Types of Cost, Revenue and Profit, Short-Run and Long-Run Production

This section explores the fundamental concepts of cost, revenue, and profit for firms, as well as the distinction between short-run and long-run production decisions. A key element is the firm's pursuit of cost-minimizing input combinations.

Types of Cost

Costs are the expenses incurred by a firm in the production of goods and services. They are typically categorized into two main types:

• Fixed Costs (FC): These costs do not vary with the level of output in the short run. Examples include rent, insurance, and salaries of permanent staff. $FC_{total} = FC$
• Variable Costs (VC): These costs change directly with the level of output. Examples include raw materials, wages of temporary staff, and energy. $VC_{total} = f(Q)$ where Q is the quantity of output.

The Total Cost (TC) is the sum of fixed costs and variable costs: $TC = FC + VC$.

Other cost classifications include:

• Total Variable Cost (TVC): The variable costs incurred at a particular level of output.
• Marginal Cost (MC): The additional cost incurred by producing one more unit of output. $MC = \frac{\Delta TC}{\Delta Q}$
• Average Variable Cost (AVC): The variable cost per unit of output. $AVC = \frac{VC}{Q}$
• Total Product Cost (TPC): The total cost divided by the total quantity of output. $TPC = \frac{TC}{Q}$
• Average Total Cost (ATC): The total cost per unit of output. $ATC = \frac{TC}{Q}$

Types of Revenue

Revenue is the income generated by the sale of goods and services.

• Total Revenue (TR): The total income from sales. $TR = P \times Q$ where P is the price per unit and Q is the quantity sold.
• Average Revenue (AR): The revenue per unit sold. $AR = \frac{TR}{Q} = P$ (in perfect competition).

The relationship between total revenue and marginal revenue is important. In perfect competition, $AR = MR = P$. However, in imperfect competition, this is not always the case.

Types of Profit

Profit is the difference between total revenue and total cost.

• Economic Profit: The difference between total revenue and total cost, including both explicit and implicit costs. $Economic Profit = TR - TC$. If economic profit is positive, the firm is earning an economic profit. If it is negative, the firm is incurring an economic loss.
• Accounting Profit: The difference between total revenue and explicit costs only. $Accounting Profit = TR - Explicit Costs$.

Short-Run Production Decisions

In the short run, at least one factor of production is fixed. A firm's goal is to maximize profit, which occurs where marginal cost (MC) equals marginal revenue (MR). This is because:

• If $MC < MR$, then increasing output will increase profit.
• If $MC > MR$, then increasing output will decrease profit.
• Profit is maximized where $MC = MR$.

The firm will produce $Q^*$ where $MC = MR$. At this quantity, $MC = MR$ and $MC = MR$ is also equal to $ATC$ at the profit-maximizing quantity. Therefore, profit is maximized when $MC = MR = ATC$.

Long-Run Production Decisions

In the long run, all factors of production are variable. The firm's goal is to minimize its average total cost (ATC). This is achieved by choosing the scale of production that minimizes ATC. This involves considering the relationship between average total cost and output.

The long-run average cost (LRAC) curve shows the minimum ATC for each level of output. The firm will produce at the quantity where its MC curve intersects its LRAC curve.

Key concepts in long-run production include:

• Economies of Scale: When the ATC decreases as output increases. This can be due to factors like specialization, efficient use of capital, and bulk purchasing.
• Diseconomies of Scale: When the ATC increases as output increases. This can be due to factors like management difficulties, communication problems, and coordination issues.

Cost-Minising Choice of Factor Inputs

Firms aim to minimise their production costs. This involves finding the combination of factor inputs (e.g., capital and labour) that achieve a given level of output at the lowest possible cost. This is often represented using isocost curves and isoproduct curves.

Isocost Curve: A curve showing all combinations of factor inputs that cost the same amount. The slope of the isocost curve represents the relative prices of the factors.

Isoproduct Curve: A curve showing all combinations of factor inputs that produce the same level of output. The slope of the isoproduct curve represents the marginal rate of technical substitution (MRTS) between the factors.

The firm will choose the input combination where the MRTS equals the relative price of the factors (the slope of the isocost curve). This ensures that the firm is using the inputs in the most cost-effective way.

Cost Type	Description
Fixed Costs	Costs that do not change with the level of output.
Variable Costs	Costs that change with the level of output.
Total Cost	The sum of fixed and variable costs.
Marginal Cost	The change in total cost resulting from producing one more unit.
Average Variable Cost	The variable cost per unit of output.