Production, Cost, Revenue, and Profit Maximization Concepts

Posted on Nov 28, 2025 in Economics

Production and Cost Analysis

Short-Run Production Concepts

Total (Physical) Product (TPP)

  • Definition: The total amount of output obtained from a given amount of input.
  • Graph: Vertical axis: Units of Output; Horizontal axis: Units of Input.

Average (Physical) Product (APP)

  • Definition: The amount of output obtained per unit of input.
  • Formula: Output / Input (APP = TPP / Input).
  • Graph: Vertical axis: Average Product; Horizontal axis: Units of Input.

Marginal (Physical) Product (MPP)

  • Definition: The additional output obtained by using one more unit of input.
  • Formula: ΔOutput / ΔInput (MPP = ΔTPP / ΔInput).
  • Graph: Vertical axis: Marginal Product; Horizontal axis: Units of Input.
  • Diminishing Marginal Product: As input use expands, the marginal product eventually begins to decline.

Short-Run Cost Concepts

Total Cost (TC)

  • Definition: All costs of production (Fixed Costs plus Variable Costs).
  • Formula: TC = FC + VC (Fixed Cost + Variable Cost).
  • Graph: Vertical axis: Total Cost; Horizontal axis: Output.

Fixed Cost (FC)

  • Definition: Costs of production that do not vary with the level of output.
  • Formula: Fixed Cost (FC).
  • Graph: Vertical axis: Fixed Cost; Horizontal axis: Output.

Sunk Cost (SC)

  • Definition: Costs of resources that have already been incurred and will not change regardless of any current or future decisions.

Variable Cost (VC)

  • Definition: Costs of production that vary with the level of output.
  • Formula: Variable Cost (VC).
  • Graph: Vertical axis: Variable Cost; Horizontal axis: Output.

Average Total Cost (AC or ATC)

  • Definition: Costs per unit of output.
  • Formula: AC = TC / Q (Total Cost / Output).
  • Graph: Vertical axis: Average Cost; Horizontal axis: Output.

Marginal Cost (MC)

  • Definition: The additional cost incurred by producing one more unit of output.
  • Formula: ΔTotal Cost / ΔOutput (MC = ΔTC / ΔQ).
  • Graph: Vertical axis: Marginal Cost; Horizontal axis: Output.

Related Average Costs

  • Average Variable Cost (AVC):
    • Formula: AVC = VC / Q (Variable Cost / Output).
  • Average Fixed Cost (AFC):
    • Formula: AFC = FC / Q (Fixed Cost / Output).

Long-Run Production and Cost Concepts

Returns to Scale (Production)

  • Decreasing Returns to Scale: If we double all inputs, output less than doubles.
  • Constant Returns to Scale: If we double all inputs, output exactly doubles.
  • Increasing Returns to Scale: If we double all inputs, output more than doubles.

Industry Cost Structures

  • Increasing Cost Industry: As industry output expands, the average cost of production rises.
  • Constant Cost Industry: As industry output expands, the average cost of production remains constant.
  • Decreasing Cost Industry: As industry output expands, the average cost of production falls.

Revenue and Profit Relationships

Total Revenue (TR)

  • Definition: The relationship between sales revenue and output.
  • Formula: TR = P × Q (Price multiplied by Quantity).
  • Graph: Vertical axis: Revenue; Horizontal axis: Output.

Average Revenue (AR)

  • Definition: The amount of revenue obtained per unit of output.
  • Formula: AR = TR / Q (Total Revenue / Output).
  • Graph: Vertical axis: Average Revenue; Horizontal axis: Output.

Marginal Revenue (MR)

  • Definition: The additional revenue obtained from selling one more unit of output.
  • Formula: ΔRevenue / ΔOutput (MR = ΔTR / ΔQ).
  • Graph: Vertical axis: Marginal Revenue; Horizontal axis: Output.

Total Profit (TP)

  • Definition: The relationship between profit and output.
  • Formula: TP = TR – TC (Total Revenue minus Total Cost).
  • Graph: Vertical axis: Profit; Horizontal axis: Output.

Marginal Profit (MP)

  • Definition: The additional profit obtained by producing and selling one more unit of output.
  • Formula 1: ΔProfit / ΔOutput (MP = ΔP / ΔQ).
  • Formula 2 (Alternative): MP = MR – MC.
  • Graph: Vertical axis: Marginal Profit; Horizontal axis: Output.

Logic of Profit Maximization

Implications of the Decision to Raise Output

  1. Profit is defined as Revenue minus Cost (Profit = R – C).
  2. Revenue depends on demand.
  3. Cost depends on input use and input costs.
  4. Marginal Revenue (MR) is the additional revenue resulting from the decision to increase output.
  5. Marginal Cost (MC) is the additional cost resulting from the decision to increase output.
  6. Marginal Profit (MP), calculated as MP = MR – MC, is the additional profit resulting from the decision.
  7. If MP > 0, the decision to raise output will increase total profit.
  8. If MP < 0, the decision to raise output will decrease total profit.
  9. The maximum profit choice occurs where MR = MC (or MP = 0).
  10. Since Fixed Costs (FC) do not affect Marginal Cost (MC), FC does not affect the optimal output choice.

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Inputs and Optimal Choice

Optimal Input Choice Rules for a Profit Maximizer

Short Run Input Rule

MRPA = MRX × MPA = PA

Long Run Input Rule

MRPA / PA = MRPB / PB