Economics of Cost Minimization Chapter 1

Costs

• Firms aim to produce a given output at the lowest possible cost.
• Production costs change as firms adjust the number and mix of inputs.

Chapter Preview

• The chapter focuses on how firms choose inputs to minimize production costs for a given output level.
• It also examines how production costs change when a firm adjusts the inputs used.

Overview

• Basic cost concepts are covered.
• Economic profits and cost minimization are discussed.
• Firm's expansion path is examined.
• Cost curves are explained.
• Short-run and long-run considerations are addressed.

Basic Cost Concepts

• Accounting cost: Reflects the actual expenses incurred for inputs (out-of-pocket, depreciation, and other bookkeeping entries).

• Economic cost: Represents the total amount required to keep an input in its present use, considering its value in its next best alternative use.

• Labor costs: Economists and accountants treat labor similarly, with wage payments being explicit current expenses.

• Capital costs: Accountants use historical costs and depreciation rules, while economists view capital costs as sunk costs that cannot be recovered. The implicit cost of capital equals its rental rate.

Economic Profits and Cost Minimization

• Two primary inputs considered: labor (L) and capital (K).
• Both inputs are hired in a perfectly competitive market.
• Total costs (TC) are calculated as wL + rK (w = wage rate, r = rental rate).
• Economic profit (π) is calculated as total revenue minus total costs (π = Total Revenue – Total Costs).
• Firm's economic profit depends on labor and capital hired.

Cost Minimizing Input Choice

• Firms aim to produce at the lowest possible cost.
• This is examined in three ways:
  • MRTS = w/r (Marginal Rate of Technical Substitution equals the input price ratio).
  • Graphical approach: the isoquant tangent to the total cost line.
  • MP₁/w = MPK/r (Marginal Product of labor per dollar equals the Marginal Product of capital per dollar).

Cost Minimizing Input Choice: MRTS = w/r

• Assume a certain output level (q) requires 10 units of capital (K) and 10 units of labor (L).
• Suppose MRTS = 2, w = $1, and r = $1.
• The calculation would indicate that if the MRTS isn't equal to w/r, the firm can lower cost by adjusting inputs.

Cost Minimizing Input Choice: Graphical Approach

• Graphically, the cost-minimizing input combination is where an isoquant is tangent to an isocost line.

Cost Minimizing Input Choice: MP₁/w = MPK/r

• Marginal products (MPL, MPK) divided by their respective prices (w, r) should be equal to minimize costs.
• If MPL/w is greater than MPK/r, the firm can increase profits by substituting labor for capital.

Firm's Expansion Path

• To expand output, firms hire more capital and labor.
• Each output increase requires a cost-minimizing input combination.

Cost Curves

• The link between output and total costs depends on the production characteristics (constant, decreasing, or increasing returns to scale).

Constant Returns to Scale

• As output rises, costs increase proportionally.

Decreasing Returns to Scale

• Costs increase more rapidly than output increases.

Increasing Returns to Scale

• Costs increase less rapidly than output increases.

Optimal Scale

• Initial stages of increasing returns are followed by decreasing returns as output expands.

Average and Marginal Costs

• Average cost (AC) is total cost divided by output (AC = TC/q).
• Marginal cost (MC) is the extra cost of producing one more unit (MC = ΔTC/Δq).
• The relationship between AC and MC is important: MC lies below AC when AC is falling and above AC when AC is rising. MC equals AC at the minimum point of the AC curve.

Average and Marginal Costs: Illustrative Example

• The height of students in a classroom illustrates the relationship between average and marginal phenomena.

Average and Marginal Cost Curves: Constant Returns

• Both marginal and average costs remain constant as output increases.

Average and Marginal Cost Curves: Decreasing Returns

• Both marginal and average costs increase as output increases.

Average and Marginal Cost Curves: Increasing Returns

• Both marginal and average costs decrease as output increases.

Average and Marginal Cost Curves: Optimal Scale

• Cost curves initially fall as output increases, and then start rising.

Also True for Average and Marginal Products

• Illustration of the similar relationship between marginal and average product.

The Short Run and the Long Run

• Short run: A period in which some inputs are fixed.
• Long run: A period in which all inputs can be varied.
• Fixed costs: Costs associated with fixed inputs in the short run.
• Variable costs: Costs associated with inputs that can be varied in the short run.

Input Inflexibility and Cost Minimization

• Firms may not always be able to use the cost-minimizing combination of inputs in the short run due to fixed inputs.

Shifts in Cost Curves

• Input price changes, technological advancement, and economies of scope can affect costs, shifting curve positions.

A Numerical Example

• Example calculation of costs for different output levels with specific fixed and variable inputs (labor and capital)

Recap (Summary Points)

• Cost minimization in the long run involves adjusting long-run input quantities.
• A firm with limited input substitution options would see minimal input changes with small price changes.
• Short-run decisions are constrained by fixed inputs.
• The graphical explanation of cost curves and how their shapes depend on the production process.

This quiz explores the principles of cost minimization for firms regarding their production inputs. It covers basic cost concepts, accounting vs economic costs, and the implications of short-run and long-run choices. Test your understanding of how firms can operate at the lowest possible costs while aiming for maximum efficiency.