Optimizing Production: The Question for Maximum Profits

This chapter pivots towards a distinct inquiry, how does a firm determine the quantity to produce? The exploration of this question is far from simple or uncontested, hinging on a critical, although somewhat unreasonable, assumption that a firm in Perfect Competition is a ruthless profit maximizer.

Under this premise, a firm’s production and sales in the Perfect Competition market are tailored to the pinnacle of profit maximisation. It’s also posited that whatever a firm produces in Perfect Competition is sold in the market, allowing for the terms ‘output’ and ‘quantity sold’ to be used interchangeably.

Essentials of Perfect Competition: A Market Analysis

• In order to analyze a firm’s profit maximization problem, the market environment in which the firm in Perfect Competition functions needs to be analysed. 
• A perfectly competitive market has the following defining features:
  • The market consists of a large number of buyers and sellers
  • Each firm produces and sells a homogenous product. i.e., The product of one firm in Perfect Competition cannot be differentiated from the product of any other firm.
  • Entry into the market as well as exit from the market are free for firms.
  • The information is perfect.

Revenue: Understand in Perfect Competition Markets

• Revenue is the money that is produced by carrying out normal business operations and is calculated by multiplying the average sales price by the number of items sold.
• In a perfectly competitive market scenario, a firm’s revenue dynamics are largely dictated by the prevailing market price. 

Price Setting Mechanism: Effective Price Setting in Perfect Competition Markets

• Firms can sell any quantity of their goods at or below the market price. 
• However, setting a price below the market price is illogical as firms can sell all their produce at the market price.

Maximizing Profits: Total Revenue in a Sales

• TR is derived from the product of the market price (p) and the quantity of the goods produced and sold (q), expressed as 

                              TR = p × q.

• Example: In a perfectly competitive market for candles priced at Rs 10 per box, the total revenue from selling two boxes is Rs 20.

Total Revenue Curve: Insights into Sales and Pricing Strategy

• The Total Revenue Curve, as illustrated in Figure, plots the quantity sold (on the x-axis) against revenue earned (on the y-axis).
• Three notable observations from the Total Revenue Curve:
  • At Zero Output: The total revenue is also zero, hence the curve passes through point O.
  • Upward-Rising Line: The curve represents a straight, upward-rising line, given the constant market price.
  • Market Price (p): The slope of this line is equal to the market price (p), deduced from the ratio of vertical height (Aq₁) to horizontal distance (Oq₁) when the output is one unit.

Average Revenue (AR): Market Prices and Price-Taking Behavior

• Definition: It is defined as the total revenue per unit of output, expressed as AR= p.
  • It’s noted that for a price-taking firm, average revenue equates to the market price.
• Graphical Representation: Figure visually represents the following key points in a perfectly competitive market.
  • The Price Line and Average Revenue: A horizontal Price Line intersects the y-axis at the market price (p), also representing the Average Revenue (AR) curve, indicating AR=p for any given output.
• Perfectly Elastic Demand Curve: This Price Line embodies a perfectly elastic demand curve, illustrating a firm’s ability to sell any quantity at the market price.
• Consistent Price Line and Price-Taking Behavior: The consistency of the Price Line across different output levels emphasizes the constant market price, underscoring the price-taking behavior of firms in such a market setting.

Price Line and Demand Curve: Perfectly Elastic Demand in Perfect Competition Markets

• The Price Line, synonymous with the Average Revenue curve under perfect competition, is a horizontal straight line at the market price level on the y-axis, depicting a perfectly elastic demand curve faced by a firm. 
• This suggests that a firm can sell any quantity of goods at the market price.

Marginal Revenue (MR): Perfect Competition with Market Prices

• Definition: The marginal revenue (MR) of a firm in Perfect Competition is defined as the increase in total revenue for a unit increase in the firm’s output.
  • It’s calculated as the change in total revenue divided by the change in quantity.
    • Consider a situation where the firm’s output is increased from q₀ to q₀+1.
    • Given market price p, notice that MR = (TR from output q₀+1) – (TR from output q₀) =(p (q₀+1))–(pq₀)=p
    • In other words, for a price-taking firm in Perfect Competition, marginal revenue equals the market price. Thus, for the perfectly competitive firm, MR=AR=p
    • For instance, with total revenues of Rs 20 and Rs 30 from selling 2 and 3 boxes of candles respectively, the marginal revenue from selling an extra box is Rs 10, which equals the market price.
  • This isn’t coincidental but inherent to a perfectly competitive market, where MR=AR=p
• The alignment of Marginal Revenue with the market price is intuitive—when a firm in Perfect Competition sells an additional unit of output, the increase in total revenue, or the Marginal Revenue, is precisely the market price as each unit is sold at this fixed price.