1.4 — Ricardian One-Factor Model

# 1.4 — Ricardian One-Factor Model

## ECON 324 • International Trade • Spring 2023

### Ryan Safner Associate Professor of Economics <a href="mailto:safner@hood.edu">safner@hood.edu</a> <a href="https://github.com/ryansafner/tradeS23">ryansafner/tradeS23</a> <a href="https://tradeS23.classes.ryansafner.com"> tradeS23.classes.ryansafner.com</a> 
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# Outline

## [Assumptions of the Ricardian One-Factor Model](#4)
## [Absolute and Comparative Advantages (Autarky)](#14)
## [An Example in Autarky](#20)
## [The Example with International Trade](#39)

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# A Note of Caution and A Judgment Call

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- Feenstra and Taylor dive right into a Ricardian model in Ch. 2 with some advanced features; Ch. 4 is H-O Model
  - A lot of moving parts are thrown at you rather quickly

- In my experience (and from using other textbooks), it's better to build up slowly:
  1. Simplified Ricardian model
  2. Standard "neoclassical model" (not in F&T)
  3. H-O Model

- So if you are reading the textbook, it won't exactly match up to class for 1-2 weeks 😕
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![](../images/tradetextbook.jpg)
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# Assumptions of the Ricardian One-Factor Model

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# Assumptions of the One-Factor Model

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1. Markets (both output and factors) are perfectly competitive
2. “Labor” is homogenous and non-specific
3. Labor is mobile *domestically*, but *not internationally*
4. Production of goods requires only varying amounts of labor as an input
  - The “one factor”
  - The marginal product of labor is constant
5. No barriers to trade or transactions costs
6. Technology is constant within each country
7. Resource endowments are fixed
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![](../images/workers.png)
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# Setting up the Model

- Imagine 2 countries, .blue[Home] and .red[Foreign]

- Each country can produce two goods, .pink[xylophones (x)] and .purple[yams (y)]

- Each country has a fixed total supply of labor
  - `$\color{blue}{L}$` for .blue[Home] and `$\color{red}{L'}$` for .red[Foreign]

- Let:
  - `$\color{magenta}{l_x}$`: amount of labor to make 1 `$\color{magenta}{x}$`
  - `$\color{purple}{l_y}$`: amount of labor to make 1 `$\color{purple}{y}$`
]

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# Setting up the Model: Home

- .blue[Home's] .hi[production set] and total possible allocations of labor within a country is:

`$$l_x x + l_y y \leq L$$`

- To find the .hi[frontier (PPF)], assume Labor Demand (left) and Labor Supply (right) are equal:
`$$l_x x + l_y y = L$$`

]

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# Setting up the Model: Home

`$$l_x x + l_y y = L$$`

- Solve for y to graph

`$$y=\frac{L}{l_y}-\frac{l_x}{l_y}x$$`

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<img src="1.4-slides_files/figure-html/BC-plot0-1.png" width="432" style="display: block; margin: auto;" />
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# Setting up the Model: Home

`$$l_x x + l_y y = L$$`

- Solve for y to graph

`$$y=\frac{L}{l_y}-\frac{l_x}{l_y}x$$`

- `$y$`-intercept: `$\frac{L}{l_y}$` (max y production)
- `$x$`-intercept: `$\frac{L}{l_x}$` (max x production)
]

<img src="1.4-slides_files/figure-html/BC-plot1-1.png" width="432" style="display: block; margin: auto;" />
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# Setting up the Model: Home

`$$l_x x + l_y y = L$$`

- Solve for y to graph

`$$y=\frac{L}{l_y}-\frac{l_x}{l_y}x$$`

- `$y$`-intercept: `$\frac{L}{l_y}$` (max y production)
- `$x$`-intercept: `$\frac{L}{l_x}$` (max x production)
- slope: `$-\frac{l_x}{l_y}$`

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<img src="1.4-slides_files/figure-html/BC-plot2-1.png" width="432" style="display: block; margin: auto;" />
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# Setting up the Model: Home

`$$l_x x + l_y y = L$$`

- Solve for y to graph

`$$y=\frac{L}{l_y}-\frac{l_x}{l_y}x$$`

- `$y$`-intercept: `$\frac{L}{l_y}$` (max y production)
- `$x$`-intercept: `$\frac{L}{l_x}$` (max x production)
- slope: `$-\frac{l_x}{l_y}$`

]

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<img src="1.4-slides_files/figure-html/BC-plot3-1.png" width="432" style="display: block; margin: auto;" />
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# Same As Before

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- Points .hi-blue[on the frontier] are efficient (uses all available labor supply)

- Points .hi-green[beneath the frontier] are feasible (in .hi-green[production set]) but inefficient (does not use all available labor supply)

- Points .hi-red[above the frontier] are impossible with current constraints (labor supply, technology, trading opportunities)
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<img src="1.4-slides_files/figure-html/unnamed-chunk-1-1.png" width="504" style="display: block; margin: auto;" />
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# Understanding the Tradeoff

- Slope of PPF: .hi[marginal rate of transformation (MRT)]

- Rate at which (domestic) market values .hi-purple[tradeoff] between goods x and y

- .hi-purple[Relative price of x] (in terms of y), or .hi-purple[opportunity cost of x]: how many units of y must be given up to produce one more unit of x

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<img src="1.4-slides_files/figure-html/unnamed-chunk-2-1.png" width="504" style="display: block; margin: auto;" />

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# Absolute and Comparative Advantages (Autarky)

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# Absolute Advantage

- A country has an .hi-purple[absolute advantage] if it requires less labor to produce (a unit of) a good

- .hi-green[Examples:]
 - if `$\color{blue}{l_x} < \color{red}{l_x'}$`, then .blue[Home] has an absolute advantage in producing x
 - if `$\color{blue}{l_y} > \color{red}{l_y'}$`, then .red[Foreign] has an absolute advantage in producing *y*

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# *Comparative* Advantage

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- A country has a .hi[*comparative* advantage] in a producing a good if the opportunity cost of producing that good is *lower* than other countries

- Recall the slope of PPF (the MRT) is the relative price (opp. cost) of `$x$`

- .hi-green[Examples:]
 - if `$\color{blue}{\frac{l_x}{l_y}} < \color{red}{\frac{l_x'}{l_y'}}$`, then .blue[Home] has a comparative advantage in producing x
 - if `$\color{blue}{\frac{l_x}{l_y}} > \color{red}{\frac{l_x'}{l_y'}}$`, then .red[Foreign] has a comparative advantage in producing x

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![](../images/absoluteadvantage.jpg)
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# *Comparative* Advantage, Some Hints

- PPF slope `$=$` opportunity cost of good x (amount of y given up per 1 x)

- If countries have different PPF slopes, have different opportunity costs

- Country with .hi[flatter slope (smaller magnitude)] has .hi[lower opportunity cost of x] (or .hi-purple[higher cost of y]) implies a .hi[comparative advantage in x]

- Country with .hi-purple[steeper slope (larger magnitude)] has .hi[higher opportunity cost of x] (or .hi-purple[lower cost of y)] implies a .hi-purple[comparative advantage in y]

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# An Example in Autarky

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# Ricardian One-Factor Model Example

- .blue[Home] has 100 Laborers
  - Requires 1 worker to make .pink[x]
  - Requires 2 workers to make .purple[y]
  
- .red[Foreign] has 100 Laborers
  - Requires 1 worker to make .pink[x]
  - Requires 4 workers to make .purple[y]
]

]

2. Which country has an *absolute* advantage in producing `$x$` and `$y$`?

3. Which country has an *comparative* advantage in producing `$x$` and `$y$`?
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