Chapter 6: Production – The Theory of the Firm

Introduction

This chapter explores the theory of the firm, focusing on how firms make cost-minimizing production decisions and how their resulting cost varies with output. The analysis covers the nature of production, input choices, and the relationship between inputs and outputs.

6.1 Firms and Their Production Decisions

Why Do Firms Exist?

• Coordination: Firms provide a means of coordination that would be difficult if workers operated independently.

• Reduction of Transaction Costs: Firms eliminate the need for each worker to negotiate every task and wage individually.

• Managerial Direction: Managers direct the production of salaried workers, specifying tasks and schedules, simplifying compensation to regular salaries.

The Technology of Production

• Factors of Production: Inputs used in the production process, typically categorized as labor, materials, and capital.

• Labor: Includes both skilled (e.g., engineers, carpenters) and unskilled workers (e.g., agricultural workers), as well as managerial and entrepreneurial efforts.

• Materials: Raw inputs such as steel, plastics, electricity, and water, which are transformed into final products.

• Capital: Land, buildings, machinery, equipment, and inventories used in production.

The Production Function

• Definition: The production function shows the highest output a firm can produce for every specified combination of inputs.

• General Form: , where is output, is capital, and is labor.

• Efficiency: Production functions describe what is technically feasible when the firm operates efficiently.

The Short Run vs. The Long Run

• Short Run: Period in which at least one input (e.g., capital) is fixed.

• Long Run: Period sufficient to make all inputs variable.

• Fixed Input: An input whose quantity cannot be changed in the short run.

6.2 Production with One Variable Input (Labor)

Average and Marginal Products

• Average Product (AP): Output per unit of a particular input.

• Marginal Product (MP): Additional output produced as an input is increased by one unit.

• The marginal product of labor depends on the amount of capital used.

Table 6.1: Production with One Variable Input

The Slopes of the Product Curve

• The total product curve shows the output produced for different amounts of labor input.

• The average product at a point is the slope of the line from the origin to that point on the total product curve.

• The marginal product at a point is the slope of the tangent to the total product curve at that point.

• When the marginal product is above the average product, the average product is rising; when below, the average product is falling.

The Law of Diminishing Marginal Returns

• Definition: As the use of an input increases with other inputs fixed, the resulting additions to output will eventually decrease.

• Even with technological improvements, most production processes exhibit diminishing returns to labor.

Labor Productivity and the Standard of Living

• Labor Productivity: Average product of labor for an entire industry or the economy as a whole.

• Long-run increases in consumption depend on increases in total output, which are closely tied to labor productivity.

• Stock of Capital: Total amount of capital available for use in production.

• Technological Change: Development of new technologies allowing factors of production to be used more efficiently.

Table 6.3: Labor Productivity in Developed Countries

6.3 Production with Two Variable Inputs

Isoquants

• Isoquant: Curve showing all possible combinations of inputs that yield the same output.

• Isoquant Map: Graph combining a number of isoquants, used to describe a production function.

Table 6.4: Production with Two Variable Inputs

Input Flexibility and Diminishing Marginal Returns

• Isoquants show the flexibility firms have in substituting one input for another to produce a given output.

• As one input increases while the other is held constant, the isoquant becomes steeper or flatter, reflecting diminishing marginal returns to each input.

Marginal Rate of Technical Substitution (MRTS)

• Definition: The amount by which the quantity of one input can be reduced when one extra unit of another input is used, keeping output constant.

• Formula: (for a fixed level of )

• Alternatively, using marginal products: So,

Special Cases of Production Functions

• Perfect Substitutes: Isoquants are straight lines; MRTS is constant. Inputs can be substituted at a constant rate.

• Fixed-Proportions (Leontief) Production Function: Isoquants are L-shaped; only one combination of labor and capital can be used to produce each output level. Methods of production are limited.

6.4 Returns to Scale

Definitions

• Returns to Scale: The rate at which output increases as inputs are increased proportionately.

• Increasing Returns to Scale: Output more than doubles when all inputs are doubled.

• Constant Returns to Scale: Output exactly doubles when all inputs are doubled.

• Decreasing Returns to Scale: Output less than doubles when all inputs are doubled.

Describing Returns to Scale

• Returns to scale may not be uniform across all output levels; a firm may experience increasing returns at low output, constant returns at moderate output, and decreasing returns at high output.

• Returns to scale vary across industries; larger returns to scale often lead to larger firm sizes.

Example: Returns to Scale in the Carpet Industry

• Carpet production is capital intensive; larger plants have achieved greater proportional increases in output due to innovation and efficient machinery.

• Smaller manufacturers often find that small changes in scale have little effect on output.

• The industry can be characterized by constant returns to scale for small plants and increasing returns for larger plants.