L13 The long run

Principles of Microeconomics

Topic 3: Producer Theory

• Focus on the long-run aspects of production and costs in firms.

Aims of the Lecture

• Learn about:

  • Costs in the long run vs. the short run.

  • Firms' decisions in choosing labor and capital for production.

  • Profit maximization in selecting output levels and production methods.

  • Analyze the shape of long-run cost curves.

  • Understand economies of scale and diseconomies of scale.

Key Concepts

• Long-Run Production:

  • All factors are variable; no fixed costs.

  • Firms decide on both the level of output and the mix of labor and capital.

  • A firm will select the least costly combination of inputs to maximize profits.

Topics Covered

1. Long-run average cost curve and economies of scale

2. A model of the long run

3. Profit maximization in the long run

Long-run Costs

• All factors are variable; no fixed production costs.

Assumptions

1. Factor prices are given:

   • Increased factor prices shift cost curves up (Labor price = w; Capital price = r).

2. Technology and factor quality are constant:

   • Improvements in quality lower cost curves.

3. Firm efficiency:

   • Firms optimize their input mix to produce a given output at minimal cost.

Long-Run Average Cost Curve (LRAC)

• Shape includes:

  • Economies of scale: decrease in average costs as output increases.

  • Constant costs: stable average costs with increased production.

  • Diseconomies of scale: increase in average costs as production increases.

Returns to Scale

• Increasing Returns to Scale: Doubling inputs raises output more than double.

• Constant Returns to Scale: Doubling inputs doubles output.

• Decreasing Returns to Scale: Doubling inputs raises output less than double.

Economies and Diseconomies of Scale

• Economies of Scale:

  • Less input required per unit produced leads to lower costs.

  • Examples include:

    • Plant Economies: Specialization in larger plants.

    • Organizational Economies: Reduced duplication of administrative tasks.

    • Financial Economies: Larger firms access better financing rates.

• Diseconomies of Scale:

  • More input is required per unit, increasing costs.

  • Increased complexity in management and communication.

Relationship Between Short and Long-Run Average Costs

• A firm evaluates its cost-effective production levels based on factory size:

  • Cost curves shift as firms expand or add factories (e.g., from SRAC1 to SRAC2).

  • The LRAC represents the lowest average cost across varying output levels.

Isoquants and Isocost Lines

Isoquants

• Represent combinations of labor (L) and capital (K) producing the same output.

• Display substitution properties between labor and capital (downward-sloping).

Isocost Lines

• Represent combinations of labor and capital that yield the same total cost:

  • Equation: TC = rK + wL (where r = price of capital, w = price of labor).

  • Slope indicates the rate at which labor can substitute capital.

Least-Cost Input Combination

• Optimal combination at the tangent point of isoquant and isocost line.

• Firm finds the level of L and K that minimizes costs and maximizes output.

Shut-Down Rule

• In the short run, if price (p) is less than average variable cost (AVC), the firm should shut down.

• Long-run rule: shut down if price < long-run average cost (LRAC).

Profit Maximization in the Long Run

• Profits maximized where marginal revenue (MR) equals long-run marginal cost (LRMC).

• Firms must cover costs while ensuring profitability; requires analyzing MR, LRAC, and AR.

Summary of Key Points

• In the long-run, all production factors are variable.

• Correct mix of inputs minimizes average costs while maximizing output.

• Recognize when a firm should shut down based on profitability indicators.