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.