Cost Theory: Short-Run and Long-Run Curves

In economics, cost refers to the expenses incurred by a firm in producing goods or services. Understanding cost behavior is crucial for business decision-making, as it directly impacts profitability and pricing strategies. We distinguish between different types of costs and analyze how they change with the level of output, particularly in the short run and the long run.

Short-Run Costs

The short run in economics is a period during which at least one factor of production is fixed. For a firm, this typically means that the size of the factory, the amount of machinery, or the number of skilled laborers might be fixed. The firm can only change its output by altering the variable factors, such as raw materials or the number of unskilled workers. In the short run, costs are divided into two main categories: total cost, which is the sum of fixed costs and variable costs.

Fixed Costs (FC)

Fixed costs are those costs that do not vary with the level of output. They are incurred even if the firm produces nothing. These costs are associated with the fixed factors of production. Examples include rent of the factory building, salaries of permanent staff, interest on loans, and insurance premiums. Even if production is zero, these costs must be paid.

Variable Costs (VC)

Variable costs are costs that change directly with the level of output. They are incurred on variable factors of production. Examples include the cost of raw materials, wages of daily laborers, electricity consumed for machinery, and fuel. As output increases, variable costs increase, and as output decreases, variable costs decrease. If output is zero, variable costs are also zero.

Total Cost (TC)

Total cost is the sum of total fixed costs and total variable costs at a given level of output.
TC = FC + VC

The total cost curve shows the total expenditure required to produce different levels of output. In the short run, the TC curve starts from the fixed cost axis (at the point where output is zero) and slopes upwards, reflecting the increase in variable costs as output rises.

Average Costs

Average costs are the costs per unit of output. They are derived from total costs.

Average Fixed Cost (AFC)

Average fixed cost is the total fixed cost divided by the total output.
AFC = FC / Q (where Q is the quantity of output)

As output increases, AFC continuously falls because the fixed cost is spread over a larger number of units. The AFC curve is a rectangular hyperbola, meaning the area under the curve at any point is equal to the fixed cost.

Average Variable Cost (AVC)

Average variable cost is the total variable cost divided by the total output.
AVC = VC / Q

The AVC curve is typically U-shaped. Initially, as output increases, AVC falls due to increasing returns to the variable factor. At some point, diminishing returns set in, causing AVC to rise.

Average Total Cost (ATC)

Average total cost is the total cost divided by the total output. It can also be calculated as the sum of AFC and AVC.
ATC = TC / Q = AFC + AVC

The ATC curve is also U-shaped. It is the sum of the downward-sloping AFC curve and the U-shaped AVC curve. The ATC curve lies above the AVC curve, and the vertical distance between them is equal to AFC. The minimum point of the ATC curve occurs at a higher output level than the minimum point of the AVC curve.

Marginal Cost (MC)

Marginal cost is the additional cost incurred by producing one more unit of output. It is the change in total cost resulting from a one-unit increase in output.
MC = ΔTC / ΔQ

Since fixed costs do not change with output, marginal cost is solely determined by the change in variable costs.
MC = ΔVC / ΔQ

The MC curve is also U-shaped. Initially, MC falls as output increases due to increasing returns. As diminishing returns set in, MC rises. The MC curve intersects the AVC and ATC curves at their minimum points.

Short-Run Cost Curves: Graphical Representation

When plotted against output (Q) on the x-axis and cost on the y-axis:

• The FC curve is a horizontal line, indicating that fixed costs remain constant regardless of output.
• The VC curve starts from the origin and slopes upward, showing that variable costs increase with output.
• The TC curve starts from the FC level on the y-axis (at Q=0) and slopes upward, parallel to the VC curve.
• The AFC curve slopes downward from left to right.
• The AVC curve is U-shaped.
• The ATC curve is also U-shaped and lies above the AVC curve.
• The MC curve is U-shaped and intersects the AVC and ATC curves at their lowest points.

Long-Run Costs

The long run is a period long enough for a firm to change all of its factors of production, including capital stock (plant size, machinery). In the long run, there are no fixed factors; all factors are variable. This means the firm can adjust its scale of operations. All costs are variable in the long run.

Long-Run Total Cost (LRTC)

Long-run total cost refers to the minimum cost of producing any given level of output when all inputs are variable. The LRTC curve shows the least cost combination of inputs for each output level. The LRTC curve is typically upward sloping, but it may initially rise at a decreasing rate and then at an increasing rate, reflecting economies and diseconomies of scale.

Long-Run Average Cost (LRAC)

Long-run average cost is the total cost divided by the output in the long run.
LRAC = LRTC / Q

The LRAC curve is often referred to as the "envelope curve." It is formed by the lower envelope of all possible short-run average total cost (SRATC) curves. Each SRATC curve represents a specific plant size or scale of operation. In the long run, a firm can choose the most efficient plant size for any given output level.

Economies and Diseconomies of Scale

The shape of the LRAC curve is explained by economies and diseconomies of scale.

Economies of Scale

Economies of scale occur when the average cost of production decreases as the scale of production increases. This happens in the initial stages of long-run expansion. Reasons for economies of scale include:

• Technical Economies: Specialization of labor and machinery, indivisibility of capital, increased efficiency of large-scale machinery.
• Managerial Economies: Specialization of management functions, professional management.
• Marketing Economies: Bulk purchasing discounts, cheaper advertising per unit.
• Financial Economies: Easier and cheaper access to credit for larger firms.
• Risk-Bearing Economies: Diversification of products and markets reduces risk.

Due to economies of scale, the LRAC curve initially slopes downwards.

Constant Returns to Scale

Beyond a certain point, a firm may experience constant returns to scale, where increasing the scale of production does not lead to any change in the average cost of production. In this phase, the LRAC curve is horizontal.

Diseconomies of Scale

Diseconomies of scale occur when the average cost of production increases as the scale of production increases. This happens when the firm becomes too large. Reasons for diseconomies of scale include:

• Managerial Diseconomies: Communication problems, coordination difficulties, bureaucracy, slower decision-making in very large organizations.
• Labor Diseconomies: Reduced worker morale, increased labor turnover, difficulty in supervision.
• Over-utilization of Resources: Strain on infrastructure and resources.

Due to diseconomies of scale, the LRAC curve slopes upwards.

The Long-Run Average Cost (LRAC) Curve

The LRAC curve is typically U-shaped. It falls initially due to economies of scale, remains flat for a range due to constant returns to scale, and then rises due to diseconomies of scale. The minimum point of the LRAC curve represents the optimal scale of production for the firm.

Long-Run Marginal Cost (LRMC)

Long-run marginal cost is the additional cost incurred by producing one more unit of output in the long run, when all factors are variable.
LRMC = ΔLRTC / ΔQ

The LRMC curve is also U-shaped and intersects the LRAC curve at its minimum point. The LRMC curve lies below the LRAC curve when LRAC is falling and above it when LRAC is rising.

Relationship between LRMC and LRAC

Similar to the short-run relationship:

• When LRMC < LRAC, LRAC falls.
• When LRMC > LRAC, LRAC rises.
• When LRMC = LRAC, LRAC is at its minimum.

The Envelope Curve Concept

The LRAC curve is called the envelope curve because it encompasses or "envelopes" the short-run average total cost (SRATC) curves. Each SRATC curve corresponds to a specific fixed plant size. In the long run, a firm can choose to operate on any of these SRATC curves by selecting the appropriate plant size. The LRAC curve represents the lowest possible average cost for each output level, achieved by choosing the best plant size for that output.

For outputs to the left of the minimum point of the LRAC curve, the firm would choose a smaller plant size (represented by an SRATC curve tangent to the LRAC from below on its downward-sloping portion). For outputs to the right of the minimum point, a larger plant size would be chosen (represented by an SRATC curve tangent to the LRAC on its upward-sloping portion). At the minimum point of the LRAC, the optimal plant size is employed.

Example: Short-Run vs. Long-Run Cost Behavior

Consider a bakery.

• Short Run: The bakery has a fixed oven size and rent. To increase bread production, they can hire more bakers (variable labor) and buy more flour (variable material). If they reach the oven's capacity, they can't produce more bread, even with more labor and flour. Fixed costs are rent and oven depreciation. Variable costs are flour, electricity, and wages.
• Long Run: The bakery can decide to rent a larger space, buy bigger ovens, or even open multiple branches. They can change everything. If demand increases significantly, they might invest in a larger, more automated oven which could lower the average cost per loaf due to efficiency (economies of scale). However, if they expand too much, managing multiple large ovens and a larger staff might lead to coordination problems and higher average costs (diseconomies of scale).

Cost Theory in Decision Making

Understanding these cost curves is vital for firms.

• Pricing Decisions: Firms compare marginal cost with marginal revenue to determine optimal output levels. They also need to ensure prices cover average total cost in the long run to remain profitable.
• Production Decisions: Firms decide how much to produce based on cost structures and market demand. They analyze whether to increase production in the short run or expand capacity in the long run.
• Investment Decisions: The concept of economies of scale influences decisions about plant size and investment in new technology.
• Shutdown Decisions: In the short run, a firm might continue to operate even if it's making a loss, as long as price covers average variable cost, to avoid losing more money by shutting down completely. If price falls below AVC, the firm should shut down to minimize losses.

Shutdown Point

The shutdown point is the level of output at which the firm is indifferent between producing and shutting down. This occurs when the price equals the minimum average variable cost (P = min AVC). If the market price falls below this level, the firm should cease production in the short run.