Chapter 8 - Producers in the Long Run: Cost, Efficiency, and Technological Change

Chapter 8: Producers in the Long Run

8.1 The Long Run: No Fixed Factors

In the long run, all inputs used by firms are variable, allowing for greater flexibility in production decisions. Firms aim to achieve both technical efficiency and economic efficiency in their operations.

• Technical efficiency: Achieved when a firm produces the maximum output from a given set of physical inputs.

• Economic efficiency: Achieved when a firm produces a given output at the lowest possible cost, considering the value (prices) of inputs.

Profit Maximization and Cost Minimization

To maximize profits, firms must choose input combinations that minimize total costs for any level of output. This involves equating the marginal product per dollar spent across all inputs.

• Let K = capital, L = labour, pK = price of capital, pL = price of labour.

• Cost is minimized when:

$\frac{MP_K}{p_K} = \frac{MP_L}{p_L}$

or equivalently,

$\frac{MP_K}{MP_L} = \frac{p_K}{p_L}$

• Principle of substitution: Firms adjust the quantities of factors in response to changes in their relative prices, using more of the cheaper factor and less of the more expensive one.

Example Calculation

Suppose:

$\frac{MP_K}{p_K} = \frac{40}{10} = 4$

$\frac{MP_L}{p_L} = \frac{20}{2} = 10$

• The last dollar spent on capital adds 4 units to output.

• The last dollar spent on labour adds 10 units to output.

• To minimize cost, the firm should use more labour and less capital.

Examples of Substitution in Practice

• Methods of producing the same product differ across countries due to factor price differences.

• Airplanes may use more fuel-efficient technologies where fuel is expensive.

• The use of electricity varies across countries depending on its relative cost.

Long-Run Cost Curves

When all factors of production are variable, firms seek the least-cost method for any output level. The long-run average cost (LRAC) curve shows the minimum achievable cost for each output level, given technology and factor prices.

• The LRAC curve is typically U-shaped.

• It separates attainable and unattainable cost levels.

• Unlike the short run, there is only one LRAC curve (not separate AVC, AFC, and ATC curves).

Table: LRAC Curve and Returns to Scale

LRAC Shape	Returns to Scale	Explanation
Falling LRAC	Increasing returns to scale	Output increases more than proportionally to inputs; often due to specialization.
Constant LRAC	Constant returns to scale	Output increases exactly in proportion to inputs.
Rising LRAC	Decreasing returns to scale	Output increases less than proportionally to inputs; often due to management difficulties.

Returns to Scale

• Increasing returns to scale: % change in output > % change in inputs

• Decreasing returns to scale: % change in output < % change in inputs

• Constant returns to scale: % change in output = % change in inputs

Minimum Efficient Scale

• The smallest level of output at which LRAC reaches its minimum.

Important Note

• Decreasing returns to scale (long run) is not the same as diminishing marginal returns (short run).

The Relationship Between LRAC and SRATC Curves

The short-run average total cost (SRATC) curve cannot fall below the LRAC curve. Each SRATC curve is tangent to the LRAC curve at the output level where the quantity of the fixed factor is optimal.

Shifts in the LRAC Curve

Changes in technology and factor prices cause the LRAC curve to shift.

• A rise in factor prices shifts the LRAC curve upward (higher costs).

• A fall in factor prices or technological improvement shifts the LRAC curve downward (lower costs).

8.2 The Very Long Run: Changes in Technology

Technological change encompasses all changes in the available techniques of production. Economists measure technological change using the concept of productivity.

• Productivity growth, driven by technological change, is the primary cause of rising material living standards over time.

Causes of Productivity Growth

• Growth in capital per worker: Investment in new machinery and equipment increases output per worker.

• Growth in quality of workforce: Better-trained or more skilled workers can produce more.

• Growth in technological knowledge: Invention of new products and improved production methods.

Types of Technological Change

• Process innovation: Introduction of new techniques for producing existing products.

• New inputs: Use of new materials or resources in production.

• Product innovation: Creation of new products.

Firms' Choices in the Very Long Run

When input prices rise, firms can respond in two main ways:

• Substituting away (Long Run): Adjusting production techniques within existing technology to use less of the expensive input.

• Innovating away (Very Long Run): Developing new production techniques or products to reduce reliance on the expensive input.

These choices have different implications for productivity and competitiveness.

Examples of Firm Responses to Rising Labour Costs

• Reallocating production to countries with lower labour costs (e.g., Mexico, Southeast Asia).

• Reducing labour use and increasing capital equipment.

• Investing in new production techniques (innovation).

While the first two are long-run choices, the third is a very long-run choice that can be riskier but may yield greater competitive advantages.

Additional info: The notes above expand on the textbook slides by providing definitions, formulas, and examples for key microeconomic concepts relevant to producers in the long run, including cost minimization, efficiency, returns to scale, and technological change.