The exchange model provides a remarkably useful tool for analyzing issues related to international trade. In the following example, we introduce independent markets for consumers A and B and trade activities which deliver goods from one market to the other.

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Example 5: Import tariffs in a simple exchange model

Consider Example 4 with the following modifications:

1) new additional parameters - ad-valorem tariffs applied on imports to each regions (A and B).

2) We introduce a separate commodity price for each agent (these prices are identical when there are no tariffs)

3) Trade activities deliver goods from one agent to the other. We will denote it by "M, good, agent" - import of "good" to "agent" - MXA, MXB, MYA, MYB.

A and B each have one input and one output. They simply deliver a good (X or Y) from one agent to the other. Adding a tax requires two new fields in this model:

1) "A:" will specify the tax agent (a consumer who collects the tax revenue as part of his income)

2) "T:" will specify the ad-valorem tax rate

Please note: MPSGE permits taxes to applied on production inputs and outputs

but it does not permit taxes on final demand

The tax applies on a net basis on input. For example, if we consider MXA sector, the price of one unit of input is given by: Px_B(1+Ta), where P_x_B is the net of tax price of a unit of x on the agent B market, Ta is the ad-valorem tariff rate.

The final portion of the model will introduce "MPSGE report variables". Report variables, in this model, are used to recover a Hicksian money metric welfare index for each of the agents:

1) "V:" field designates a variable name that must be distinct

2) "W:" field indicates that the variable is to return a welfare index for the specified consumer

First, we will compute the tariff-ridden equilibrium which defines benchmark welfare levels. After this calculation we set all tariffs to zero and compute the free-trade equilibrium. Using welfare indices from the counterfactual and welfare levels from the benchmark, we are able to report the change in welfare associated with the removal of tariff distortions.

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The money metric utility function gives the minimum expenditure at prices p necessary to purchase a bundle at least as good as x.

Consider some prices p and some given bundle x. How much money would consumer need at the price p to be as well off as he could be by consuming the bundle of goods x? We have to solve the following problem: min pz s.t. U(z)³U(x). The solution of this problem will be

(1) an expenditure function, e(p,U(x)),

(2) replacing U by utility function in the expenditure function we will get a money metric utility function, m(p,x).

When p is fixed, m(p,x) is in fact a utility function.