (AFC) plus average variable cost (AVC).
  2. Marginal cost is the addition to total cost from producing one more unit.
  3. Total and average cost describe the whole output, while marginal cost focuses on the next unit.
Note
  • Average cost is the figure firms compare with price to judge profitability.
  • Marginal cost is central to the firm's decision on how much to produce.
Example
  • Suppose total fixed cost (TFC) is £100 and, at an output of 4 units, total variable cost (TVC) is £160, so total cost (TC) is TC=£100+£160=£260\text{TC} = \pounds 100 + \pounds 160 = \pounds 260TC=£100+£160=£260.
  • Average fixed cost (AFC) is AFC=£1004=£25\text{AFC} = \dfrac{\pounds 100}{4} = \pounds 25AFC=4£100​=£25, and average variable cost (AVC) is AVC=£1604=£40\text{AVC} = \dfrac{\pounds 160}{4} = \pounds 40AVC=4£160​=£40.
  • Average total cost (ATC) is ATC=£2604=£65\text{ATC} = \dfrac{\pounds 260}{4} = \pounds 65ATC=4£260​=£65, which must equal AFC + AVC (£25+£40=£65\pounds 25 + \pounds 40 = \pounds 65£25+£40=£65), a handy check on your working.
  • If total cost at 3 units had been £220, the marginal cost of the 4th unit is MC=£260−£220=£40\text{MC} = \pounds 260 - \pounds 220 = \pounds 40MC=£260−£220=£40, the extra cost of that single unit.

Short-Run Costs Have a Fixed Factor; Long-Run Costs Do Not

  1. In the short run at least one factor is fixed, so costs split into fixed and variable.
  2. In the long run all factors can vary, so every cost is variable.
  3. Short-run costs assume a fixed plant size, while long-run costs allow the firm to change its scale.

Anchor Every Cost to Time and Output

Exam technique
  • Say whether you mean the short run or the long run before labelling a cost.
  • Split total cost into its fixed and variable parts, then find average and marginal cost.
Common Mistake
  • Do not label a cost fixed or variable without stating the time period.
  • In the long run, every cost is variable.
  • Do not confuse average cost (cost per unit) with marginal cost (cost of the next unit).
Self review
  • Define fixed and variable costs.
  • What is total, average and marginal cost?
  • With TFC of £100 and TVC of £160 at 4 units, work out ATC, AFC and AVC.
  • How do short-run and long-run costs differ?
  • Why are all costs variable in the long run?

1.4.4b Cost curves and factor inputs

Average and Marginal Cost Curves Have Characteristic Shapes

Definition

Marginal cost: the addition to total cost of producing one more unit of output.

  1. Average total cost is total cost divided by output.
  2. It splits into average fixed cost and average variable cost.
  3. Marginal cost is the cost of producing one more unit.
Note
  • The short-run average cost curve is typically U-shaped.
  • Marginal cost cuts average variable and average total cost at their lowest points.

Short-run cost function

How to Read the Cost Curves

  1. Average fixed cost falls continuously as output spreads it thinner.
  2. Average variable and average total cost fall, then rise, giving the U shape.
  3. The upturn reflects diminishing marginal returns.
Example
  • At low output, spreading fixed costs pulls average cost down; at high output, diminishing returns push marginal and average cost up.
  • Put numbers on the crossing rule. If total cost for 4 units is £160, average cost is £1604=£40\dfrac{\pounds 160}{4} = \pounds 404£160​=£40. A 5th unit costing a marginal £30 (below £40) lifts total cost to £160+£30=£190\pounds 160 + \pounds 30 = \pounds 190£160+£30=£190 and pulls average cost down to £1905=£38\dfrac{\pounds 190}{5} = \pounds 385£190​=£38.
  • Had the 5th unit instead cost £60 (above £40), total cost would be £160+£60=£220\pounds 160 + \pounds 60 = \pounds 220£160+£60=£220 and average cost would rise to £2205=£44\dfrac{\pounds 220}{5} = \pounds 445£220​=£44, which is exactly why marginal cost drags average cost up once it exceeds it, and so must cross it at the minimum.

Why MC Cuts AC at the Bottom

  1. While marginal cost is below average cost, it drags the average down.
  2. While marginal cost is above average cost, it pulls the average up.
  3. So marginal cost must cross average cost at its lowest point.

Factor Prices and Productivity Shift the Cost Curves

  1. A rise in factor prices, such as higher wages or dearer raw materials, raises costs and shifts the cost curves upward.
  2. Higher productivity means more output per unit of input, which lowers unit costs and shifts the cost curves downward.
  3. Firms choose the combination of factor inputs that produces a given output at least cost.
Note
  • When labour becomes relatively expensive, firms tend to substitute capital for labour, and vice versa.
  • The least-cost mix balances each factor's price against its productivity.

Total Cost Starts at Fixed Cost and Steepens as Marginal Cost Rises

  1. Total cost is the sum of fixed cost and variable cost at each level of output.
  2. At zero output there is no variable cost, so the total cost curve starts at the level of fixed cost rather than at the origin.
  3. Total cost then rises with output, and its slope at any point equals marginal cost.
    1. So total cost rises slowly at first while marginal returns are rising, then more steeply as diminishing returns raise marginal cost.
Note
  • The vertical gap between the total cost curve and the total variable cost curve stays constant and equals fixed cost.
  • The total cost curve is steepest where marginal cost is highest.
Exam technique
  • Draw MC cutting both AVC and ATC at their minimum points.
  • Link the U shape to diminishing marginal returns, and shifts to factor prices and productivity.
Common Mistake
  • Do not draw marginal cost missing the lowest point of ATC and AVC.
  • Marginal cost always passes through their minimum points.
Self review
  • Define average total, average fixed, average variable and marginal cost.
  • Why is the short-run ATC curve U-shaped?
  • Where does MC cross AVC and ATC, and why?
  • How do factor prices and productivity affect costs and the choice of factor inputs?
  • Why does the total cost curve start at the level of fixed cost, and what does its slope measure?
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1.4.4 Costs of production Revision Guide

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