1.4 — Ricardian One-Factor Model

ECON 324 • International Trade • Spring 2023

Ryan Safner
Associate Professor of Economics
safner@hood.edu
ryansafner/tradeS23
tradeS23.classes.ryansafner.com

Outline

Assumptions of the Ricardian One-Factor Model

Absolute and Comparative Advantages (Autarky)

An Example in Autarky

The Example with International Trade

A Note of Caution and A Judgment Call

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 😕

Assumptions of the Ricardian One-Factor Model

Assumptions of the One-Factor Model

Markets (both output and factors) are perfectly competitive
“Labor” is homogenous and non-specific
Labor is mobile domestically, but not internationally
Production of goods requires only varying amounts of labor as an input
- The “one factor”
- The marginal product of labor is constant
No barriers to trade or transactions costs
Technology is constant within each country
Resource endowments are fixed

Setting up the Model

Imagine 2 countries, Home and Foreign
Each country can produce two goods, xylophones (x) and yams (y)
Each country has a fixed total supply of labor
- $L$ for Home and $L^{'}$ for Foreign
Let:
- $l_{x}$ : amount of labor to make 1 $x$
- $l_{y}$ : amount of labor to make 1 $y$

Setting up the Model: Home

Home's production set and total possible allocations of labor within a country is:

$l_{x} x + l_{y} y \leq L$

To find the frontier (PPF), assume Labor Demand (left) and Labor Supply (right) are equal: $l_{x} x + l_{y} y = L$

Setting up the Model: Home

$l_{x} x + l_{y} y = L$

Solve for y to graph

$y = \frac{L}{l_{y}} - \frac{l_{x}}{l_{y}} x$

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)

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: $- \frac{l_{x}}{l_{y}}$

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: $- \frac{l_{x}}{l_{y}}$

Same As Before

Points on the frontier are efficient (uses all available labor supply)
Points beneath the frontier are feasible (in production set) but inefficient (does not use all available labor supply)
Points above the frontier are impossible with current constraints (labor supply, technology, trading opportunities)

Understanding the Tradeoff

Slope of PPF: marginal rate of transformation (MRT)
Rate at which (domestic) market values tradeoff between goods x and y
Relative price of x (in terms of y), or opportunity cost of x: how many units of y must be given up to produce one more unit of x

Absolute and Comparative Advantages (Autarky)

Absolute Advantage

A country has an absolute advantage if it requires less labor to produce (a unit of) a good
Examples:
- if $l_{x} < l_{x}^{'}$ , then Home has an absolute advantage in producing x
- if $l_{y} > l_{y}^{'}$ , then Foreign has an absolute advantage in producing y

Comparative Advantage

A country has a 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 $x$
Examples:
- if $\frac{l_{x}}{l_{y}} < \frac{l_{x}^{'}}{l_{y}^{'}}$ , then Home has a comparative advantage in producing x
- if $\frac{l_{x}}{l_{y}} > \frac{l_{x}^{'}}{l_{y}^{'}}$ , then Foreign has a comparative advantage in producing x

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

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 flatter slope (smaller magnitude) has lower opportunity cost of x (or higher cost of y) implies a comparative advantage in x

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 flatter slope (smaller magnitude) has lower opportunity cost of x (or higher cost of y) implies a comparative advantage in x
Country with steeper slope (larger magnitude) has higher opportunity cost of x (or lower cost of y) implies a comparative advantage in y

An Example in Autarky

Ricardian One-Factor Model Example

Example: Suppose the following facts to set up:

Home has 100 Laborers
- Requires 1 worker to make x
- Requires 2 workers to make y
Foreign has 100 Laborers
- Requires 1 worker to make x
- Requires 4 workers to make y

Ricardian One-Factor Model Example

Example: Suppose the following facts to set up:

Home has 100 Laborers
- Requires 1 worker to make x
- Requires 2 workers to make y
Foreign has 100 Laborers
- Requires 1 worker to make x
- Requires 4 workers to make y

For each country, find the equation of the PPF and graph it.
Which country has an absolute advantage in producing $x$ and $y$ ?
Which country has an comparative advantage in producing $x$ and $y$ ?

Ricardian One-Factor Model Example: Solving for PPFs

Home

$\begin{aligned} l_{x} x + l_{y} y & = L \end{aligned}$

Foreign

Ricardian One-Factor Model Example: Solving for PPFs

Home

$\begin{aligned} l_{x} x + l_{y} y & = L \\ 1 x + 2 y & = 100 \end{aligned}$

Foreign

Ricardian One-Factor Model Example: Solving for PPFs

Home

$\begin{aligned} l_{x} x + l_{y} y & = L \\ 1 x + 2 y & = 100 \\ 2 y & = 100 - x \end{aligned}$

Foreign

Ricardian One-Factor Model Example: Solving for PPFs

Home

$\begin{aligned} l_{x} x + l_{y} y & = L \\ 1 x + 2 y & = 100 \\ 2 y & = 100 - x \\ y & = 50 - 0.5 x \end{aligned}$

Foreign

Ricardian One-Factor Model Example: Solving for PPFs

Home

$\begin{aligned} l_{x} x + l_{y} y & = L \\ 1 x + 2 y & = 100 \\ 2 y & = 100 - x \\ y & = 50 - 0.5 x \end{aligned}$

Foreign

$\begin{aligned} l_{x}^{'} x + l_{y}^{'} y & = L^{'} \end{aligned}$

Ricardian One-Factor Model Example: Solving for PPFs

Home

$\begin{aligned} l_{x} x + l_{y} y & = L \\ 1 x + 2 y & = 100 \\ 2 y & = 100 - x \\ y & = 50 - 0.5 x \end{aligned}$

Foreign

$\begin{aligned} l_{x}^{'} x + l_{y}^{'} y & = L^{'} \\ 1 x + 4 y & = 100 \end{aligned}$

Ricardian One-Factor Model Example: Solving for PPFs

Home

$\begin{aligned} l_{x} x + l_{y} y & = L \\ 1 x + 2 y & = 100 \\ 2 y & = 100 - x \\ y & = 50 - 0.5 x \end{aligned}$

Foreign

$\begin{aligned} l_{x}^{'} x + l_{y}^{'} y & = L^{'} \\ 1 x + 4 y & = 100 \\ 4 y & = 100 - x \end{aligned}$

Ricardian One-Factor Model Example: Solving for PPFs

Home

$\begin{aligned} l_{x} x + l_{y} y & = L \\ 1 x + 2 y & = 100 \\ 2 y & = 100 - x \\ y & = 50 - 0.5 x \end{aligned}$

Foreign

$\begin{aligned} l_{x}^{'} x + l_{y}^{'} y & = L^{'} \\ 1 x + 4 y & = 100 \\ 4 y & = 100 - x \\ y & = 25 - 0.25 x \end{aligned}$

Ricardian One-Factor Model Example: Graphing PPFs

Home

$y = 50 - 0.5 x$

Foreign

$y = 25 - 0.25 x$

Example: Absolute Advantage

Home

$l_{x} = 1$

$l_{y} = 2$

Foreign

$l_{x}^{'} = 1$

$l_{y}^{'} = 4$

Example: Absolute Advantage

Home

$l_{x} = 1$ (Equal)

$l_{y} = 2$ (Absolute advantage)

Foreign

$l_{x}^{'} = 1$ (Equal)

$l_{y}^{'} = 4$ (Absolute disadvantage)

Comparative Advantage and Autarky Relative Prices

So far, we assume countries are in autarky, they are not trading with one another
To find comparative advantage for each country, we need to compare opportunity costs of producing each good in each country, or relative prices in autarky
A country with a lower autarky relative price of a good than another country has a comparative advantage in producing that good

Example: Comparative Advantage

Home

Autarky relative price of x: 0.5y [PPF slope!]

Autarky relative price of y: 2x

Foreign

Autarky relative price of x: 0.25y [PPF slope!]

Autarky relative price of y: 4x

Example: Comparative Advantage

Autarky Relative Prices (Opportunity Costs)

	1x	1y
Home	0.5y	2x
Foreign	0.25y	4x

Example: Comparative Advantage

Autarky Relative Prices (Opportunity Costs)

	1x	1y
Home	0.5y	2x
Foreign	0.25y	4x

Home has a comparative advantage in producing y
Foreign has a comparative advantage in producing x

Example: Opening up Trade

Autarky Relative Prices (Opportunity Costs)

	1x	1y
Home	0.5y	2x
Foreign	0.25y	4x

Suppose now countries open up trade
We considered the relative prices in autarky
We next need to consider what might relative prices be under international trade

The Example with International Trade

Example: Opening up Trade

Autarky Relative Prices (Opportunity Costs)

	1x	1y
Home	0.5y	2x
Foreign	0.25y	4x

A bit of handwaiving here:
Ricardo assumes a labor theory of value and constant marginal products of labor
We have hidden the $M P L$ ^† for simplicity here
We are also in direct exchange (barter) between goods, there is no money here
Suffice it to say that we can show that the ratio of labor requirements (PPF slope) is equal to the ratio of prices of the final goods: $\underset{s l o p e}{\underset{⏟}{\frac{l_{x}}{l_{y}}}} = \frac{p_{x}}{p_{y}}$
- a clearer explanation of this with our next model!

Example: Opening up Trade

Autarky Relative Prices (Opportunity Costs)

	1x	1y
Home	0.5y	2x
Foreign	0.25y	4x

Home will:
- buy x if $p_{x} < 0.5 y$
- sell y if $p_{y} > 2 x$
The autarky price of y:
- At Home: 2x
- In Foreign: 4x
Home can export y to Foreign and sell at higher price!
- All L in Home will move to (higher-paying) y industry

Example: Opening up Trade

Autarky Relative Prices (Opportunity Costs)

	1x	1y
Home	0.5y	2x
Foreign	0.25y	4x

Foreign will:
- sell x if $p_{x} > 0.25 y$
- buy y if $p_{y} < 4 x$
The autarky price of x:
- At Home: 0.5y
- In Foreign: 0.25y
Foreign can export x to Home and sell at higher price!
- All L' in Foreign will move to (higher-paying) x industry

Example: Opening up Trade

Autarky Relative Prices (Opportunity Costs)

	1x	1y
Home	0.5y	2x
Foreign	0.25y	4x

Possible range of world relative prices:

$0.25 y < p_{x} < 0.5 y$

$2 x < p_{y} < 4 x$

Example: Specialization

Home

Home specializes in only producing y at point A

Foreign

Foreign specializes in only producing x at point A'

International Trade Equilibrium: Price AdjustmentsHome exports y ⟹⟹ less y sold in Home ⟹⟹ ↑py↑py in Home

  

International Trade Equilibrium: Price Adjustments

Home exports y $⟹$ less y sold in Home $⟹$ $↑ p_{y}$ in Home
As y arrives in Foreign $⟹$ more y sold in Foreign $⟹$ $↓ p_{y}$ in Foreign

International Trade Equilibrium: Price Adjustments

Home exports y $⟹$ less y sold in Home $⟹$ $↑ p_{y}$ in Home
As y arrives in Foreign $⟹$ more y sold in Foreign $⟹$ $↓ p_{y}$ in Foreign
Foreign exports x $⟹$ less x sold in Foreign $⟹$ $↑ p_{x}$ in Foreign

International Trade Equilibrium: Price Adjustments

Home exports y $⟹$ less y sold in Home $⟹$ $↑ p_{y}$ in Home
As y arrives in Foreign $⟹$ more y sold in Foreign $⟹$ $↓ p_{y}$ in Foreign
Foreign exports x $⟹$ less x sold in Foreign $⟹$ $↑ p_{x}$ in Foreign
As x arrives in Home $⟹$ more x sold in Home $⟹$ $↓ p_{x}$ in Home

International Trade Equilibrium: World Relative Prices

International trade equilibrium: relative prices adjust so they equalize across countries

$\frac{p_{x}^{⋆}}{p_{y}^{⋆}} = \frac{p_{x}}{p_{y}} = \frac{p_{x}^{'}}{p_{y}^{'}}$

Must be within mutally agreeable range: $0.25 y < p_{x} < 0.5 y$ $2 x < p_{y} < 4 x$
Suppose the world relative price of x settles to $\frac{p_{x}^{⋆}}{p_{y}^{⋆}} = 0.4 y$

International Trade Equilibrium: World Relative Prices

Home

Foreign

World relative price of x: $\frac{p_{x}^{⋆}}{p_{y}^{⋆}} = 0.4 y$

Both countries face same international exchange rate with slope $= - 0.4$

International Trade Equilibrium: “Trade Triangles”

Home

Home exports 20y to Foreign

Foreign

International Trade Equilibrium: “Trade Triangles”

Home

Home exports 20y to Foreign

Foreign exports 50x to Home

Foreign

International Trade Equilibrium: “Trade Triangles”

Home

Foreign

Trade along world exchange rate (world relative prices) from specialization points (A and A') to consumption points (B and B') beyond PPFs!

Another Example: You Try!

Example: Suppose the following facts to set up:

Home has 100 Laborers
- Requires 5 workers to make wheat
- Requires 10 workers to make cars
Foreign has 200 Laborers
- Requires 2 workers to make wheat
- Requires 8 workers to make cars

Plot wheat (w) on the horizontal axis and cars (c) on the vertical axis.

For each country, find the equation of the PPF and graph it.
Which country has an absolute advantage in producing wheat and cars?
Which country has an comparative advantage in producing wheat and cars?
What will the range of possible terms of trade be?

1.4 — Ricardian One-Factor Model

ECON 324 • International Trade • Spring 2023

Ryan Safner
Associate Professor of Economics
safner@hood.edu
ryansafner/tradeS23
tradeS23.classes.ryansafner.com

Outline

Assumptions of the Ricardian One-Factor Model

Absolute and Comparative Advantages (Autarky)

An Example in Autarky

The Example with International Trade

A Note of Caution and A Judgment Call

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 😕

Assumptions of the Ricardian One-Factor Model

Assumptions of the One-Factor Model

Markets (both output and factors) are perfectly competitive
“Labor” is homogenous and non-specific
Labor is mobile domestically, but not internationally
Production of goods requires only varying amounts of labor as an input
- The “one factor”
- The marginal product of labor is constant
No barriers to trade or transactions costs
Technology is constant within each country
Resource endowments are fixed

Setting up the Model

Imagine 2 countries, Home and Foreign
Each country can produce two goods, xylophones (x) and yams (y)
Each country has a fixed total supply of labor
- $L$ for Home and $L^{'}$ for Foreign
Let:
- $l_{x}$ : amount of labor to make 1 $x$
- $l_{y}$ : amount of labor to make 1 $y$

Setting up the Model: Home

Home's production set and total possible allocations of labor within a country is:

$l_{x} x + l_{y} y \leq L$

To find the frontier (PPF), assume Labor Demand (left) and Labor Supply (right) are equal: $l_{x} x + l_{y} y = L$

Setting up the Model: Home

$l_{x} x + l_{y} y = L$

Solve for y to graph

$y = \frac{L}{l_{y}} - \frac{l_{x}}{l_{y}} x$

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)

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: $- \frac{l_{x}}{l_{y}}$

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: $- \frac{l_{x}}{l_{y}}$

Same As Before

Points on the frontier are efficient (uses all available labor supply)
Points beneath the frontier are feasible (in production set) but inefficient (does not use all available labor supply)
Points above the frontier are impossible with current constraints (labor supply, technology, trading opportunities)

Understanding the Tradeoff

Slope of PPF: marginal rate of transformation (MRT)
Rate at which (domestic) market values tradeoff between goods x and y
Relative price of x (in terms of y), or opportunity cost of x: how many units of y must be given up to produce one more unit of x

Absolute and Comparative Advantages (Autarky)

Absolute Advantage

A country has an absolute advantage if it requires less labor to produce (a unit of) a good
Examples:
- if $l_{x} < l_{x}^{'}$ , then Home has an absolute advantage in producing x
- if $l_{y} > l_{y}^{'}$ , then Foreign has an absolute advantage in producing y

Comparative Advantage

A country has a 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 $x$
Examples:
- if $\frac{l_{x}}{l_{y}} < \frac{l_{x}^{'}}{l_{y}^{'}}$ , then Home has a comparative advantage in producing x
- if $\frac{l_{x}}{l_{y}} > \frac{l_{x}^{'}}{l_{y}^{'}}$ , then Foreign has a comparative advantage in producing x

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

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 flatter slope (smaller magnitude) has lower opportunity cost of x (or higher cost of y) implies a comparative advantage in x

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 flatter slope (smaller magnitude) has lower opportunity cost of x (or higher cost of y) implies a comparative advantage in x
Country with steeper slope (larger magnitude) has higher opportunity cost of x (or lower cost of y) implies a comparative advantage in y

An Example in Autarky

Ricardian One-Factor Model Example

Example: Suppose the following facts to set up:

Home has 100 Laborers
- Requires 1 worker to make x
- Requires 2 workers to make y
Foreign has 100 Laborers
- Requires 1 worker to make x
- Requires 4 workers to make y

Ricardian One-Factor Model Example

Example: Suppose the following facts to set up:

Home has 100 Laborers
- Requires 1 worker to make x
- Requires 2 workers to make y
Foreign has 100 Laborers
- Requires 1 worker to make x
- Requires 4 workers to make y

For each country, find the equation of the PPF and graph it.
Which country has an absolute advantage in producing $x$ and $y$ ?
Which country has an comparative advantage in producing $x$ and $y$ ?

Ricardian One-Factor Model Example: Solving for PPFs

Home

$\begin{aligned} l_{x} x + l_{y} y & = L \end{aligned}$

Foreign

Ricardian One-Factor Model Example: Solving for PPFs

Home

$\begin{aligned} l_{x} x + l_{y} y & = L \\ 1 x + 2 y & = 100 \end{aligned}$

Foreign

Ricardian One-Factor Model Example: Solving for PPFs

Home

$\begin{aligned} l_{x} x + l_{y} y & = L \\ 1 x + 2 y & = 100 \\ 2 y & = 100 - x \end{aligned}$

Foreign

Ricardian One-Factor Model Example: Solving for PPFs

Home

$\begin{aligned} l_{x} x + l_{y} y & = L \\ 1 x + 2 y & = 100 \\ 2 y & = 100 - x \\ y & = 50 - 0.5 x \end{aligned}$

Foreign

Ricardian One-Factor Model Example: Solving for PPFs

Home

$\begin{aligned} l_{x} x + l_{y} y & = L \\ 1 x + 2 y & = 100 \\ 2 y & = 100 - x \\ y & = 50 - 0.5 x \end{aligned}$

Foreign

$\begin{aligned} l_{x}^{'} x + l_{y}^{'} y & = L^{'} \end{aligned}$

Ricardian One-Factor Model Example: Solving for PPFs

Home

$\begin{aligned} l_{x} x + l_{y} y & = L \\ 1 x + 2 y & = 100 \\ 2 y & = 100 - x \\ y & = 50 - 0.5 x \end{aligned}$

Foreign

$\begin{aligned} l_{x}^{'} x + l_{y}^{'} y & = L^{'} \\ 1 x + 4 y & = 100 \end{aligned}$

Ricardian One-Factor Model Example: Solving for PPFs

Home

$\begin{aligned} l_{x} x + l_{y} y & = L \\ 1 x + 2 y & = 100 \\ 2 y & = 100 - x \\ y & = 50 - 0.5 x \end{aligned}$

Foreign

$\begin{aligned} l_{x}^{'} x + l_{y}^{'} y & = L^{'} \\ 1 x + 4 y & = 100 \\ 4 y & = 100 - x \end{aligned}$

Ricardian One-Factor Model Example: Solving for PPFs

Home

$\begin{aligned} l_{x} x + l_{y} y & = L \\ 1 x + 2 y & = 100 \\ 2 y & = 100 - x \\ y & = 50 - 0.5 x \end{aligned}$

Foreign

$\begin{aligned} l_{x}^{'} x + l_{y}^{'} y & = L^{'} \\ 1 x + 4 y & = 100 \\ 4 y & = 100 - x \\ y & = 25 - 0.25 x \end{aligned}$

Ricardian One-Factor Model Example: Graphing PPFs

Home

$y = 50 - 0.5 x$

Foreign

$y = 25 - 0.25 x$

Example: Absolute Advantage

Home

$l_{x} = 1$

$l_{y} = 2$

Foreign

$l_{x}^{'} = 1$

$l_{y}^{'} = 4$

Example: Absolute Advantage

Home

$l_{x} = 1$ (Equal)

$l_{y} = 2$ (Absolute advantage)

Foreign

$l_{x}^{'} = 1$ (Equal)

$l_{y}^{'} = 4$ (Absolute disadvantage)

Comparative Advantage and Autarky Relative Prices

So far, we assume countries are in autarky, they are not trading with one another
To find comparative advantage for each country, we need to compare opportunity costs of producing each good in each country, or relative prices in autarky
A country with a lower autarky relative price of a good than another country has a comparative advantage in producing that good

Example: Comparative Advantage

Home

Autarky relative price of x: 0.5y [PPF slope!]

Autarky relative price of y: 2x

Foreign

Autarky relative price of x: 0.25y [PPF slope!]

Autarky relative price of y: 4x

Example: Comparative Advantage

Autarky Relative Prices (Opportunity Costs)

	1x	1y
Home	0.5y	2x
Foreign	0.25y	4x

Example: Comparative Advantage

Autarky Relative Prices (Opportunity Costs)

	1x	1y
Home	0.5y	2x
Foreign	0.25y	4x

Home has a comparative advantage in producing y
Foreign has a comparative advantage in producing x

Example: Opening up Trade

Autarky Relative Prices (Opportunity Costs)

	1x	1y
Home	0.5y	2x
Foreign	0.25y	4x

Suppose now countries open up trade
We considered the relative prices in autarky
We next need to consider what might relative prices be under international trade

The Example with International Trade

Example: Opening up Trade

Autarky Relative Prices (Opportunity Costs)

	1x	1y
Home	0.5y	2x
Foreign	0.25y	4x

A bit of handwaiving here:
Ricardo assumes a labor theory of value and constant marginal products of labor
We have hidden the $M P L$ ^† for simplicity here
We are also in direct exchange (barter) between goods, there is no money here
Suffice it to say that we can show that the ratio of labor requirements (PPF slope) is equal to the ratio of prices of the final goods: $\underset{s l o p e}{\underset{⏟}{\frac{l_{x}}{l_{y}}}} = \frac{p_{x}}{p_{y}}$
- a clearer explanation of this with our next model!

Example: Opening up Trade

Autarky Relative Prices (Opportunity Costs)

	1x	1y
Home	0.5y	2x
Foreign	0.25y	4x

Home will:
- buy x if $p_{x} < 0.5 y$
- sell y if $p_{y} > 2 x$
The autarky price of y:
- At Home: 2x
- In Foreign: 4x
Home can export y to Foreign and sell at higher price!
- All L in Home will move to (higher-paying) y industry

Example: Opening up Trade

Autarky Relative Prices (Opportunity Costs)

	1x	1y
Home	0.5y	2x
Foreign	0.25y	4x

Foreign will:
- sell x if $p_{x} > 0.25 y$
- buy y if $p_{y} < 4 x$
The autarky price of x:
- At Home: 0.5y
- In Foreign: 0.25y
Foreign can export x to Home and sell at higher price!
- All L' in Foreign will move to (higher-paying) x industry

Example: Opening up Trade

Autarky Relative Prices (Opportunity Costs)

	1x	1y
Home	0.5y	2x
Foreign	0.25y	4x

Possible range of world relative prices:

$0.25 y < p_{x} < 0.5 y$

$2 x < p_{y} < 4 x$

Example: Specialization

Home

Home specializes in only producing y at point A

Foreign

Foreign specializes in only producing x at point A'

International Trade Equilibrium: Price AdjustmentsHome exports y ⟹⟹ less y sold in Home ⟹⟹ ↑py↑py in Home

  

International Trade Equilibrium: Price Adjustments

Home exports y $⟹$ less y sold in Home $⟹$ $↑ p_{y}$ in Home
As y arrives in Foreign $⟹$ more y sold in Foreign $⟹$ $↓ p_{y}$ in Foreign

International Trade Equilibrium: Price Adjustments

Home exports y $⟹$ less y sold in Home $⟹$ $↑ p_{y}$ in Home
As y arrives in Foreign $⟹$ more y sold in Foreign $⟹$ $↓ p_{y}$ in Foreign
Foreign exports x $⟹$ less x sold in Foreign $⟹$ $↑ p_{x}$ in Foreign

International Trade Equilibrium: Price Adjustments

Home exports y $⟹$ less y sold in Home $⟹$ $↑ p_{y}$ in Home
As y arrives in Foreign $⟹$ more y sold in Foreign $⟹$ $↓ p_{y}$ in Foreign
Foreign exports x $⟹$ less x sold in Foreign $⟹$ $↑ p_{x}$ in Foreign
As x arrives in Home $⟹$ more x sold in Home $⟹$ $↓ p_{x}$ in Home

International Trade Equilibrium: World Relative Prices

International trade equilibrium: relative prices adjust so they equalize across countries

$\frac{p_{x}^{⋆}}{p_{y}^{⋆}} = \frac{p_{x}}{p_{y}} = \frac{p_{x}^{'}}{p_{y}^{'}}$

Must be within mutally agreeable range: $0.25 y < p_{x} < 0.5 y$ $2 x < p_{y} < 4 x$
Suppose the world relative price of x settles to $\frac{p_{x}^{⋆}}{p_{y}^{⋆}} = 0.4 y$

International Trade Equilibrium: World Relative Prices

Home

Foreign

World relative price of x: $\frac{p_{x}^{⋆}}{p_{y}^{⋆}} = 0.4 y$

Both countries face same international exchange rate with slope $= - 0.4$

International Trade Equilibrium: “Trade Triangles”

Home

Home exports 20y to Foreign

Foreign

International Trade Equilibrium: “Trade Triangles”

Home

Home exports 20y to Foreign

Foreign exports 50x to Home

Foreign

International Trade Equilibrium: “Trade Triangles”

Home

Foreign

Trade along world exchange rate (world relative prices) from specialization points (A and A') to consumption points (B and B') beyond PPFs!

Another Example: You Try!

Example: Suppose the following facts to set up:

Home has 100 Laborers
- Requires 5 workers to make wheat
- Requires 10 workers to make cars
Foreign has 200 Laborers
- Requires 2 workers to make wheat
- Requires 8 workers to make cars

Plot wheat (w) on the horizontal axis and cars (c) on the vertical axis.

For each country, find the equation of the PPF and graph it.
Which country has an absolute advantage in producing wheat and cars?
Which country has an comparative advantage in producing wheat and cars?
What will the range of possible terms of trade be?

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1.4 — Ricardian One-Factor Model

ECON 324 • International Trade • Spring 2023

Ryan Safner Associate Professor of Economics safner@hood.edu ryansafner/tradeS23 tradeS23.classes.ryansafner.com

Outline

A Note of Caution and A Judgment Call

Assumptions of the Ricardian One-Factor Model

Assumptions of the One-Factor Model

Setting up the Model

Setting up the Model: Home

Setting up the Model: Home

Setting up the Model: Home

Setting up the Model: Home

Setting up the Model: Home

Same As Before

Understanding the Tradeoff

Absolute and Comparative Advantages (Autarky)

Absolute Advantage

Comparative Advantage

Comparative Advantage, Some Hints

Comparative Advantage, Some Hints

Comparative Advantage, Some Hints

An Example in Autarky

Ricardian One-Factor Model Example

Ricardian One-Factor Model Example

Ricardian One-Factor Model Example: Solving for PPFs

Home

Foreign

Ricardian One-Factor Model Example: Solving for PPFs

Home

Foreign

Ricardian One-Factor Model Example: Solving for PPFs

Home

Foreign

Ricardian One-Factor Model Example: Solving for PPFs

Home

Foreign

Ricardian One-Factor Model Example: Solving for PPFs

Home

Foreign

Ricardian One-Factor Model Example: Solving for PPFs

Home

Foreign

Ricardian One-Factor Model Example: Solving for PPFs

Home

Foreign

Ricardian One-Factor Model Example: Solving for PPFs

Home

Foreign

Ricardian One-Factor Model Example: Graphing PPFs

Home

Foreign

Example: Absolute Advantage

Home

Foreign

Example: Absolute Advantage

Home

Foreign

Comparative Advantage and Autarky Relative Prices

Example: Comparative Advantage

Home

Foreign

Example: Comparative Advantage

Example: Comparative Advantage

Example: Opening up Trade

The Example with International Trade

Example: Opening up Trade

Example: Opening up Trade

Example: Opening up Trade

Example: Opening up Trade

Example: Specialization

Home

Foreign

International Trade Equilibrium: Price Adjustments

International Trade Equilibrium: Price Adjustments

International Trade Equilibrium: Price Adjustments

International Trade Equilibrium: Price Adjustments

International Trade Equilibrium: World Relative Prices

International Trade Equilibrium: World Relative Prices

Home

Foreign

Ryan Safner
Associate Professor of Economics
safner@hood.edu
ryansafner/tradeS23
tradeS23.classes.ryansafner.com

Ryan Safner
Associate Professor of Economics
safner@hood.edu
ryansafner/tradeS23
tradeS23.classes.ryansafner.com