Cost Output Relationship in Short Run

Cost-Output Relationship in the Short run refers to how the costs incurred by a firm change as the level of output changes when at least one factor of production is fixed, typically capital. In the short run, some inputs are variable, like labor, while others remain fixed, such as plant size or machinery. Understanding this relationship is critical for firms to determine optimal production levels, pricing, and profitability.

The short-run cost-output relationship can be analyzed through several key cost concepts: Total Cost (TC), Fixed Cost (FC), Variable Cost (VC), Average Costs (AC), and Marginal Cost (MC). These concepts help in explaining how costs behave with changes in output.

Key Short-Run Costs and Their Behavior

Total cost represents the sum of all costs incurred by a firm in producing a certain level of output. In the short run, the total cost (TC) is the sum of Fixed Costs (FC) and Variable Costs (VC).

TC = FC+VC

• Fixed Costs (FC): These are costs that remain constant, regardless of the level of output produced. Examples include rent, salaries of permanent staff, and insurance. In the short run, fixed costs do not change with output; they are incurred even when production is zero.
• Variable Costs (VC): These costs vary directly with the level of output. As production increases, variable costs such as raw materials, energy, and wages of hourly workers increase. If production falls, variable costs decline.

Thus, as output increases in the short run, total cost rises due to the increase in variable costs, while fixed costs remain unchanged.

2. Average Cost (AC)

Average cost, also known as per-unit cost, is the total cost divided by the number of units produced. It is composed of two components: Average Fixed Cost (AFC) and Average Variable Cost (AVC).

AC = TCQ = FC / Q + VC / Q = AFC + AVC

• Average Fixed Cost (AFC):

AFC is the fixed cost per unit of output. Since total fixed costs do not change, but output increases, the average fixed cost declines as output increases. This is because the fixed cost is spread over a larger number of units.

• Average Variable Cost (AVC):

AVC is the variable cost per unit of output. Initially, AVC tends to decrease as production increases, due to increasing efficiency in using variable inputs. However, beyond a certain point, AVC begins to rise as production expands, leading to inefficiencies (e.g., labor becoming overcrowded or machinery overused).

• Average Total Cost (ATC):

The sum of AFC and AVC gives the ATC, or per-unit cost of producing a good. ATC typically follows a U-shaped curve, decreasing at first as output increases due to the spreading of fixed costs and initial efficiency gains, but rising after a certain point due to rising variable costs.

3. Marginal Cost (MC)

Marginal cost is the additional cost incurred to produce one more unit of output. It is calculated as the change in total cost (TC) divided by the change in output (Q).

MC = ΔTC / ΔQ

Initially, marginal cost tends to decline due to increasing returns to the variable factor (e.g., labor) and more efficient utilization of fixed inputs. However, as production continues to increase, marginal cost rises due to the Law of Diminishing Marginal Returns. This law states that as more units of a variable factor (like labor) are added to a fixed factor (like capital), the additional output from each new unit of the variable factor eventually diminishes.

U-Shape of Cost Curves

The cost-output relationship in the short run is often depicted through U-shaped cost curves:

• Average Variable Cost (AVC) curve

AVC initially decreases due to efficient utilization of variable inputs, reaching a minimum point before increasing as inefficiencies and overcrowding occur.

• Average Total Cost (ATC) curve

ATC also follows a U-shaped pattern. At first, it declines due to both spreading fixed costs and decreasing AVC. After reaching its minimum point, ATC starts to increase as rising AVC outweighs the effect of declining AFC.

• Marginal Cost (MC) curve

MC initially falls as production expands, reflecting increasing returns to variable factors. Eventually, it rises due to diminishing returns to the variable factor. The MC curve intersects the AVC and ATC curves at their respective minimum points, which signifies the most efficient level of production.

Law of Diminishing Returns and Its Impact on Costs

A central concept in the short-run cost-output relationship is the Law of Diminishing Returns. This law states that if additional units of a variable input (e.g., labor) are added to a fixed input (e.g., capital or land), the marginal product (additional output) of the variable input will eventually decline after a certain point.

As marginal product falls, marginal cost begins to rise, which, in turn, drives up AVC and ATC. This phenomenon explains the upward-sloping part of the MC, AVC, and ATC curves.

For example, consider a factory with a fixed number of machines. Initially, adding more workers increases output significantly, as the workers are able to use the available machines more efficiently. However, as more workers are added beyond the optimal point, they begin to crowd each other, reducing the efficiency of the fixed inputs (machines). This causes marginal cost to rise, signaling diminishing returns.

Relationship Between Costs and Output Decisions

Understanding the cost-output relationship is critical for firms when making production and pricing decisions. Some of the key implications are:

• Profit Maximization

Firms aim to produce at the level where Marginal Cost (MC) equals Marginal Revenue (MR). Producing beyond this point results in higher marginal costs than marginal revenue, leading to losses on additional units produced.

• Economies of Scale

In the early stages of production, firms can benefit from economies of scale, where increasing output leads to declining average costs (due to spreading fixed costs and efficient use of resources). However, beyond a certain level, diseconomies of scale may occur as rising variable costs push average costs higher.

• Short-Run Shutdown Decision

Firms must cover their average variable costs (AVC) in the short run to remain operational. If the price falls below AVC, the firm would be better off shutting down production temporarily because it cannot cover even its variable costs.

• Pricing Strategy

Firms often set prices above average total cost (ATC) to ensure profitability. The position of the ATC curve and its relationship with the demand curve help firms decide whether to increase or decrease output.

Short-Run Output Cost Curves

The cost-output relationships can also be shown through the use of graphs. It will be seen that the average fixed cost curve (AFC curve) falls as output rises from lower levels to higher levels. The shape of the average fixed cost curve, therefore, is a rectangular hyperbola.

However, the average variable cost curve (AVC curve) starts rising earlier than the ATC curve. Further, the least cost level of output corresponds to the point L_T on the ATC curve and not to the point L_V which lies on the AVC curve.

Another important point to be noted is that in Fig. the marginal cost curve (MC curve) intersects both the AVC curve and ATC curve at their minimum points. This is very simple to explain. If marginal cost (MC) is less than the average cost (AC), it will pull AC down. If the MC is greater than AC, it will pull AC up. If the MC is equal to AC, it will neither pull AC up nor down. Hence, MC curve tends to intersect the AC curve at its lowest point.

Similar is the position about the average variable cost curve. It will not make any difference whether MC is going up or down. L_T is the lowest point of total cost and L_V is the lowest point of variable cost.

The inter-relationships among AVC, ATC, and AFC can be summed up as follows:

1. If both AFC and AVC fall, ATC will also fall.
2. If AFC falls but AVC rises

(a) ATC will fall where the drop in AFC is more than the rise in AVC.

(b) ATC will not fall where the drop in AFC is equal to the rise in AVC.

(c) ATC will rise where the drop in AFC is less than the rise in AVC.