Unit 2: Technology and Incentives notes

Introduction to Technology and Incentives

The Context of Unit 2: The recent history of humanity is marked by a rapid and sustained increase in income and living standards, primarily driven by technological progress. This shift occurred suddenly approximately 200 years ago.
Key Questions:
- How did the technological revolution begin?
- Why did this revolution not occur earlier in human history?
Unit Objective: To utilize economic models to explain the significant growth in real wages and population observed over the last two centuries.

Decision Making and Economic Rents

Model of Decision Making:
- Opportunity Cost: Represented as the value of the next best action that is not taken.
- Reservation Option: The single next best alternative available to a decision-maker.
- Economic Cost: Calculated as the sum of direct costs incurred by taking an action plus the opportunity cost ( $\text{Economic Cost} = \text{Direct Costs} + \text{Opportunity Cost}$ ).
- Economic Rent: The net benefit derived from the chosen option minus the opportunity cost ( $\text{Economic Rent} = \text{Net Benefit} - \text{Opportunity Cost}$ ).
Decision Scenario: Attending a Concert:
- Direct Cost: A ticket costs $25.
- Values: The enjoyment value of the concert is $55.
- Net Benefit of Concert: Calculated as $\$55 - \$25 = \$30$ .
- Reservation Option: The alternative is earning $22 for babysitting.
- Opportunity Cost: $22.
- Total Economic Cost: $\$25 + \$22 = \$47$ .
- Economic Rent of Concert: $\$55 - \$47 = \$8$ .
Innovation Rents and Relative Prices:
- Innovation Rents: A specific form of economic rent involving the extra profits earned by exploiting a new invention. These rents provide the essential incentives for firms and individuals to take action and innovate.
- Relative Prices: The price of one option expressed relative to another, typically shown as a ratio ( $\frac{P_1}{P_2}$ ). These are critical factors in determining economic incentives.

Specialization and Trade

Specialization: The practice of individuals focusing on one or a few tasks within a larger project or goal. This is driven by:
- Learning by doing: Skills improve with repetition.
- Difference in ability: Individuals have innate or acquired strengths in different areas.
- Economies of scale: Larger-scale production can be more efficient.
Absolute vs. Comparative Advantage:
- Absolute Advantage: Being more productive in producing a specific good than another entity.
- Comparative Advantage: Having a lower relative cost (opportunity cost) of producing a good compared to another entity.
Table: Comparative Advantage Examples (100% time spent on one good):
- Greta: $1,250$ apples or $50$ tonnes of wheat.
- Carlos: $1,000$ apples or $20$ tonnes of wheat.
Opportunity Cost Analysis:
- Opportunity Cost of 1 Tonne of Wheat:
  - Greta: $25$ apples.
  - Carlos: $50$ apples.
- Opportunity Cost of 1 Apple:
  - Greta: $0.04$ tonnes of wheat.
  - Carlos: $0.02$ tonnes of wheat.
Self-Sufficiency vs. Specialization and Trade Table:
- In Self-Sufficiency:
  - Greta uses 40% of time for apples and 60% for wheat: Produces/Consumes $500$ apples and $30$ tonnes wheat.
  - Carlos uses 30% of time for apples and 70% for wheat: Produces/Consumes $300$ apples and $14$ tonnes wheat.
- Complete Specialization and Trade:
  - Greta: Total production is $50$ tonnes of wheat and $0$ apples. She sells $15$ tonnes of wheat and buys $600$ apples. Final consumption: $600$ apples and $35$ tonnes wheat.
  - Carlos: Total production is $1,000$ apples and $0$ tonnes of wheat. He sells $600$ apples and buys $15$ tonnes of wheat. Final consumption: $400$ apples and $15$ tonnes wheat.
  - Total Output: Increases from $800$ to $1,000$ apples and from $44$ to $50$ tonnes of wheat through specialization.

Firms, Technology, and Production Choice

Key Definitions:
- Division of Labour: Specialization in production tasks within a firm or across society.
- Production Technology: The process used to convert sets of inputs into sellable outputs.
- Factors of Production: Inputs including raw materials, labour, capital goods, and energy.
- Production Function: The relationship defining how much output is produced for given amounts of inputs.
Fixed-Proportions Technology and Constant Returns to Scale (CRS):
- Variables: Machines ( $M$ ), Workers ( $N$ ), Energy ( $E$ in kWh), Output ( $Y$ in litres).
- Scenario 1: $M=3, N=1, E=80, Y=50$ .
- Scenario 2: $M=6, N=2, E=160, Y=100$ .
- Scenario 3: $M=9, N=3, E=240, Y=150$ .
- Scenario 4: $M=12, N=4, E=320, Y=200$ .
Technology Choice and Profit Maximization:
- Firms aim to maximize profit by minimizing cost.
- Cost Formula: $\text{Cost} = (\text{wage} \times \text{workers}) + (\text{price of coal} \times \text{number of tons})$ .
- Example Variables: Wage ( $w$ ) = $£10$ , Price of coal ( $p$ ) = $£20$ .
Isocost Lines:
- Isocost lines join all combinations of workers and coal that result in the same total cost.
- Slope of Isocost Lines: Calculated as $-w/p$ .
- The slope changes based on relative prices.

The Industrial Revolution in Britain

Rationale for the British Industrial Revolution:
- Labour was expensive relative to energy in Britain.
- English wages were significantly higher than in other regions.
- Coal was cheaper in Britain due to local abundance.
- In the 18th century, wages relative to energy and capital goods rose compared to earlier times and other countries.
Comparing Isocosts (1600s vs. 1700s):
- 1600s (Isocost HJ): Firms used "Technology B." At these relative prices, there was no incentive to develop "Technology A" because Technology A sat outside the line HJ (meaning it was more expensive).
- 1700s (Isocost FG): The isocost line became steeper as the relative price of labour to coal increased. Now, Technology A was lower cost than Technology B (B lies outside line FG).
Spread of Technology:
- Technological progress continued, leading to wage growth and falling energy costs (shifting costs from $£80$ lines toward $£40$ lines).

Escaping the Malthusian Trap

Historical Timeline (UK):
- 1764: Hargreaves' spinning jenny.
- 1781: Watt's steam engine.
- 1833: Factory Act (prohibits child labour under 9 years).
- 1844: Factory Act (children restricted to 6.5 hours a day).
- 1847: Ten Hours Act (limits hours for women and children).
- 1918: Voting rights for all males.
- 1928: Universal suffrage.
Economic Mechanism of the Industrial Revolution:
- The Industrial Revolution introduces more and better capital goods per worker.
- Average output per worker rises; however, some workers are displaced.
- Initial Stage: Worker power falls, wages remain low, and factory production expands due to high profits.
- Development Stage: Demand for labour rises. Extension of the right to vote and labour market regulations (restrictions on hours and child labour) cause labour supply to fall.
- Outcome: Power of workers rises, leading to rising wages and escaping the stagnation of the Malthusian trap.

Economic Models and Building Strategy

Model-Building Process:
1. Define a specific question.
2. Create a simplified description of conditions for human action.
3. Describe the determinants of those actions.
4. Determine the mutual interaction of actions.
5. Identify the outcome (often an equilibrium).
6. Study variable changes (comparative statics) for further insight.
Key Model Concepts:
- Equilibrium: A self-perpetuating situation with no tendency to change unless acted upon by an external force.
- Endogenous variables: Values determined by internal model relationships.
- Exogenous variables: Values determined outside the model.
- Ceteris paribus: The practice of holding other variables constant.
The Malthusian Model Logic:
- Improved farming technology initially raises average output per farmer.
- Rising living standards lead to population growth.
- Population growth leads to less land per farmer.
- Average output per farmer falls until living standards return to the original "subsistence" level, albeit with a larger population.

Capitalism and Climate Change

The Transition: The Industrial Revolution shifted economies from photosynthesis-based energy (constrained by land) to fossil-fuel-based energy. This caused an unprecedented "hockey-stick" growth in per capita income but also an unprecedented rise in Earth's surface temperature.
The Problem: Ongoing poverty reduction cannot rely on the same "coal-plus-capitalism" model used historically.
The Science of CO2:
- Drivers: Burning carbon produces $CO_2$ emissions.
- Atmospheric Stock: The stock of atmospheric $CO_2$ is the primary cause of climate change.
- Mitigation: Natural decay of $CO_2$ and absorption by forests reduces the stock.
Unsustainable Paths (2018 Data):
- High GDP per capita is strongly correlated with high $CO_2$ emissions per capita.
- Countries with exceptionally high emissions: Bahrain, UAE, Australia, USA, Canada, Kazakhstan.
- Countries on the line of best fit: China, South Africa, Germany, UK, France, India.
Technological Hope:
- Solar PV Module Costs: Dramatic decline from over $128$ 2019 US dollars in 1976 to approximately $0.25$ in 2019.
- Price of Electricity ($/MWh) 2009 vs 2019:
  - Solar photovoltaic: fell from $\$359$ to $\$40$ .
  - Onshore wind: fell from $\$135$ to $\$41$ .
  - Coal: remained stagnant (approx. $\$111$ to $\$109$ ).
  - Nuclear: rose from $\$123$ to $\$155$ .
- Decoupling: Recent data shows GDP per capita rising while domestic and consumption-based energy use per capita remains flat or declines (since 1995).