Question

What is the relationship between a perfectly competitive firm's marginal cost curve and its supply curve?

Short answer

In a perfectly competitive market, the firm's Marginal Cost (MC) curve, above its minimum, serves as the firm's supply curve, since the firm equates the market price to its marginal cost to maximize profit. However, this holds true only when the firm operates at an optimum scale and the market is perfectly competitive.

Step-by-step solution

Title

Firstly, understand the concept of Marginal Cost (MC). MC is the change in total cost that arises when the quantity produced changes by one unit. Mathematically, MC could be represented as \(MC = \Delta TC / \Delta Q\), which represents the ratio of change in total cost (\(\Delta TC\)) to change in quantity (\(\Delta Q\)).

Title

Next, get familiar with the principle of perfect competition. In a perfectly competitive market, firms are price-takers, i.e., each firm takes the market price as given. Hence, it equates its own marginal cost to the market price to maximize profit.

Title

Now, identify the connection between the MC curve and the firm's supply curve. The MC curve above its minimum point is the firm’s short-run supply curve in a perfectly competitive market. The portion of the MC curve that lies above the average variable cost (AVC) curve forms the supply curve of the perfectly competitive firm since the firm won't operate where price is less than average variable cost.

Title

Remember that this connection holds true only under certain circumstances. For the MC to serve as the supply curve, two conditions must be satisfied: (1) The market must be perfectly competitive & (2) The scale of operation of the firm should be optimum, i.e., the firm must be operating in conditions of ‘Equilibrium’ (MC=MR).

Key concepts

Marginal Cost

Marginal cost (MC) is a fundamental concept in economics that refers to the cost incurred from producing one additional unit of a good or service. It's a helpful tool for decision-making, especially for firms in determining how much to produce. Mathematically, marginal cost is expressed as:\[MC = \frac{\Delta TC}{\Delta Q}\]where \(\Delta TC\) is the change in total cost and \(\Delta Q\) is the change in quantity produced.

In simple terms:

• Marginal cost helps firms decide whether increasing production is beneficial or not.
• If the selling price of the additional unit is greater than the marginal cost, producing more adds to the profit.

In a perfectly competitive market, firms equate their marginal cost to the market price to maximize profit. This is because they can sell as much as they want at the market price. Hence, marginal cost becomes a critical signal for production decisions.

Supply Curve

The supply curve is a graphical representation illustrating the relationship between the price of a good and the quantity supplied by a firm. In a perfectly competitive market, the supply curve for a firm is unique.

In this market:

• The supply curve is actually the marginal cost curve above the minimum point of the average variable cost.
• Firms operate where the price equals the marginal cost, hence depicting the upward-sloping part of the MC curve.
• The part of the MC curve that forms the firm's supply curve is above the AVC curve because firms wouldn't operate where price is below AVC.

This demonstrates that only motions where price covers all variable costs plus a bit for fixed costs are valid for firm's supply decisions in perfectly competitive markets.

Average Variable Cost

Average variable cost (AVC) is the cost per unit of output based on variable inputs. It’s calculated by dividing total variable costs by the quantity of output produced:\[AVC = \frac{TVC}{Q}\]where \(TVC\) is total variable cost and \(Q\) is the quantity of output.

Understanding AVC is essential because:

• It helps firms know the minimum price at which they should produce to cover variable costs.
• If the market price falls below AVC, the firm will incur a loss by continuing production and might choose to shut down temporarily.

The role of AVC in perfectly competitive markets is crucial as it sets the lower bound for the firm's short-run supply decisions. If the price is above AVC, firms cover variable costs and contribute to fixed costs. If below, they risk making a loss and may stop production.