Chapter 14: The Costs of Production

Chapter 14: The Costs of Production

Key Questions

• What is a production function?
• What is marginal product? How are they related?
• What are the various costs? How are they related to each other and to output?
• How are costs different in the short run vs. the long run?
• What are “economies of scale”?

Total Revenue, Total Cost, Profit Assumption

• Objective of a Firm:

  • The primary goal of a firm is to maximize profit.

• Profit Calculation:

  • Profit = Total Revenue - Total Cost

• Total Revenue (TR):

  • Formula: TR = P imes Q
  • Definition: The amount a firm receives from the sale of its output where (P) is price and (Q) is quantity sold.

• Total Cost (TC):

  • Formula: TC = Explicit Cost + Implicit Cost
  • Definition: The market value of the inputs that a firm uses in production.

Costs: Explicit vs. Implicit

• Definition of Cost:

  • The cost of something is what you give up to get it.

• Explicit Costs:

  • Definition: Costs that require an outlay of money.
  • Example: Paying wages to workers.

• Implicit Costs (Opportunity Cost):

  • Definition: Costs that do not require a cash outlay.
  • Example: The opportunity cost of the owner’s time.

• Example Scenario:

  • To start a business, you need $100,000. If the interest rate is 5%:
  • Using Savings:
    • Implicit cost = $5,000 (foregone interest).
  • Borrowing:
    • Explicit cost = $5,000 (interest on loan).

Economic Profit vs. Accounting Profit

• Accounting Profit:

  • Definition: Total revenue minus total explicit costs.

• Economic Profit:

  • Definition: Total revenue minus total costs (including both explicit and implicit costs).

• Comparison Example:

  • Situation: Rent on office space has increased by $500/month.
  • Rent Office:
    • Accounting Profit decreases, Economic Profit decreases.
  • Own Office:
    • Accounting Profit remains the same, Economic Profit decreases.

Economists vs. Accountants

Economic Perspective on Firms

• Views a firm's profits in terms of economic profit, which includes implicit costs.

Accounting Perspective on Firms

• Focuses on accounting profit that only considers explicit costs.

The Production Function

• Definition:

  • The relationship between the quantity of inputs (e.g., workers) and the quantity of output (e.g., cookies produced).

• Marginal Product (MP):

  • Definition: The increase in output that arises from an additional unit of input.
  • Principal: Rational people think at the margin.

• Marginal Product of Labor (MPL):

  • Formula: MPL = \frac{\Delta Q}{\Delta L}
  • Explanation: Change in Output per Change in Labor.

Total & Marginal Product

• Example Table:
  • Number of Workers (L): 0 to 5
  • Corresponding Output in Bushels of Wheat (Q): 0, 1000, 1800, 2400, 2800, 3000
  • Change in Output (AQ) declines as more workers are added.

Importance of MPL

• Hiring an Extra Worker:
  • Marginal Benefit (MB): Output rises by MPL.
  • Marginal Cost (MC): Wage paid to the worker.
  • Decision Rule:
  • If MPL > w , then hire the worker.
  • If MPL < w , then do not hire.

Diminishing Marginal Product

• Definition:

  • Marginal product of an input declines as the quantity of the input increases.
  • Graphical interpretation: The slope of the production function decreases.

• Reason for Diminishing MPL:

  • Adding more workers results in the average worker having less fixed input to work with, leading to decreased productivity.
  • Fixed inputs include land, equipment, machines, etc.

The Costs

• Total Cost Function:
  • Definition: Relationship between quantity produced and total costs.
  • Formula: TC = FC + VC
  • Fixed Costs (FC):
    • Costs that do not vary with output; e.g., equipment, loans, rent.
  • Variable Costs (VC):
    • Costs that vary with output; e.g., materials, wages.

Marginal Cost (MC)

• Formula: MC = \frac{\Delta TC}{\Delta Q}
• Definition: The increase in total cost arising from producing an extra unit.
• Importance of MC:
  • To determine profit maximization:
  • If MC < MB , produce more.
  • If MC > MB , produce less.

Total and Marginal Cost Curve

• Analysis of cost levels at various quantities of wheat produced, indicating changes in total and marginal costs across output levels.

Average Total Cost (ATC)

• U-shaped Average Total Cost Curve:

  • Formula: ATC = AFC + AVC
  • Average Fixed Cost (AFC): Always decreases as output increases.
  • Average Variable Cost (AVC): Typically increases as output increases due to diminishing marginal product.

• Relationship Between MC and ATC:

  • The marginal-cost curve intersects the average-total-cost curve at its minimum point.
  • If MC < ATC , average total cost is falling.
  • If MC > ATC , average total cost is rising.

Costs in Short Run and Long Run

• Short Run:

  • Some inputs are fixed (e.g., factories, land) resulting in fixed costs.

• Long Run:

  • All inputs are variable allowing greater flexibility.
  • The long-run average total cost (LRATC) at any quantity is the most efficient mix of inputs.

Economies of Scale

• Definition:
  • Long-run average total cost (ATC) decreases as the quantity of output increases due to increasing specialization among workers.
• Constant Returns to Scale:
  • Long-run average total cost remains constant as output changes.
• Diseconomies of Scale:
  • Long-run average total cost increases as output increases due to management challenges in controlling costs.

Summary of Key Costs Definitions

• Term Definitions:
  • Explicit Costs: Costs requiring an outlay of money by the firm.
  • Implicit Costs: Costs that do not require an outlay of money.
  • Fixed Costs: Costs that do not vary with output levels.
  • Variable Costs: Costs that vary with output levels.
  • Total Cost (TC): Market value of all inputs used in production, where TC = FC + VC .
  • Average Fixed Cost (AFC): AFC = \frac{FC}{Q} .
  • Average Variable Cost (AVC): AVC = \frac{VC}{Q} .
  • Average Total Cost (ATC): ATC = \frac{TC}{Q} .
  • Marginal Cost (MC): MC = \frac{\Delta TC}{\Delta Q} .