Of course it would. I have a BA in Economics with Honors from COLA and an MBA with a concentration in Finance from Yale. There is a formalized term for these very decisions in economics - Opportunity Cost.
In your scenario, Mexican firms evaluate the (opportunity) cost of maintaining their operating/profit margins versus maximizing revenues/earnings/and cash flow. The problem with your premise is that it's not an economic decision at all. Ultimately, cash flow and earnings are the only metrics fiduciarally responsible managers maximize in an efficient market. They wouldn't just "pass along the cost to consumers." They don't have the market power to do so (other Mexican firms would just undercut them) and it doesn't make any sense, because it would hurt their bottom line if they tried. Mexican companies would produce at the prevailing tariff price and the Treasury would collect the tariff tax to build the Wall.
What you are suggesting are agents acting irrationally/inefficiently, which is a characteristic of Behavioral Economics. Empirically, we've observed this to occur time to time. If the Mexican managers are acting irrationally, then there is also cost - an opportunity cost of Mexican lost/transferred revenues perfectly captured by US companies that these manager are paying for to satisfy their irrationality (e.g. preserving operating/profit margins).
Other things to consider with tariffs - there is some deadweight loss when international production drops, domestic production increases, and tariff revenues are collected. However, much of the deadweight loss assumes international, in this case Mexican, imports are perfect substitutes for domestic goods in everything except cost. That's how you're taught it academically. In the real world, especially with Mexico, that is decidedly NOT the case and DWL from price increases are much softer in reality because peoples' demand preferences between quality and value are relatively elastic. Additionally, tariff revenues are being invested to reduce domestic macroeconomic supply costs of illegal immigration further reducing or completely eliminating net dead weight losses.
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Last edited: Jan 27, 2017