The Determinants of Supply in a Competitive Market

Introduction to Market Supply and the Competitive Firm

Market supply represents the specific relationship between the price of a good or service and the total quantity offered by all producing firms in the market. Economists model firms within a perfectly competitive market as agents that must make decisions based on several exogenous and endogenous factors. Specifically, a firm in a competitive market considers the relationship between the quantity produced and production costs as given and exogenous. The revenue per unit of the good or service sold, which is the market price, is also considered given and exogenous. The firm’s primary objective is to select the quantity of output—an endogenous variable—that results in the maximization of its own profit.

Production Costs: Opportunity and Accounting Perspectives

Economists and accountants view costs through different lenses. Economists utilize the concept of opportunity cost, which is defined as everything that must be sacrificed to obtain a specific item. In contrast, accountants typically focus only on explicit costs, which are those that require a direct monetary outlay. To illustrate, consider a pizzeria with the following annual expenses: $50\text{K Euro}$ spent on raw materials, $150\text{K Euro}$ spent on employee salaries, and an occupancy cost for a building that originally cost $600\text{K Euro}$. The building's purchase was financed using $300\text{K Euro}$ of the owner's personal savings and a $300\text{K Euro}$ bank loan, both subject to a $5\%$ interest rate. Furthermore, if the owner were not running the pizzeria, they could earn $50\text{K Euro}$ per year as a computer scientist.

From an accounting perspective, the total cost for this pizzeria is the sum of the raw materials, salaries, and the interest paid on the bank loan: $50\text{K} + 150\text{K} + (300\text{K} \times 0.05) = 215\text{K Euro}$. From an economic perspective, the opportunity cost includes everything the accountant counts plus the implicit costs, which do not require a cash outlay. These implicit costs include the interest the owner could have earned on their savings and the forgone salary from the IT job. Thus, the economic cost is calculated as follows: $50\text{K} + 150\text{K} + (600\text{K} \times 0.05) + 50\text{K} = 280\text{K Euro}$. A significant distinction is that if the alternative salary for a computer scientist were to double, the accounting cost would remain unchanged at $215\text{K Euro}$, while the economic opportunity cost would increase by another $50\text{K Euro}$.

The Production Function and Total Cost

A production function describes the relationship between the quantity of inputs used to make a good and the quantity of output of that good, expressed as $Q$. In a simplified model of a pizzeria, the inputs might be limited to the number of employees—labor ($L$)—and the square footage of the building—capital ($K$). When capital ($K$) is held constant and labor ($L$) is increased, the production function typically shows two characteristics: it is increasing in $L$, but the contribution of each additional worker decreases. This phenomenon is known as the diminishing marginal product of labor.

The production function serves as the basis for deriving the total cost function. Total cost ($CT$) represents the total cost of production for every possible quantity of goods produced. If the hourly cost of the building is assumed to be $30\text{ Euro}$ (derived from an annual cost of $30\text{K Euro}$ divided by $1000$ working hours), this cost exists even if production is zero. Total cost increases as output increases, and notably, the rate of increase in total cost accelerates as more is produced. This acceleration in cost is a direct consequence of the diminishing marginal product of labor.

Fixed, Variable, and Average Costs

Total cost is the sum of fixed costs ($CF$) and variable costs ($CV$). Fixed costs are independent of the quantity produced and remain even when production is zero, such as the building cost in the pizzeria example ($30\text{ Euro}$ per hour). Variable costs change as the firm alters the quantity of output. For instance, the cost of employees may rise from $10$ for $60$ pizzas, to $20$ for $90$ pizzas, and $30$ for $120$ pizzas.

From these totals, we derive several average cost metrics. Average total cost ($CMT$) is calculated by dividing total cost by the quantity produced: $CMT = \frac{CT}{Q}$. Similarly, average fixed cost is $CMF = \frac{CF}{Q}$, and average variable cost is $CMV = \frac{CV}{Q}$. Because $CF$ is constant, $CMF$ always decreases as quantity ($Q$) increases. Conversely, $CMV$ typically increases with $Q$ because of diminishing marginal productivity. The $CMT$ curve is usually U-shaped because it initially falls due to declining $CMF$ and eventually rises due to increasing $CMV$.

Marginal Cost and its Relationship to Average Cost

Marginal cost ($C'$) is the increase in total cost resulting from an additional unit of production: $C' = \frac{\Delta CT}{\Delta Q}$. The marginal cost curve is typically upward-sloping because of the diminishing marginal product of labor; when a firm already employs many workers, adding another worker yields a smaller increase in output, making it more expensive to produce that extra unit.

A fundamental mathematical relationship exists between marginal cost and average total cost: the $C'$ curve intersections the $CMT$ curve at its minimum point. When marginal cost is lower than average total cost (C' < CMT), the average total cost must be falling. When marginal cost is higher than average total cost (C' > CMT), the average total cost must be rising. This logic dictates that the marginal cost curve must pass through the lowest point of the U-shaped average total cost curve.

Production Costs in the Short and Long Run

In the short run, certain factors of production, such as the size of a building ($K$), are fixed. In the long run, however, all costs are variable, and a firm can change its scale of production by moving to a larger or smaller facility. This flexibility allows for more efficient expansion or contraction. The long-run average total cost curve ($CMT$ of long period) is the envelope of various short-run $CMT$ curves, each representing a different fixed level of capital.

The shape of the long-run $CMT$ curve reveals the firm's returns to scale. If doubling all inputs results in a doubling of output, the long-run $CMT$ remains constant, indicating constant returns to scale. If output more than doubles, the long-run $CMT$ falls, representing economies of scale. Economies of scale often arise from increased labor specialization. If output increases by less than double, the long-run $CMT$ rises, representing diseconomies of scale. Diseconomies of scale are frequently caused by coordination problems inherent in managing a large organization.

Revenue and Profit Maximization

In a competitive market, a firm's total revenue is defined as $RT = P \times Q$. Because the price ($P$) is exogenous and does not change based on the firm's output level, the average revenue ($RM$) and marginal revenue ($R'$) are both equal to the price ($P$). Profit ($\pi$) is defined as total revenue minus total cost ($\pi = RT - CT$).

Economists distinguish between economic profit and accounting profit. Economic profit uses opportunity cost as the total cost measure. A situation where economic profit equals zero is called a "normal profit." In such a case, the business owner is exactly compensated for the alternative uses of their resources. In the pizzeria example, a normal profit would still mean the owner brings home $65\text{K Euro}$ per year (the sum of the forgone $50\text{K}$ salary and the $15\text{K}$ return on savings). Anything above this is considered "extra-profit."

To maximize profit, a firm produces the quantity where marginal revenue equals marginal cost ($R' = C'$). Since $R' = P$ in a competitive market, the maximization condition is $P = C'$. If a firm produces at a quantity $Q_1$ where R' > C', it can increase profit by producing more. If it produces at $Q_2$ where R' < C', it can increase profit by producing less.

The Individual Firm's Supply Curve

The decision to supply depends on whether the firm can cover its costs. In the short run, the building cost is a sunk cost with an opportunity cost of zero, but employees can be let go. Therefore, the firm's short-run shutdown condition is based on variable costs. An enterprise will continue to produce in the short run as long as the price is greater than or equal to the average variable cost ($P \geq CMV$). If P < CMV, the firm shuts down. Thus, the individual firm’s short-run supply curve is the portion of its marginal cost curve that lies above its $CMV$ curve.

In the long run, all costs are variable, and the firm can exit the market if it cannot cover all its costs. The long-run exit condition is P < CMT. A firm will only enter or stay in the market in the long run if the price is at least equal to the minimum of the average total cost ($P \geq CMT$). Consequently, the firm's long-run supply curve is the portion of its marginal cost curve that lies above the $CMT$ curve.

Market Supply and the Effects of Demand Shifts

The market supply curve is the horizontal summation of the supply curves of all individual firms. In the short run, the number of firms is fixed, and the market supply curve is upward-sloping. In the long run, however, firms can freely enter or exit the market. If prices are high enough to generate extra-profit (economic profit > 0), new firms will enter. This entry increases market supply and pushes the price down. Conversely, if firms suffer losses, they will exit, reducing supply and pushing the price back up.

This entry and exit process continues until economic profit is zero. Therefore, in the long run, the market price must equal the minimum average total cost ($P = CMT_{\text{min}}$). This results in a long-run market supply curve that is horizontal at this price level. While the long-run supply is theoretically horizontal, it may become upward-sloping if the cost of production factors increases as the industry expands (e.g., higher wages for specialized pizza chefs) or if different firms have different cost structures.

When market demand increases, the short-run effect is a movement along the short-run supply curve, leading to a higher price and higher profits for existing firms. However, in the long run, these profits attract new entrants, shifting the supply until the price returns to the level of minimum average total cost. Thus, an increase in demand leads to a higher quantity sold in the long run, but the price remains at the minimum of the $CMT$.