CORE Econ Micro

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.title[
# CORE Econ Micro
]
.subtitle[
## <div class="line-block">Technology and incentives</div>
]
.author[
### Guillermo Woo-Mora
]
.date[
### <div class="line-block">Paris Sciences et Lettres<br />
Autumn 2025</div>
]

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# Economic decisions: Opportunity costs, economic rents, and incentives
]

---
## Economic decisions: Opportunity costs, economic rents, and incentives

What happens in the economy is the result of decisions by individuals, firms (or their owners and managers), and governments.

We need to understand how people make decisions, and the factors they take into account when they choose what action to take.

#### Example #1: Concert

$$ 
`\begin{align*}
\text{net benefit of concert} &= \text{enjoyment from attending} - \text{cost of ticket} \\
&= \$55 - \$25 \\
&= \$30
\end{align*}`
$$

#### Example #2: Babysitting

$$
`\begin{align*}
\text{net benefit of babysitting} &= \text{payment received} - \text{cost of effort involved} \\
&= \$40 - \$18 \\
&= \$22
\end{align*}`
$$

---
## Opportunity and Economic costs

Economic decisions often involve choosing between alternative and mutually exclusive courses of action.

By taking an action (concert) you lose the opportunity of taking the next best action (babysitting).

**Opportunity cost**:
What you lose when you choose one action rather than the next best alternative. Also **reservation option**.

Actions have both direct costs and opportunity costs.

The economic cost of an action is the sum of these two components:

$$
\text{economic cost of an action} = \text{direct costs incurred by taking the action} + \text{opportunity cost}
$$

For the concert example:

$$
\text{benefit} = \text{enjoyment of concert} = $55
$$

$$
\text{economic cost} = \text{cost of ticket} + \text{opportunity cost} = $25 + $22 = $47
$$

What to do?

---
## Opportunity and Economic costs

Another way to express the decision rule is:
take the action if the net benefit is greater than the opportunity cost.

For the concert example:

$$
\text{net benefit} = \text{enjoyment of concert} - \text{cost of ticket} = $55 - $25 = $30
$$

$$
\text{opportunity cost} = \text{net benefit from babysitting} = $22
$$

Since the net benefit ($30) is greater than the opportunity cost ($22), you should go to the concert.

**Economic rent**: the difference between the net benefit (monetary or otherwise) that an individual receives from a chosen action, and the net benefit from the next best alternative

---
## Incentives and Relative Prices

Economic rents exist throughout the economy and serve as incentives for people to take action.

For example, potential innovation rents may encourage firms to switch from one technology to another.

Economics focuses on alternatives and choices—people are free to select different actions, and their decisions depend on economic incentives such as potential rewards or penalties.

Typically, owners and managers choose the option that provides the highest profit, but other motivations—such as love, duty, ethics, or a desire for approval—can also influence decisions.

**Relative prices**: the price of one good or service compared to another (usually expressed as a ratio of the two prices).

A key determinant of economic incentives: they reflect the price of one option relative to another and guide decision-making for both firms and consumers.

Example: if goods are significantly cheaper at a supermarket than at a corner shop, and the distance is reasonable, shoppers will likely choose the supermarket.

If all prices rise by the same percentage (say 5%), the relative prices remain the same, and decisions are unlikely to change.

---
.center2[
# Comparative advantage, specialization, and markets
]

---
## Comparative advantage, specialization, and markets

People do not typically produce the full range of goods and services that they use or consume in their daily lives.

We **specialize**:

- People specialize: some producing one good, others producing other goods; some working as welders, others as teachers or architects.

- Firms specialize: particular goods, or in just one part of the production process for a good.

- Countries specialize: Cambodia’s largest exports are gold and knitwear; Singapore specializes in integrated circuits.

Why?

- **Learning by doing**: We acquire skills as we produce things.

- **Difference in ability**: Because of skill, or the characteristics of the natural surroundings (such as soil quality, for example), some people are better at producing certain things than others.

- **Economies of scale**: Producing a large number of units of a good is often more cost-effective than producing a smaller number.

---
## Comparative advantage: Gains from specialization

**Specialization**: each person does just one or a few of the large number of tasks necessary to complete some project or reach some goal.

Counter intuitive: all producers can benefit, even when this means that one producer specializes in a good that another could produce at lower cost.

|               | Production if 100% of time is spent on one good |
|----------------|-------------------------------------------------|
| **Greta**      | 1,250 apples or 50 tons of wheat                |
| **Carlos**     | 1,000 apples or 20 tons of wheat                |

**Absolute advantage**: a situation where a person or country can produce more of a good than another person or country using the same amount of resources or inputs.

`$$\textit{# Apples}_{Greta} = 1,250 > \textit{# Apples}_{Carlos} = 1000$$`

`$$\textit{# Tons of wheat}_{Greta} = 50 > \textit{# Tons of wheat}_{Carlos} = 20$$`

`$\Rightarrow$` Greta has absolute advantage producing both goods

---
## Comparative advantage: Gains from specialization

**Specialization**: each person does just one or a few of the large number of tasks necessary to complete some project or reach some goal.

Counter intuitive: all producers can benefit, even when this means that one producer specializes in a good that another could produce at lower cost.

**Comparative advantage**: when a person or country can produce a good at a *lower opportunity cost* than another person or country.

|               | Opportunity cost of 1 ton of wheat | Opportunity cost of 1 apple |
|----------------|------------------------------------|------------------------------|
| **Greta**      | 1,250/50 = 25 apples                         | 50/1,250 = 0.04 tons of wheat           |
| **Carlos**     | 1,000/20 = 50 apples                         | 20/1,000 = 0.02 tons of wheat           |

`$\Rightarrow$` Carlos has a comparative advantage⁠ in apples because his relative cost of producing apples (that is, relative to wheat) is lower than Greta’s.

---
## Comparative advantage: Gains from specialization

If Carlos and Greta cannot trade with each other, they must each be self-sufficient, consuming exactly what they produce.

- Suppose that Greta chooses to use 40% of her time in apple production, and the rest producing wheat. 
- Similarly Carlos spends 30% of his time producing apples, and 70% producing wheat.

|              |  | **Self-sufficiency** | **Specialization and trade** |     | |
|---|---|---|---|---|
|  | |  | Production | Consumption | Trade |
|  | | (1) | (2) | (3) | (4) |
|           | | | | | |
| **Greta** | Apples | 500 | | | |
|           | Wheat  | 30 | | | |
| **Carlos** | Apples | 300 | | | |
|           | Wheat  | 14 | | | |
|           | | | | | |
| **Total** | Apples | 800 | | | |
|           | Wheat  | 44 | | | | |

---
## Comparative advantage: Gains from specialization

If they were to specialize, each producing only the crop in which they have a comparative advantage:

- Greta would produce 50 tons of wheat
- Carlos would produce 1,000 apples

Suppose that they reach an agreement that both will specialize, and then Greta will sell 15 tons of wheat to Carlos in return for 600 apples.

|              |  | **Self-sufficiency** | **Specialization and trade** |     | |
|---|---|---|---|---|
|  | |  | Production | Consumption | Trade |
|  | | (1) | (2) | (3) | (4) |
|           | | | | | |
| **Greta** | Apples | 500 | 0 | 600 | Buys 600 apples |
|           | Wheat  | 30  | 50 | 35 | Sells 15t wheat |
| **Carlos** | Apples | 300 | 1,000 | 400 | Sells 600 apples |
|           | Wheat  | 14 | 0 | 15 | Buys 15t wheat |
|           | | | | | |
| **Total** | Apples | 800 | 1,000 | 1,000 | |
|           | Wheat  | 44 | 50 | 50 | | |

---
.center2[
# Firms, technology, and production
]

---
## Firms, technology, and production

**Technology**: The description of a process using a set of materials and other inputs, including the work of people and machines, to produce an output.

Having chosen a technology, need to decide on the amount of inputs to employ, which will determine how much output it can produce.

---
## Firms, technology, and production

A labour-intensive technology for producing olive oil.

---
## Firms, technology, and production

A capital-intensive olive technology.

---
## Firms, technology, and production

A **technology can be represented by a production function**⁠: a relationship that tells us how much output it will produce, given the amounts of inputs used.

$$
Y = f(M, N, E)
$$

`$N$` number of workers employed, `$M$` number of machines, and `$E$` amount of energy used per day.

A hypothetical technology for olive oil:

| Number of machines, *M* | Number of workers, *N* | Amount of energy, *E* (kWh) | Output, *Y* (litres) |
|--------------------------|------------------------|------------------------------|----------------------|
| 3                        | 1                      | 80                           | 50                   |
| 6                        | 2                      | 160                          | 100                  |
| 9                        | 3                      | 240                          | 150                  |
| 12                       | 4                      | 320                          | 200                  |

1. **fixed-proportions technology**⁠: for every three machines, one worker, and 80 kWh of energy are needed.
2. **constant returns to scale**⁠:if you double (or halve) the inputs, the amount of output doubles (or halves) accordingly.

---
## Comparing two technologies

`$$f_A(N = 2, E =160) = 100$$`

---
## Comparing two technologies

`$$f_A(N = 2, E =160) = 100 \quad \Rightarrow  \textit{Average product of labour}_A = f_A(N = 2, E =160)/2 = 100/2 = 50$$`

---
## Comparing two technologies

`$$f_A(N = 2, E =160) = 100 \quad \Rightarrow  \textit{Energy–labour ratio}_A = 160/2 = 80$$`

---
## Comparing two technologies

`$$f_B(N = 1, E =400) = 100$$`

---
## Comparing two technologies

`$$f_B(N = 1, E =400) = 100 \quad \Rightarrow  \textit{Average product of labour}_B = f_B(N = 1, E =400)/1 = 100/1 = 100$$`

---
## Comparing two technologies

`$$f_B(N = 1, E =400) = 100 \quad \Rightarrow  \textit{Energy–labour ratio}_B = 400/1 = 400$$`

---
## Comparing two technologies

Which technology should be used?

---
.center2[
# Modelling a dynamic economy: Technology and costs
]

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## Modelling a dynamic economy: Technology and costs

Five different technologies to produce 100 metres of cloth.

Inputs: labour (number of workers) and energy (tons of coal).

| Technology | Number of workers | Coal required (tons) |
|-------------|-------------------|----------------------|
| A           | 1                 | 6                    |
| B           | 4                 | 2                    |
| C           | 3                 | 7                    |
| D           | 5                 | 5                    |
| E           | 10                | 1                    |

---
## Modelling a dynamic economy: Technology and costs

.left-column[
| Tech. | No. of workers | Coal (tons) |
|-------------|-------------------|----------------------|
| A           | 1                 | 6                    |
| B           | 4                 | 2                    |
| C           | 3                 | 7                    |
| D           | 5                 | 5                    |
| E           | 10                | 1                    |

Technology A is the most energy-intensive, using one worker and six tons of coal.

]

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<img src="imgs/figure-02-05-a.png" width="85%" style="display: block; margin: auto;" />
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## Modelling a dynamic economy: Technology and costs

Technology B : it is more labour-intensive than technology A, because the ratio of workers to coal required to produce the given output is higher for B than A.
]

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## Modelling a dynamic economy: Technology and costs

Technology E is the most labour-intensive of the five technologies: it uses ten workers and one ton of coal.

]

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## Modelling a dynamic economy: Technology and costs

Which technology would the firm choose?

---
## Modelling a dynamic economy: Technology and costs

Technology A dominates the C-technology: the same amount of cloth can be produced using A with fewer inputs of labour and energy. This means that, whenever A is available, you would never use C.

---
## Modelling a dynamic economy: Technology and costs

Technology B dominates the D-technology: the same amount of cloth can be produced using B with fewer inputs of labour and energy. Note that B would dominate any other technology that is in the shaded area above and to the right of point B.

---
## Modelling a dynamic economy: Technology and costs

Technology E does not dominate any of the available technologies. None of them are in the area above and to the right of E. Technology E is also not dominated by any other available technology.

---
### How does a firm evaluate the cost of production using different technologies?

Firms aim to maximize their profit,
--
 which means producing cloth at the least possible cost.
 
--

This is why the firms’ choice of technology depends on economic information about relative prices of inputs.

$$ cost = (wage \times workers ) + (\textit{price of a tonne of coal} \times \textit{number of tonnes of coal}) $$

$$ c = (w \times L ) + (p \times R) $$

$$ c = w L + p R $$

--
Then
$$ p R = c - w L $$

$$ R = \frac{c}{p} - \frac{w}{p} L $$
--

** `$R$` =  Isocost lines**: combinations of inputs that give the same cost (slope = relative price of inputs)

** `$- \frac{w}{p}$` **: slope `$\rightarrow$` **relative price of labour**

---

**Suppose that the wage is £10 and the price of coal is £20 per tonne**
--
 `$\rightarrow \textit{Relative price}:  \frac{w}{p} = \frac{10}{20} = .5$`

The total cost of employing 2 workers with 3 tonnes of coal is (2 × 10) + (3 × 20) = £80.

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