7.1 Short run costs analysis and size of the firm’s total cost, fixed cost, average cost, variable costs and marginal cost

The short run is a period of production in which at least one factor of production, usually capital such as buildings and machines, cannot be changed, while other factors such as labour and raw materials can be varied. Short run cost analysis studies how a firm's costs change as it changes its output within this limit. It matters because managers use it to decide how much to produce, what price covers their costs and when it is better to stop production. Example: a bakery in a market town cannot build a second oven within a week, but it can hire extra bakers and buy more flour to raise output.

7.1.1 Concept of the short run

In the short run, some inputs are fixed and others are variable. The firm can raise output only by using more variable inputs with the fixed inputs it already has, and this produces the changes in cost studied in this topic.

• Fixed inputs: These are resources whose quantity cannot be changed quickly, such as factory buildings, heavy machinery and land. A school bus company cannot add a depot overnight.
• Variable inputs: These are resources that change directly with output, such as casual labour, raw materials, fuel and electricity used in production.
• Length of the period: The short run is not a fixed number of days or months. It differs from one industry to another, so it may be a few weeks for a tailor and several years for a power plant.
• Law of diminishing returns: As more units of a variable input are added to a fixed input, the extra output from each additional unit eventually falls. This law explains why short run costs first fall and then rise.
• Link to long run: In the long run all inputs can be varied, and that analysis belongs to a separate topic.

7.1.2 Total cost (TC)

Total cost is the whole expenditure a firm incurs to produce a given level of output. It is the sum of the fixed and the variable costs.

Formula: TC = TFC + TVC

Total cost is never zero in the short run, because fixed costs must be paid even when nothing is produced. It rises as output rises, because more variable inputs are needed. Example: a poultry farm that spends Ksh 40,000 on rent and licences and Ksh 60,000 on feed and labour for a month has a total cost of Ksh 100,000.

7.1.3 Total fixed cost (TFC)

Total fixed cost is the cost of the fixed inputs, and it stays the same whatever the level of output. It is also called overhead or sunk cost in the short run.

• Rent of premises: A hotel pays the same monthly rent whether its rooms are full or empty.
• Interest on loans: Repayment of interest on a loan for equipment is due regardless of production.
• Depreciation of machinery: The loss in value of equipment through use and age is charged each period.
• Insurance premiums and licences: County business permits and insurance are paid at fixed amounts.
• Salaries of permanent staff: Managers and security guards are paid even when output falls.

On a graph, TFC is a horizontal line because it does not change with output.

7.1.4 Total variable cost (TVC)

Total variable cost is the cost of the variable inputs, and it changes directly with the quantity produced. It is zero when output is zero and rises as output increases.

• Raw materials: A furniture workshop spends more on timber as it makes more chairs.
• Wages of casual or piece-rate workers: Pay rises with hours or units produced.
• Fuel and power: A milling company uses more electricity as it grinds more maize.
• Packaging and transport: Boxes and delivery costs rise with the number of units sold.

TVC first rises at a decreasing rate, because of efficient use of inputs, and then rises at an increasing rate once diminishing returns set in. On a graph it starts at the origin and curves upward.

7.1.5 Average cost (AC)

Average cost is the cost of producing one unit of output. It shows the firm the cost per unit, which it compares with the price to find whether it earns a profit.

Average fixed cost (AFC)

Formula: AFC = TFC ÷ Q

Average fixed cost falls continuously as output rises, because the same fixed cost is spread over more units. Its curve slopes downward and never touches the axis.

Average variable cost (AVC)

Formula: AVC = TVC ÷ Q

Average variable cost first falls and then rises because of increasing and then diminishing returns, so its curve is U-shaped.

Average total cost (ATC)

Formula: ATC = TC ÷ Q = AFC + AVC

Average total cost is also U-shaped. It falls at first because both AFC and AVC fall, and it rises later when the increase in AVC outweighs the fall in AFC. The lowest point of ATC marks the output at which the cost per unit is smallest.

7.1.6 Marginal cost (MC)

Marginal cost is the addition to total cost caused by producing one more unit of output. It guides decisions on whether to increase or reduce production.

Formula: MC = change in TC ÷ change in Q

Since fixed cost does not change, MC is also equal to the change in TVC divided by the change in output. MC is U-shaped, falling at first and then rising because of diminishing returns. It cuts both the AVC and the ATC curves at their lowest points, because when MC is below the average, the average falls, and when MC is above the average, the average rises.

7.1.7 Numerical illustration of short run costs

Example: a tailoring workshop has a total fixed cost of Ksh 600 per day and produces shirts. The table shows its costs at each level of output.

Calculation for the fourth shirt:

Formula: MC = change in TC ÷ change in Q

Substitution: MC = (1,750 − 1,500) ÷ (4 − 3)

Working: MC = 250 ÷ 1

Result: MC = Ksh 250

Reading the table: MC falls to Ksh 200 at the third shirt and rises afterwards. ATC is lowest at Ksh 420 at five shirts, where MC (Ksh 350) is below ATC but about to cross it, and at six shirts MC (Ksh 500) is clearly above ATC, which is why ATC begins to rise.

7.1.8 Relationships among the short run cost curves

The cost curves are linked, and understanding these links helps in reading graphs and in making production decisions.

• TC and TVC: The two curves are parallel, and the vertical distance between them equals TFC at every level of output.
• AFC and output: AFC falls continuously, so the gap between ATC and AVC narrows as output increases.
• AVC and ATC: Both are U-shaped, and ATC lies above AVC by the amount of AFC. The minimum of ATC occurs at a higher output than the minimum of AVC.
• MC and averages: MC cuts AVC and ATC from below at their minimum points.
• Shape of the curves: The U-shape of AVC, ATC and MC results from the law of diminishing returns.

7.1.9 Uses of short run cost analysis

Cost analysis is not only a theoretical exercise, as managers use it in everyday decisions.

• Pricing: A firm must set a price that covers at least average cost if it wants to make a profit in the long term.
• Output decisions: A firm increases output while marginal cost is below price, and stops where marginal cost equals marginal revenue to maximise profit.
• Shutdown decision: If price falls below the minimum AVC, the firm cannot cover even its variable costs and should stop production in the short run. If price is above AVC but below ATC, it can continue producing to cover part of its fixed costs.
• Cost control: Separating fixed from variable costs shows which expenses can be reduced when sales fall.
• Budgeting and planning: Cost information helps in preparing budgets, estimating break-even output and deciding whether to accept an extra order at a special price.