7.15 - Short-run Cost Function
The nature of firms and their costs
A firm is an organisation that converts factor inputs, including raw materials, capital equipment, labour, and enterprise, into goods and services for sale in the market. In economic theory, every firm is led by an entrepreneur who oversees these transformations.
Objectives of firms
- Profit maximisation - Balancing revenues and costs to achieve maximum profit.
- Risk minimisation - Ensuring stability and reducing uncertainty.
- Long-term growth - Expanding through investment and market development.
Types of costs considered by firms
Firms focus on private costs, which are the direct expenses borne by the owners, such as wages and materials. They do not account for external costs, like environmental impacts on society.
Types of short-run costs
In the short run, some costs remain constant regardless of production levels, while others vary with output.
Fixed costs
Fixed costs (FC) do not change with the level of output. They form a horizontal straight line on a cost diagram. At zero output, all costs incurred are fixed. In certain industries, such as airlines where capacity is fixed or products are perishable, fixed costs make up a large share of total costs.
Variable costs
Variable costs (VC) change directly with the level of output. They include expenses like labour and raw materials or components. These costs arise specifically from the production process.
Calculations for different types of costs
Various cost measures help firms analyse their expenses and make decisions. Total costs combine fixed and variable elements, while average and marginal costs provide per-unit insights.
Formula for total cost
Where:
- TC = Overall cost of production (£)
- TFC = Costs independent of output (£)
- TVC = Costs that vary with output (£)
Formula for average fixed cost
Where:
- AFC = Fixed cost per unit (£ per unit)
- Total fixed cost = Total fixed expenses (£)
- Output = Quantity produced (units)
Formula for average variable cost
Where:
- AVC = Variable cost per unit (£ per unit)
- Total variable cost = Total variable expenses (£)
- Output = Quantity produced (units)
Formula for average total cost
Where:
- ATC = Total cost per unit (£ per unit)
- Total cost = Overall production cost (£)
- Output = Quantity produced (units)
ATC can also be calculated as AFC + AVC.
Formula for marginal cost
Where:
- MC = Additional cost of producing one more unit (£ per unit)
- Change in total cost = Increase in TC (£)
- Change in output = Increase in quantity produced (units)
Worked example - Calculating different types of costs
A firm has total fixed costs of £5,000. When output is 250 units, total variable costs are £2,500. When output rises to 270 units, total variable costs increase to £2,800. Calculate the AFC, AVC, ATC, and MC for the new output level.
Step 1: Identify the values
- TFC = £5,000
- TVC at 250 units = £2,500
- TVC at 270 units = £2,800
- Initial output = 250 units
- New output = 270 units
Step 2: Calculate TC at new output
TC = TFC + TVC = £5,000 + £2,800 = £7,800
Step 3: Calculate AFC, AVC, and ATC at new output
AFC = TFC / output = £5,000 / 270 = £18.52
AVC = TVC / output = £2,800 / 270 = £10.37
ATC = TC / output = £7,800 / 270 = £28.89
Step 4: Calculate MC
Change in TC = £7,800 - (£5,000 + £2,500) = £300
Change in output = 270 - 250 = 20 units
MC = £300 / 20 = £15.00
Characteristics and shapes of short-run cost curves
Cost curves illustrate how expenses change with output, reflecting economic principles like diminishing returns. The average total cost curve is particularly important as it shows the cost per unit.
Key characteristics of cost curves
- Marginal cost represents the extra cost of producing one additional unit.
- As output increases, total cost always rises, so marginal cost is positive.
- Firms expand production if the expected revenue from extra sales exceeds the additional cost.
- Rising marginal cost reflects the law of diminishing returns: as more variable inputs (like labour) are added to fixed inputs (like machinery), each additional input contributes less to total output.
Shape of the average total cost curve
The short-run ATC curve has a U-shape due to the interaction of AFC and AVC:
- AFC decreases as output rises because fixed costs are spread over more units.
- AVC increases with output due to diminishing returns.
- Initially, falling AFC dominates, lowering ATC; eventually, rising AVC dominates, causing ATC to increase.
- MC intersects AVC and ATC at their minimum points.
Optimum output in the short run
The optimum output occurs where average total cost is at its lowest point on the ATC curve. At this level, the firm achieves productive efficiency in the short run, minimising cost per unit.
Factors to consider with optimum output:
- This output level represents the most efficient use of resources.
- However, it may not be the most profitable output, as profitability depends on the balance between costs and revenues.