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Economics 200: Technology and Incentives

Production Functions and Technology

  • Production Function: Relationship showing output based on input quantity.

    • Output (Y) depends on inputs:

    • Machines (M)

    • Labor (N)

    • Energy (E)

    • Formula: Y = f(M, N, E)

Factors of Production

  • Input categories include machinery, manpower, and energy sources needed for production.

Fixed-Proportions Technology

  • Example of fixed-proportions technology showing outputs with fixed input ratios:

    • 1 machine + 4 workers + 80 kWh energy = 500 yards of cloth

    • Doubling inputs results in doubling output (constant returns to scale).

Constant Returns to Scale

  • With fixed-proportions technology:

    • Input combinations produce proportional outputs consistently.

    • Examples:

    • 1M + 4N + 80E
      ightarrow 500Y

    • 2M + 8N + 160E
      ightarrow 1000Y

Introduction of New Technology

  • When a new technology is available (1:1 input ratio):

    • Technology exhibits potential for different combinations leading to equal output with fewer inputs.

  • Example output changes with the new ratio:

    • Inputs:

    • 4M + 4N
      ightarrow 500Y

    • More flexibility in input use can lead to cost savings.

Cost Considerations

  • Firms consider cost when adopting technology.

    • Cost equation:

    • ext{Cost} = ext{Wage} imes N + ext{Price} imes M

  • Example:

    • Cost A: 20 imes 4 + 10 imes 4 = 120

    • Cost E: 20 imes 5 + 10 imes 3 = 130

  • Iso-cost lines join input combinations at the same cost across technologies.

Relative Price Changes

  • Changes in relative prices (wages vs. machine costs) impact technology choice.

  • Example with wage drop to $5:

    • New Cost A: 5 imes 4 + 10 imes 4 = 60

    • New Cost E: 5 imes 5 + 10 imes 3 = 55

Innovation Rents

  • Additional profits earned from adopting advanced technologies can be significant.

  • Change in profit example:

    • Transitioning from technology A to E shifts costs from $60 to $55; hence innovation rent = 60 - 55 = 5.

Average Product of Labor (APL)

  • APL measures efficiency:

    • ext{APL} = rac{ ext{Output}}{ ext{Number of Workers}}

  • Example calculation shows improvements using newer technologies:

    • Each combination reflects greater productivity as technology evolves.

Choosing Technology

  • Firms evaluate different technology inputs based on maximum efficiency and cost-effectiveness.

    • Example inputs needed to produce 1000 yards of cloth for chosen technologies at specific costs.

    • Choice determined by total cost calculations:

    • Example A: 3 imes 125 + 7 imes 100 = 1075

    • Example B: 2 imes 125 + 5 imes 100 = 750 (cheapest option).

Model Building in Economics

Steps

  1. Define clear questions.

  2. Simplify conditions for decision-making.

  3. Analyze actions and interactions.

  4. Determine equilibrium outcomes.

  5. Adjust parameters for insights.

Economic Equilibrium

  • Equilibrium: A self-sustaining situation without changing forces unless acted upon by external changes.

    • Endogenous Variables: Influenced by the model's structure.

    • Exogenous Variables: Independent of the inherent model structure.

Historical Context

  • Malthusian Model: Living standards remain static without external changes; enduring technological advancements did not elevate living conditions.

    • Industrial Revolution in Britain:

    • High labor prices and affordable energy shaped production and technological adoption.

    • Shifts in relative costs spurred the adoption of different technological approaches over time.

Impact of the Industrial Revolution

  • Resulted in better capital allocation per worker and increased productivity over time.

  • Economic dynamics led to rising wages and the evolution of labor market regulations, impacting labor supply and workers' bargaining power.