HOS Model with Interventions (Live Version)

This is a version of the 'live' Heckscher-Ohlin-Samuelson (HOS) model of production in a single economy that incorporates interventions in the form of taxes/subsidies at various levels of the economy. The solution is embedded directly in the sheet, making the use of Solver unnecessary. The base model is the same as the HOS 'live' version, but the baseline equilibrium is one in which trade is occurring. The model should work in any version of Excel. Exogenous variables and parameters are in white, endogenous variables in blue. The user can change endowments, prices, technology or preferences, as in the basic model, plus input, output, consumption and trade taxes/subsidies. The model features both general and partial equilibrium geometry of interventions, useful because most texts use the partial approach, and this emphasizes the connection between the two. Many topics from the neoclassical theory of commercial policy can be explored. A similar Solver/macro based version is also available. A description of how the model was built is in Gilbert (2009b).

Model Layout Guide


Basic General Equilibrium Effects of Interventions

The model can simulate the general equilibrium effect of any type of price intervention. For example, to simulate a tariff, increase the value in cell E16. Note how as the tariff increases, producers of X respond by increasing production, while consumers respond by decreasing consumption, the net result being that imports fall, and the welfare index declines. Note also that the Y sector is affected also, as resources are drawn into X production, output of Y declines, as do exports. The tariff also filters down to incomes. Because X is capital intensive, the tariff raises the return to capital and lowers the return to labor. Hence, we might expect owner of capital to be in favor, and owners of labor to be opposed, to the measure. Import subsidies can be examined using a negative value in E16. Export taxes/subsidies by changing F16, consumption taxes/subsidies by changing E13 or F13, production taxes by changing E10 or F10, and input taxes by changing E6, F6, E7 or F7.

Tariff Size and Welfare Costs

Try increasing the tariff gradually using the spinner next to cell E16. As you hold the spinner down, watch what happens to the welfare index in cell E22. As the tariff increases, the welfare index falls - the tariff introduces deadweight losses into the economy. As you continue to increase the tariff you should also notice that the welfare index begins to decline at a faster and faster rate, the deadweight loss is increasing in the size of the tariff, so larger tariffs have a much greater welfare cost than smaller ones. Similar results hold for all other types of intervention.

Taxes or Subsidies?

A consequence of the no money illusion property of general equilibrium models is that (in the two-sector model) production and consumption taxes are closely related. Consider the following experiment. Place a value of 25 in cell E10. This is a production subsidy to X. Observe the effects. Now remove the subsidy and place a tax on sector Y using the value -20 in cell F10. What is the difference? The answer is nothing, these two interventions have the same effect on relative prices, since 1/0.8=1.25. Try the same experiment for consumption or factor taxes. You will get the same result. In the literature we often see the term production (or consumption or factor) tax cum subsidy, to draw attention to the fact that the sector in which the intervention occurs does not really matter.

Intervention Concordances

There are other basic relationships among the interventions. Simulate a tariff using a positive value (say 25 percent) in cell E16. Observe the effects. Now remove the tariff, and simulate a tax of 25 percent on consumption of X (cell E13) and a subsidy of 25 percent on production of X (cell E10). Any difference? No, these policies are the same. A tariff is equivalent to a production subsidy plus a consumption tax at the same percentage rate. Given that this is the case, why do more people tend to support tariffs than production/consumption taxes/subsidies? In a similar way, you should be able to establish that an export tax is equivalent to a production tax plus consumption subsidy, that an export subsidy is equivalent to a production subsidy plus a consumption tax, and that a uniform factor tax on a sector is equivalent to an output tax.

Lerner Symmetry Theorem

A related principle applies to trade taxes. The Lerner symmetry theorem (Lerner, 1936) states that an import tax is equivalent to an export tax. To see this consider a tariff of 25 percent (cell E16). Observe the results. Now consider an export tax of the same magnitude instead. Put -20 in cell F16. Any difference? No, the policies are identical. One way to think about this is as follows. A tariff is equivalent to a production subsidy plus a consumption tax in X. But this is equivalent to production tax and a consumption subsidy in Y, as we have established. But, this in turn is equivalent to an export tax. The symmetry theorem basically says that if you want to restrict imports, you will be restricting exports too.

Tariff Compensation Principle

A corollary to the symmetry theorem is the tariff compensation principle. This states that it is possible to offset the pro-import competing sector bias of a tariff with a pro-export sector policy, i.e., an export subsidy. To simulate, consider a tariff of 25 percent in cell E16. Leaving this in place, put a subsidy of 25 percent in the cell F16. What happens? Nothing seems to change except income and factor prices, everything real is at the same level as with free trade. But did income and factor prices really change? No, the prices have all just risen by 25 percent. In other words, this is just like the numeraire shock considered under the HOS model. Another way of thinking about the result is this: A tariff is equivalent to an export tax. So a tariff plus an export subsidy is just an export tax plus an export subsidy. Hence, if they are at the same rate, the policy simply gives to exporters with one hand and takes with the other. It should not therefore, and does not, have any real effect.

Non-economic Objectives and Specificity

Suppose that for security reasons, the government of the country represented by the model wanted to ensure that production of X was at least 100 units. A tariff of 26.2 percent would work (verify this for yourself), but would it be the best policy? To answer the question we can consider all of the possible policies that would achieve the objective, and rank them in order of efficiency (i.e., those with higher welfare index values are better). Notice that we are not saying anything about whether the objective is good. Verify that the objective could also be achieved with a production subsidy of 26.2 percent, or a capital subsidy of roughly -33.3 percent, or with a labor subsidy of roughly -39.8 percent. Which is the most efficient? The production subsidy. Why? It follows the specificity rule - the most efficient intervention is the one that most closely affects the objective. Using a similar approach, verify that the most efficient way to achieve a consumption objective is with a consumption tax/subsidy, an employment objective is with a factor tax/subsidy, and a trade objective is with a trade tax/subsidy. The classic reference is Bhagwati and Srinivasan (1969).

Tariff Jumping Investment 

Tariff jumping investment is where the existence of a tariff prompts a foreign supplier to invest in a country to supply domestically (and thus avoid the tariff). What are the consequences? Try imposing a tariff of, say, 50 percent. Now, with the tariff in place, increase the endowment of capital by 1 unit (cell L4), this represents the investment. Keep a close eye on income in cell E20. It increases by 1.15, and welfare increases too. Thus it appears that a tariff would raise welfare if it attracted investment from overseas. But not so fast... Income increases by 1.15, but the value of the unit of new capital in the market is 1.44 (i.e., the price of a unit of capital). Our model doesn't identify foreign/domestic capital, it simply assumes all capital is domestically owned. But if this is really foreign capital, then the income is owned by foreign interests, and must be subtracted from the total. But this means that domestic income must have fallen. Hence, tariff jumping investment lowers the value of domestic production at world prices, and lowers welfare. For full analysis of this result see Brecher and Diaz-Alejandro (1977)