2.8 Deriving the Autarky Terms of Trade

The Ricardian model assumes that all workers are identical, or homogeneous, in their productive capacities and that labor is freely mobile across industries. In autarky, assuming at least one consumer demands some of each good, the country will produce on the interior of its PPF. That is, it will produce some wine and some cheese.

Question: Profit-maximizing firms would never set a wage rate above the level set in the other industry. Why?

Answer: Suppose the cheese industry set a higher wage such that w_C > w_W. In this case, all the wine workers would want to move to the cheese industry for any wage greater than w_W. Since their productivity in cheese is the same as the current cheese workers and since it does not cost anything for them to move to the other industry, the cheese industry could lower their costs and raise profit by paying a lower wage. To maximize profit, they must lower their wage. Thus only equal wage rates can be sustained between two perfectly competitive producing industries in the Ricardian model.

In autarky, then, w_C = w_W. Plugging in the relationships derived in the previous section yields

$$\frac{P_W}{a_{LW}}=\frac{P_C}{a_{LC}}$$

or

$${\left(\frac{P_C}{P_W}\right)}^{Aut}=\frac{a_{LC}}{a_{LW}}\text{.}$$

This means that the autarky price ratio (cheese over wine) or terms of trade equals the opportunity cost of producing cheese. Another way to say the same thing is that the price of cheese (in terms of wine) in autarky equals the opportunity cost of producing cheese (in terms of wine).

Question: Why is there an autarky terms of trade when there is no trade in autarky?

Answer: The Ricardian model represents a barter economy. Even though we define prices and wages in monetary terms, all relevant solutions in the model are described in terms of ratios in which the money or dollars cancel out. Never will we solve explicitly for the dollar price of wine or cheese or the dollar wage rate.

Thus a good way to think about how the model works is to imagine that workers go to work in their respective industries and produce wine or cheese. At the end of the day, they are paid not in dollars but in goods. The cheese workers’ wage is a quantity of cheese. The wine workers earn a quantity of wine. Since workers, as consumers, presumably will desire some wine and some cheese for their evening dinner, they must first go to a market to trade some of their wages (goods) for some of the other goods available at the market.

In autarky, cheese workers and wine workers come together on the domestic market to trade their goods. The autarky price ratio or terms of trade represents the amount of wine that exchanges per unit of cheese on the domestic barter market.