Question

Which of the following are the same at all levels of output under perfect competition? a. Marginal cost and marginal revenue b. Price and marginal revenue c. Price and marginal cost d. All of the above

Short answer

Under perfect competition, the correct option is b. Price and marginal revenue, as they are the same at all levels of output. Marginal cost is not equal to marginal revenue or price at all levels of output; it equals them only at the profit-maximizing output level.

Step-by-step solution

Relationship between price and marginal revenue

In a perfectly competitive market, individual firms are said to be price takers as they have no control over the market price of the product. Therefore, in such a market, the marginal revenue (extra revenue earned by selling one more unit) is equal to the price (P) as the firm can sell any number of units at this price. So, Price (P) = Marginal Revenue (MR). // step 2: Identifying the relationship between marginal cost and marginal revenue under perfect competition //

Relationship between marginal cost and marginal revenue

For a perfectly competitive firm, the profit-maximizing output level is achieved when marginal cost (MC) equals marginal revenue (MR). However, this condition does not mean that MC and MR are the same at all levels of output. The firms adjust their output levels to make MC = MR, but they can be different when production levels change. // step 3: Identifying the relationship between price and marginal cost under perfect competition //

Relationship between price and marginal cost

In a perfectly competitive market, when a firm maximizes its profit, the condition MC = MR occurs. And since we know from step 1 that Price (P) = Marginal Revenue (MR), we can conclude that at the profit-maximizing output level, Price (P) = Marginal Cost (MC). However, this does not imply that P and MC are the same at all levels of output. // step 4: Answering the question and explaining the correct option(s) //

Selecting the correct option(s)

Based on our analysis in steps 1, 2, and 3, we can conclude the following relationships under perfect competition: Price (P) = Marginal Revenue (MR) However, we can't confirm that Marginal cost (MC) equals either marginal revenue (MR) or price (P) at all levels of output. Therefore, the correct option is: b. Price and marginal revenue

Key concepts

Marginal Cost

Marginal Cost (MC) is a crucial concept in economics that refers to the additional cost incurred when producing one more unit of a good or service. In a perfectly competitive market, the goal is to ensure that the cost of producing each additional unit is as low as possible while still meeting the market demand. The Marginal Cost is calculated by the change in total cost when an extra unit is produced and can be represented by the formula: \[MC = \frac{\Delta TC}{\Delta Q}\]where \(\Delta TC\) is the change in total cost and \(\Delta Q\) is the change in quantity.In practice, firms aim to align their output so that the marginal cost aligns with other economic factors like marginal revenue, which we will explore in the next sections.

Marginal Revenue

Marginal Revenue (MR) is the additional income generated from selling one more unit of a product. For firms operating under perfect competition, the market dictates this revenue, as such firms are price takers. This means they do not have the power to influence the price of their goods or services. In a perfectly competitive environment, the price remains consistent across all units sold, resulting in the marginal revenue equating to the market price. Expressed as:\[MR = P\]Where \(MR\) represents marginal revenue and \(P\) stands for price.This relationship is crucial because it allows firms to determine the most financially advantageous level of production, particularly when paired with marginal cost calculations.

Profit Maximizing Output

The concept of Profit Maximizing Output is central to understanding how firms operate within a perfectly competitive market. Profit maximization occurs when a firm adjusts its level of production such that the marginal cost (MC) is equal to the marginal revenue (MR). This equality can be expressed by the equation:\[MC = MR\]This equation guides firms in determining the optimal quantity of goods to produce where profits are maximized. Some key points to consider include:

• Firms should expand production as long as MR > MC, as this indicates each unit is adding to profit.
• If MR < MC, they should reduce production, preventing a decrease in overall profit.
• The exact level of output where MR equals MC is where firms make the highest possible profit, given their cost structure and the prevailing market price.

By maintaining this balance, firms ensure they are not wasting resources and are operating efficiently within the market.