Costs

This section explains costs and focusses on the formulae used to calculate costs and understand the relationship between total costs, total fixed costs and total variable costs and the Derivation of Short-Run Cost Curves from the Assumption of Diminishing Marginal Productivity.

Formulae to Calculate and Understand the Relationship Between:

Total Cost (TC)

Definition: Total cost is the sum of all costs incurred by a firm in the production of goods and services, including both fixed and variable costs.

Formula:

$$\text{Total Cost (TC)} = \text{Total Fixed Cost (TFC)} + \text{Total Variable Cost (TVC)}$$ 

Explanation: Total cost reflects the entire cost of production, including both costs that do not change with output (fixed costs) and those that vary with output (variable costs).

Example: If a firm has total fixed costs of £1000 and total variable costs of £500, the total cost is:

TC = 1000 + 500 = £1500 

Total Fixed Cost (TFC)

Definition: Total fixed cost is the cost that does not change with the level of output. It includes costs such as rent, salaries of permanent staff, and insurance.

Formula:

$$\text{Total Fixed Cost (TFC)} = \text{Constant costs regardless of output}$$ 

Explanation: Fixed costs remain the same no matter how much the firm produces, and they are incurred even when output is zero.

Example: A factory pays a fixed rent of £1000 per month, regardless of how many units it produces. Therefore, TFC = £1000.

Total Variable Cost (TVC)

Definition: Total variable cost is the cost that changes with the level of output. It includes costs such as raw materials, labour directly involved in production, and utilities.

Formula:

$$\text{Total Variable Cost (TVC)} = \text{Variable cost per unit} \times \text{Quantity (Q)}$$ 

Explanation: As production increases, variable costs also increase. For example, if it costs £5 to produce each unit and the firm produces 100 units, the total variable cost would be £500.

Example: If the variable cost per unit is £5, and the firm produces 100 units, then:

TVC=5×100=£500TVC = 5 \times 100 = £500TVC=5×100=£500 

Average (Total) Cost (AC or ATC)

Definition: Average cost is the total cost per unit of output. It is the total cost divided by the quantity produced.

Formula:

$$\text{Average Cost (AC or ATC)} = \frac{\text{Total Cost (TC)}}{\text{Quantity (Q)}}$$ 

Explanation: Average cost tells the firm how much it costs, on average, to produce each unit of output. It is derived by dividing total cost by the number of units produced.

Example: If total cost is £1500 and the firm produces 100 units, then:

$$AC = \frac{1500}{100} = £15 \text{ per unit}$$ 

Average Fixed Cost (AFC)

Definition: Average fixed cost is the fixed cost per unit of output. It is calculated by dividing total fixed costs by the quantity produced.

Formula:

$$\text{Average Fixed Cost (AFC)} = \frac{\text{Total Fixed Cost (TFC)}}{\text{Quantity (Q)}}$$ 

Explanation: Average fixed cost decreases as output increases because the same fixed costs are spread over a larger number of units.

Example: If total fixed cost is £1000 and the firm produces 100 units, then:

$$AFC = \frac{1000}{100} = £10 \text{ per unit}$$ 

Average Variable Cost (AVC)

Definition: Average variable cost is the variable cost per unit of output. It is calculated by dividing total variable costs by the quantity produced.

Formula:

$$\text{Average Variable Cost (AVC)} = \frac{\text{Total Variable Cost (TVC)}}{\text{Quantity (Q)}}$$ 

Explanation: Average variable cost reflects the variable costs incurred in the production of each unit. It typically decreases initially as output increases but may rise at higher levels of production due to diminishing returns.

Example: If total variable cost is £500 and the firm produces 100 units, then:

$$AVC = \frac{500}{100} = £5 \text{ per unit}$$ 

Marginal Cost (MC)

Definition: Marginal cost is the additional cost incurred from producing one more unit of output.

Formula:

$$\text{Marginal Cost (MC)} = \frac{\Delta \text{Total Cost (TC)}}{\Delta \text{Quantity (Q)}}$$ 

Explanation: Marginal cost helps the firm determine how much additional cost is associated with producing one more unit. It is the change in total cost divided by the change in quantity.

Example: If the total cost of producing 100 units is £1500 and the total cost of producing 101 units is £1510, then:

$$MC = \frac{1510 - 1500}{101 - 100} = \frac{10}{1} = £10$$ 

Derivation of Short-Run Cost Curves from the Assumption of Diminishing Marginal Productivity

The short-run cost curves are derived from the assumption of diminishing marginal returns. This concept explains that as more units of a variable input (e.g., labour) are added to a fixed amount of capital, the additional output produced by each new unit of labour will eventually decrease.

Diminishing Marginal Returns: Initially, as more workers are hired, output increases at an increasing rate because of better utilisation of fixed resources. However, after a certain point, each additional worker contributes less to total output, causing the marginal product of labour to fall. As a result, marginal cost rises.

Short-Run Cost Curves:

• Marginal Cost (MC): As diminishing returns set in, marginal cost starts to increase. Initially, MC falls, but after the point of diminishing returns, MC begins to rise. The MC curve typically has a U-shape.
• Average Total Cost (ATC): The ATC curve also tends to be U-shaped. Initially, average cost decreases as fixed costs are spread over more units of output. But as diminishing returns increase the variable cost per unit, ATC rises again.
• Average Variable Cost (AVC): Similar to ATC, the AVC curve is U-shaped. Initially, AVC decreases as variable costs are spread over more units. However, due to diminishing returns, AVC rises as output increases beyond a certain point.
• Average Fixed Cost (AFC): The AFC curve is always downward sloping. As output increases, the fixed costs are spread over more units, causing AFC to decrease continuously.

Diagram: A typical short-run cost curve diagram would show:

• The MC curve initially falling, reaching a minimum, and then rising due to diminishing returns.
• The AVC curve and ATC curve both U-shaped, with the ATC curve lying above the AVC curve by the amount of average fixed cost.
• The AFC curve continuously decreasing as output increases.

Relationship Between Short-Run and Long-Run Average Cost Curves

The long-run average cost (LRAC) curve represents the lowest possible cost for each level of output when a firm has had enough time to adjust all its inputs. It is derived from a series of short-run cost curves, each representing a different scale of operation.

• Short-Run Cost Curves: In the short run, the firm has some fixed inputs and can only adjust variable inputs. The short-run cost curves (MC, AVC, ATC) reflect the production capacity of the firm at fixed levels of capital.
• Long-Run Average Cost Curve (LRAC): In the long run, all factors of production are variable, and the firm can adjust its plant size and capacity. The LRAC curve is derived from the envelope of the various short-run cost curves, representing the lowest cost for each level of output when the firm can change its scale of production.

Key Points:

• The LRAC curve is typically U-shaped due to economies of scale at first, followed by diseconomies of scale as output increases.
• Economies of Scale: In the downward-sloping section of the LRAC curve, the firm experiences economies of scale, meaning that as output increases, average costs decrease due to more efficient use of resources.
• Diseconomies of Scale: In the upward-sloping section of the LRAC curve, the firm faces diseconomies of scale, where increasing output leads to higher per-unit costs due to inefficiencies associated with larger scale production.

Diagram: The LRAC curve is typically U-shaped and lies beneath the short-run cost curves. Each point on the LRAC curve represents the lowest possible cost for that output level, considering the firm has the flexibility to adjust its input mix in the long run.

Summary

• Total Cost (TC) = Total Fixed Cost (TFC) + Total Variable Cost (TVC)
• Average Cost (AC or ATC) = Total Cost (TC) ÷ Quantity (Q)
• Average Fixed Cost (AFC) = Total Fixed Cost (TFC) ÷ Quantity (Q)
• Average Variable Cost (AVC) = Total Variable Cost (TVC) ÷ Quantity (Q)
• Marginal Cost (MC) = Change in Total Cost (TC) ÷ Change in Quantity (Q)

The short-run cost curves are derived from diminishing marginal returns, where marginal cost initially falls, then rises as output increases. The long-run average cost curve (LRAC) is derived from a combination of different short-run cost curves and reflects the minimum cost achievable when all inputs are variable.