Strategic Profit maximization: Balancing Revenue and Resources for Business Success

Profit maximization means increasing profits by business firms using a proper strategy to equal marginal revenue and marginal cost. 

This strategy is not only about revenue generation but also the efficient allocation of resources, essential for a firm’s longevity and success in a competitive market landscape.

Profit maximization: Breaking down the concept into key points

• Fundamental Goal for Firms: Profit maximization is a fundamental goal for firms, driving their production and selling decisions.
• The Profit of a Firm: It is determined by the difference between its Total Revenue (TR) and Total Cost of production (TC), expressed as =TR−TC. This difference represents the firm’s earnings net of costs.
• Determining the Profit: The objective is to find the quantity q₀​ at which Profit maximization. Here’s how the firm navigates this objective.
  •  At quantity profit maximization quantity (q₀​), the firm’s profit reaches its pinnacle.
  •  Any other quantity would result in lesser profits compared to q₀​.

Conditions for Profit Maximization: Conditions and Analysis for Success

Three cardinal conditions must be satisfied at q₀​ to achieve profit maximization:

• Price Equals Marginal Cost: The price (p) should be equal to the Marginal Cost (MC).
• Non-Decreasing Marginal Cost: Marginal Cost should be non-decreasing at q₀​.
• Price and Average Cost Relations
  • Short Run: In the short run, the price should be greater than the Average Variable Cost (p>AVC).
  • Long Run: In the long run, the price should be greater than the Average Cost (p>AC).

Condition 1: Output, Revenue, and Cost Relationships

Profit maximization is defined as the difference between total revenue and total cost.

Relation Between Output, Revenue, and Cost: Maximizing Profits Insightfully

• Output: It is the amount of something that is produced by a person or thing, 
• Cost: It is the price of something or the amount of money needed to pay for or buy something.
  • Both total revenue and total cost are observed to increase as the level of output increases.
• Marginal Revenue (MR): The change in total revenue per unit increase in output is termed the marginal revenue (MR), 
• Marginal Cost (MC): The change in total cost per unit increase in output is termed the marginal cost (MC).
• Case 1: Profits will continue to increase as long as the marginal revenue (MR) is greater than the marginal cost (MC).
• Case 2: Conversely, profits will decrease when the marginal revenue (MR) is less than the marginal cost (MC).

Profit Maximization Condition: Balancing Marginal Revenue and Cost

• Profits are maximised at the level of output (denoted as q0​) where marginal revenue (MR) equals marginal cost (MC), i.e., MR=MC.

Perfect Competition Scenario: Equating Price and Marginal Cost

• In a perfectly competitive market scenario, it’s established that marginal revenue (MR) is equal to the price (P) of the product.
• Therefore, the Profit maximization output level is where the price (P) equals the marginal cost (MC), i.e., P=MC.

Condition 2: Positive Output and Marginal Cost Analysis

The second condition for profit maximization is that the output level is positive. The focus is on the slope of the marginal cost curve at the Profit maximization output level.

Marginal Cost Curve Slope Significance

• Non feasibility of Marginal Cost Curve: It’s highlighted that a downward-sloping marginal cost curve at the Profit maximization output level is not feasible.
• The output levels q1​ and q4​ refer to Figure. At both output levels q1​ and q4​, the market price equates to the marginal cost.
• However, at output level q1​, the marginal cost curve is downward sloping, which is argued to be incompatible with profit maximization. 
• For all output levels slightly left of q1​, the market price is found to be lower than the marginal cost.

Drawing from the argument in Condition 1, it’s inferred that the firm’s profit at an output level in Condition 2 slightly smaller than q1​ surpasses the profit at output level q1​.

Condition 3: Short and Long Run Strategies Illustrated

Condition 3 is crucial for determining the Profit maximization output level when it’s positive, with distinct implications in the short run and long run.

Short Run Scenario (Case 1): Avoiding Losses in Short-Run Production

Price ≥ Average Variable Cost (AVC) Refer to figure The assertion is that a Profit maximization firm will avoid production at an output level where the market price falls below the AVC in the short run.

Analysis at Output Level q₁​: Price vs. Costs in Short-Run Production

• At output level q₁​, the market price p is found to be lower than the AVC.
• Total Revenue (TR) at q₁​ is calculated as Price × Quantity, visually represented by the area of rectangle OpAq₁.
• Total Variable Cost (TVC) at q₁​ is calculated as Average variable cost × visually represented by the area of rectangle OEBq₁.
• The firm’s profit at q1​ is given by TR−(TVC+TFC), which translates to [area of rectangle OpAq₁] − [area of rectangle OEBq₁] − [area of rectangle OpAq₁] − [area of rectangle OEBq₁] −TFC.

Profit Comparison at Zero Output: Short-Run Comparison at q₁

• At zero output, both TR and TVC are zero, resulting in a profit of -TFC.
• However, at q1​, the area of rectangle OpAq1 is strictly smaller than the area of rectangle OEBq1, leading to a profit of [area EBAp] − [area EBAp] − TFC, which is less than the profit at zero output.

Long Run Scenario (Case 2): Price ≥ Average Cost (AC) Refer to Figure

• The assertion for the long-run scenario is that a Profit maximization firm will not produce at an output level where the market price is lower than the AC.

Analysis at Output Level q₁​: Price, Revenue, and Total Cost Dynamics

• At output level q₁​, the market price p is found to be lower than the (long run) AC.
• Total Revenue (TR) at q₁​ is calculated as Price × Quantity, visually represented by the area of rectangle OpAq₁.
• Total Cost (TC) at q₁​ is calculated as Average cost × Quantity, visually represented by the area of rectangle OEBq₁.

Profit and Loss Analysis: Profitability Evaluation

• Since the area of rectangle OEBq₁ (representing TC) is larger than the area of rectangle OpAq₁ (representing TR), the firm incurs a loss at output level q₁​.
• In the long run, a firm that ceases production achieves a profit of zero.

The Profit Maximisation Problem: Graphical Representation

• Problem in the Short run: Utilising the insights from previous cases, a graphical representation is constructed to illustrate a firm’s profit maximization problem in the short run, as depicted in Figure.
  • Output Level q₀​ and The market price is denoted as p.
  • By equating the market price with the (short-run) marginal cost, the output level q₀​ is obtained.
• At q₀​, the Short Run Marginal Cost (SMC) is upward-sloping, and the market price p exceeds the Average Variable Cost (AVC).
• Verification of Profit Maximization Conditions: Analysis at q₀ for Revenue, Cost, and Profit
  • All three conditions discussed in previous conditions are satisfied at output level q₀​, affirming q₀​ as the profit-maximizing output level for the firm.
  • Revenue, Cost, and Profit Analysis at q₀​: Total Revenue (TR) at q₀​ is represented by the area of rectangle OpAq₀, calculated as Price × Quantity.
  • Total Cost (TC) at q₀​ is represented by the area of rectangle OEBq₀, calculated as the product of short-run average cost and quantity.
  • The profit earned by the firm at q₀​ is equal to the area of the rectangle EpAB, which is the difference between the areas representing TR and TC.