ch07

Chapter 7: Costs and Cost Minimization

Overview

  • Cost Concepts for Decision Making

  • The Cost-Minimization Problem

  • Comparative Statics Analysis of the Cost-Minimization Problem

  • Short-Run Cost Minimization

  • Minimizing Long-Run Costs Using Lagrange Multipliers

  • Advanced Topics in Cost Minimization

Key Terms

  • Explicit Costs: Costs involving direct monetary outlay.

  • Implicit Costs: Non-monetary costs that do not involve cash outlays.

  • Opportunity Cost: The value of a resource in its best alternative use; focuses only on the best alternative.

  • Economic Costs: Total of explicit and implicit costs.

  • Accounting Costs: Total of only explicit costs.

Sunk Costs

  • Definition: Costs that have already been incurred and cannot be recovered, thus irrelevant to decision-making.

  • Example: Building a factory costs $5M; this cost is a sunk cost when deciding whether to operate or shut it down, not when deciding to build it.

Cost Minimization

  • Cost Minimization Problem: Finding the input combination that minimizes total production costs for a specific output level.

  • Cost Minimizing Firm: A firm aiming to minimize costs for a given output level.

  • Long Run: A period where all input quantities can vary.

  • Short Run: A period when at least one input quantity is fixed.

Long-Run Cost Minimization

  • Goal: Minimize costs while achieving targeted output (Q0).

  • Cost Structure:

    • Total Cost (TC)

    • Wage Rate (w)

    • Quantity of Labor (L)

    • Price per unit of Capital Services (r)

    • Quantity of Capital (K)

Isocost Line

  • Combinations of Labor and Capital: Expresses combinations yielding the same total cost.



  • Example: $1 million total cost; if w = $10/hour and r = $20/hour, the equation becomes:$1 million = $10L + $20K.Solving for K provides K in terms of L.

Cost-Minimization Inputs

  • Output Function: Q = f(L,K)

  • Owner's Problem:

    • Minimize Total Cost: TC = rK + wL

    • Subject to Output Condition: Q0 = f(L,K)

  • Isocost Line Equation: TC = rK + wL or K = TC/r - (w/r)L

Cost-Minimization Condition

  • Tangency Condition: Ensures that the marginal rate of technical substitution is equal to the ratio of input prices (MRTS = -MPL/MPK = -w/r).

Corner Solution

  • Optimal Input Combination: Occurs at point A where only one input (labor) is used if the isocost line is flatter than the isoquant.

Comparative Statics

  • Effect of Pricing on Input Choice:

    • Increase in w leads to decreased labor usage and increased capital usage.

    • Increase in r leads to decreased capital usage and increased labor usage.

Expansion Path**

  • Shows connections between cost-minimizing input combinations as output quantity varies.

  • Normal Inputs: Demand for input increases as output increases.

  • Inferior Inputs: Demand decreases as output increases, leading to a downward sloping expansion path.

Input Demand

  • Describes how the quantity of input varies with the price changes of that input.

  • Labor Demand Curve: Shows how cost-minimizing labor quantity varies with labor cost.

  • Capital Demand Curve: Shows how cost-minimizing capital quantity varies with capital cost.

Short-Run Cost Minimization

  • Total Variable Costs: Sum of expenses on variable inputs (labor, materials) at short-run cost-minimizing input combination.

  • Total Fixed Costs: Costs that do not change with output.

Classifying Costs in the Short Run

  • Cost of Input: Avoidable vs Non-Avoidable Costs.

    • Variable Costs: Change with output (e.g., labor).

    • Fixed Costs: Stable regardless of output.

    • Nonsunk vs Sunk Costs: Nonsunk costs are only incurred upon specific decisions.

More Variable Inputs in the Short Run

  • Short Run Analysis: Usually focuses on fixed vs variable input (capital vs labor).

  • Short Run Demand for Labor: Depends on the level of production.

  • More Variable Inputs: Analyzes multiple inputs similarly to long-run conditions.