Week 10 - Production/Cost Theory

Learning Objectives

• Understanding the Firm's Production Function:

  • Importance of the production function in linking inputs to outputs.

  • Relationship between quantity of inputs and quantity of output.

• Diminishing Marginal Returns:

  • Explanation of why production often sees diminishing returns with additional inputs.

• Types of Costs:

  • Overview of various costs faced by firms, including how they inform marginal and average cost curves.

• Short Run vs Long Run Costs:

  • Analysis of the differences in costs a firm may experience in the short run compared to the long run.

Production

DEFN: The process of turning inputs into outputs

• Production Process:

  • Defined as the process of transforming inputs into outputs.

  • The cost structure of a firm is contingent upon the nature of the production process.

Production Function:

• The production function is the relationship between the quantity of inputs the firm uses and the quantity of outputs the firm produces

• Fixed Input:

• An input with a fixed quantity over a certain period, which cannot be altered in the short run.

• Variable Input:

• An input whose quantity can vary at any time, providing flexibility in production.

Time Periods in Production

• Long Run vs Short Run:

  • Long Run:

  • All inputs can be varied, allowing for full flexibility in production methods.

  • Short Run:

  • One or more inputs are fixed, determining a firm's capacity to respond to changes in output.

  • The Total Product Curve illustrates how output relies on variable input quantity with a constant fixed input.

Marginal Product

• Marginal Product (MP):

  • It is the change in output resulting from a one-unit increase in the amount of labour input
    MP = \frac{\Delta Q}{\Delta L}

  • Initially rises as more workers are hired, but will decrease after a certain point due to diminishing returns.

  • Example:

  • The marginal product may decline if, for instance, adding field workers leads to overcrowding, reducing their productivity relative to previous workers.

Total Product and Marginal Product Relationships

• The connection between inputs and outputs is characterized by a non-constant relationship; the marginal product of labor fluctuates along the production function, as shown in numerical examples involving labor and output of wheat (bushels).

Analyzing Production Function and Total Product Curve

• Worker Output Example:

  • Contributions from workers in basket production indicate differing marginal products. For instance, one worker making 14 baskets, two producing 34, three yielding 45, and a fourth achieving only 50 baskets indicates a decline in marginal productivity.

• Total and Marginal Product Curves:

  • Adding land (fixed input) enables each worker to yield higher outputs, consequently shifting the total product curve upwards.

Transitioning from Production Function to Cost Curves

• Fixed and Variable Costs:

  • Fixed Costs (FC):

  • Costs remaining unchanged irrespective of output level, associated with fixed inputs.

  • Variable Costs (VC):

  • Costs that vary based on the output levels, relating to variable inputs.

• Total Cost (TC):

  • Defined as:
    TC = FC + VC

  • The total cost curve becomes steeper with increased output, primarily due to diminishing returns.

Cost Analysis

• Marginal Cost (MC):

  • Represents the additional cost incurred from producing one more unit, given by the formula:
    MC = \frac{\Delta TC}{\Delta Q}

  • Highlights the relationship between increased production outputs and cost.

• Example with Salsa Production:

  • Demonstrating fixed and variable costs in the context of salsa production, incorporating total cost and marginal cost calculations based on quantity produced.

Cost Curve Dynamics

• Total and Marginal Cost Curves:

  • The upward slope of the marginal cost curve is attributed to diminishing returns when output increases.

  • Analysis of average costs shows layered impacts from fixed and variable cost changes against output variability.

Summary of Cost Curve Interaction

• Marginal cost intersects average total cost (ATC) at its minimum point, illustrating fundamental relationships between different cost metrics. Namely:

  1. Marginal cost slopes upwards due to diminishing returns.

  2. Average variable cost also trends upwards but at a gentler slope.

  3. Average fixed cost curves downwards due to the spreading effect on output.

Long Run vs Short Run Costs

• Long Run Implications:

  • In the long run, all input factors are variable, allowing firms to adjust fixed costs flexibly based on expected output levels.

  • The trade-off between higher fixed vs lower variable costs is a critical factor in overall cost strategy.

Long-Run Average Total Cost Curve

• Demonstrates minimal average total cost selections for varying output levels, essential for determining cost efficiency.

Returns to Scale

• Increasing Returns to Scale (Economies of Scale):

  • Occur when long-run average total cost diminishes with increased output.

• Decreasing Returns to Scale (Diseconomies of Scale):

  • Associated with rising long-run average total costs as production escalates.

• Constant Returns to Scale:

  • Exhibited when long-run average total costs remain consistent despite output changes.

Summary points to note

1. The production function establishes how inputs translate into outputs, with fixed inputs in the short run and all inputs variable in the long run.

2. Diminishing returns to input occur when the incremental output (marginal product) starts to decrease due to input saturation.

3. Total costs integrate fixed and variable costs, highlighting dependencies on output levels.

4. Analysis of average and marginal costs reveals complex relationships in cost management, especially related to production scale variances.

5. Long-run adjustments to fixed inputs can optimize average total costs across output levels, contingent on production technology.