import numpy as np
import matplotlib.pyplot as plt
%matplotlib inline
x = np.arange(0.,101, 5)
y = 50 - x/2
plt.plot(x,y)
plt.ylabel('canons')
plt.xlabel('books')
plt.title('Figure 1: The Production Possibility Frontier (PPF) in Castle Black')
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What’s the opportunity cost of one book? one cannon?
Winterfell (W) is not as good as Castle Back in producing cannons and books. Now, the opportunity cost of producing one book is 3 cannons, and Winterfell can produce at most 10 books.
In autarky (no trade), CB prefers to consume 90 books. How many units of cannons are they able to consume?
W consumes 18 cannons in autarky. How many units of books are they able to consume?
Oh! But what if we allow them to trade? Who is better in producing books?
Assume that both regions decide to exchange one-to-one books for canons, and CB still prefers to consume 90 books. How many units of canons CB consume? What about W?
What determines the terms of trade between CB and W? We can think that they enter in a negotiation.
Negotiations between two parties is a different trading mechanism compared to the double auction game we play. Usually, the terms of trade depend on the outside options each party has, and the bargaining power. This concept is due to John Nash.
The key idea of the Ricardian model is that two countries specialize in what they are better at, i.e. the good in which they have lower opportunity cost compared to the other country, they can gain from trading the other good with each other.
In sum, an entity (individual, country, etc.) has comparative advantage in producing a good or service, if it faces a lower opportunity cost in the production of that good or service compared to other entities.
Notice that our results hold in spite of the fact that Castle Back is, in absolute terms, better at producing both books and canons. With the same amount of resources, CB can produce more books and more canons than Winterfell. Thus, CB has absolute advantage in producing both books and canons.
Technically, an entity has absolute advantage in producing a good or a service, if it is better at producing that good or service compared to another entity (e.g. a country can produce more output per worker than another country).
In our example, we have assume a constant opportunity cost between books and canons. Probably, it makes more sense to assume that it is easier that opportunity cost is increasing in terms of production. In this case, the relationship between cannons and books look like
a= 100**2
b =.8
z = (a- b*x**2)**(.5)-(a-b*100**2)**(.5)
plt.plot(x,z)
plt.ylabel('canons')
plt.xlabel('books')
plt.title('Figure 2: Increasing opportunity cost PPF')
plt.plot([20,40,80], [20,(a- b*40**2)**(.5)-(a-b*100**2)**(.5),50], 'ro')
plt.annotate("A", xy=(40,50), xytext=(41,51))
plt.annotate("B", xy=(20,20), xytext=(21,21))
plt.annotate("C", xy=(80,50), xytext=(81,51))
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from IPython.core.display import HTML
def css_styling():
styles = open("custom.css", "r").read()
return HTML(styles)
css_styling()