HOS Model with Interventions (Solver Version)

This is version of the 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. It is very similar to the corresponding 'live' version, but is implemented using Solver and macros, and can be used for a few other advanced experiments. Exogenous variables and parameters are in white, endogenous variables in grey. The user can change endowments, price, technology or preferences, as in the basic model, plus input, output, consumption and trade taxes/subsidies. Using macros, it is also possible to alter the closure of the model, swapping exogenous and endogenous variables to examine various issues. Finally, the model introduces a (potentially) downward sloping foreign demand curve, enabling some large country trade policy issues to be explored in general equilibrium, as opposed to the partial equilibrium trade war model. The model is described fully in Gilbert (2008).

Model Layout Guide


All of the experiments discussed on the page for the 'live' version can also be implemented using this model, with only minor changes in location of the relevant cells. To solve the model you can just click the Solve model button if you have enabled macros, or launch Solver directly (some functionality requires macros).

Optimal Tariffs

By default, the elasticity of foreign demand has been set at -1000, making the economy effectively small (unable to influence world prices). However, if a smaller number is used, say -10, the economy will have an influence over prices. To see this, change the elasticity in cell D40 and solve the model, and then increase the tariff to say 10 percent (cell D18), and solve again. Notice that the welfare index rises as the economy exploits its monopsony power. What is the best tariff? To find out restore the original solution using the Restore back button, then deselect the box next to cell D18. This endogenizes the tariff. Hit the Solve model button and the value 11 (percent) appears in the box. This is the optimal tariff. To verify, reselect the box next to D18, and try increasing the tariff slightly, or decreasing it slightly. You should find that welfare falls. Restore the backup solution and try the same experiment with the elasticity at -5. You should find the solution is 25 percent. The optimal tariff is equal to 1/(|E|-1) (as a percentage), where |E| is the absolute value of the foreign import demand elasticity. For a partial equilibrium model dealing with optimal tariffs and retaliation see here.

Tariff Quota Equivalence

A fundamental result from the theory of commercial policy is the equivalence of tariffs and quotas under perfect competition. To show this result, consider a tariff of say, 50 percent. Solve the model. Now, with the tariff still in place, deselect the box next to the volume of imports (D17) and select the box next to the tariff (D18). This swaps the two variables in the closure. Now, the volume of imports is fixed (the quota) and the tariff will vary to determine the domestic price (much like a variable import levy). Solve the model again. You should note that nothing at all changes. This establishes the equivalence of tariffs and quotas under perfect competition, provided that the quota rent is spent in the same way as the tariff revenue. See Bhagwati (1965) for further details. For the non-equivalence of tariffs and quotas under imperfect competition see this model.

Non-economic Objectives and Specificity Again

Non-economic objectives can be examined in the 'live' model by directly altering the policy instruments. This approach is not really feasible here because Solver must be launched to re-solve the model after every change. But we can examine the problem another way. For example, try checking the box next to D11. This makes output of X exogenous. Type a target value in the cell, say 100. Because output of X is now exogenous, we need another endogenous variable. We can choose a policy instrument and deselect the box next to it to make it endogenous. Solving the model again will then give us the level of the tax/subsidy that is consistent with the target. Hence, if we endogenize the output taxes/subsidies, we find an output subsidy of around -45 percent solves the problem, as does a tariff of 83 percent. Other interventions can also be tried (some, like consumption taxes/subsidies, will not work for this target). By comparing the welfare index with each intervention, we again find that the output subsidy is the most efficient.