BackProducers in the Long Run: Cost Minimization, Long-Run Cost Curves, and Technological Change
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Chapter 8: Producers in the Long Run
8.1 The Long Run: No Fixed Factors
In microeconomics, the long run refers to a period in which all inputs used in production are variable, allowing firms to adjust their production processes fully. This contrasts with the short run, where at least one input is fixed.
Short Run vs. Long Run:
In the short run, at least one factor of production (such as capital) is fixed.
In the long run, all inputs (labour, capital, etc.) are variable, enabling firms to choose among various production methods.
Technical Efficiency:
Occurs when a given number of inputs are combined to maximize output.
Firms strive for technical efficiency but must also consider costs to maximize profits.
Profit Maximization:
Profit maximization requires firms to select the technically efficient option with the lowest cost.
Firms choose the lowest cost combination of labour and capital to maximize profit.
Profit Maximization and Cost Minimization
Cost minimization is a direct implication of profit maximization. Firms aim to produce any given level of output at the lowest possible cost by choosing the optimal combination of inputs.
Cost Minimization:
If a firm can substitute one factor for another to reduce total cost while keeping output constant, it is not minimizing costs.
Mathematical Condition for Cost Minimization:
Let K = capital, L = labour, pK = price of capital, pL = price of labour, MPK = marginal product of capital, MPL = marginal product of labour.
The necessary condition for cost minimization is: or equivalently,
Factor Substitution:
If the ratio of marginal product to price is not equal for all factors, firms can substitute between inputs to reduce costs.
Profit-maximizing firms adjust their production methods in response to changes in factor prices.
Principle of Substitution:
When relative prices of inputs change, firms use more of the cheaper input and less of the more expensive input.
Long-Run Cost Curves
Long-run cost curves illustrate the lowest possible cost of producing each level of output when all inputs are variable. The most important of these is the Long-Run Average Cost (LRAC) curve.
Long-Run Average Cost (LRAC) Curve:
Shows the lowest possible cost per unit of output for each output level, given variable inputs.
Represents the boundary between attainable and unattainable cost levels, given technology and input prices.
In the long run, there is only one LRAC curve for a given set of input prices.
Figure: Saucer-Shaped LRAC Curve
The LRAC curve typically has a 'saucer' shape, reflecting different returns to scale as output increases.
Economies of Scale:
Over the range from zero to QM, LRAC is falling.
Economies of scale refer to reductions in LRAC as the scale of operations expands.
Increasing Returns:
Output increases more than proportionally to inputs.
Minimum Efficient Scale:
The smallest output at which LRAC reaches its minimum.
All available economies of scale are realized at this point.
Constant Returns:
Output increases in direct proportion to inputs.
Decreasing Returns and Diseconomies of Scale:
Beyond QM, output increases less than proportionally to inputs.
Diseconomies of scale occur when LRAC rises as output increases.
Table: Returns to Scale and Cost Behavior
Output Range | Returns to Scale | LRAC Behavior |
|---|---|---|
0 to QM | Increasing Returns | LRAC Falling (Economies of Scale) |
QM | Constant Returns | LRAC Minimum |
Above QM | Decreasing Returns | LRAC Rising (Diseconomies of Scale) |
The Relationship Between LRAC and SRATC Curves
The LRAC curve represents the lowest attainable cost for each output level when all inputs are variable, while the Short-Run Average Total Cost (SRATC) curve shows the lowest cost when some inputs are fixed.
Key Relationships:
No SRATC curve can fall below the LRAC curve.
Each SRATC curve is tangent to the LRAC curve at the output level where the fixed factor is optimally chosen.
The LRAC curve is the 'lower envelope' of all possible SRATC curves.
Historical Note:
Jacob Viner's mistake was to connect all minimum points of SRATC curves, rather than constructing the lower envelope (the LRAC curve).
8.2 The Very Long Run: Changes in Technology
In the very long run, technological change and resource availability can shift the LRAC curve, affecting firms' cost structures and production possibilities.
Technological Change:
Any change in available production techniques.
Measured by productivity, defined as output per unit of input.
Common measures: output per worker, output per hour of work.
Endogenous Technological Change:
Firms invent and innovate in search of profits, making technological change endogenous to the economic system.
Three Aspects of Technological Change:
New techniques
Improved inputs
New products
Firms' Choices in the Very Long Run:
Faced with rising input prices, firms may substitute away from or innovate away from the input.
Invention and innovation are uncertain and require large potential profits to justify the risks.
Applying Economic Concepts: The Significance of Productivity Growth
Productivity growth is crucial for economic progress and disproves pessimistic predictions about resource constraints.
Historical Context:
Thomas Malthus predicted that population growth would outpace food production, leading to widespread poverty.
These predictions were proven wrong because:
Populations did not expand as quickly as predicted.
Technological advancements increased output and productivity.
Example:
Canadian labour productivity has steadily increased over the past century, as shown by the rising index of output per employed worker.
Additional info: Productivity growth enables higher living standards and economic growth, and is a central focus of long-run economic policy.
