What exactly would this "widget" on the Tiger be? It was made from steel, it used basically the same gun as the FlaK 88 having been produced in its thousands, it used the same optics as other German tanks, it used an enlarged Maybach engine that was mechanically similar to the Maybachs powering the PzKpfw III and IV. There was nothing special about the Tiger I, it was just very big and heavy. Technologically and design wise it wasn't very advanced at all and was actually a pre-war design. It cost about four times as much as a PzKpfw IV and took about twice as long to build.
Offhand, I can think of three: the much thicker armor required considerably more skill and time to be welded, the hull required extensive machining (and thus more skill, time, and scarce machine tools) in comparison to the T-34, and the transmission was extremely complex with low tolerances which, again, required more skill, time, and scarce tools to make than other tanks, especially the Sherman. The Panther had the same problems to a lesser extent.
None of those factors is going to appear in the dollar (RM) expense because normal market conditions didn't apply. A master welder might make 2 or 3 times what a novice does, but if you can easily train a million novices but have no way to train many more masters within the necessary time frame, the labor of the master has a value and scarcity far out of proportion to his pay. That applies to time as well - it's not how much time it takes, it's how much of the time of the most scarce laborers it takes.
And the question isn't how many Mark IVs could have been built for the same monetary price, it's how many of the equivalent of a T-34 or Sherman Germany could have produced under wartime conditions.
Technologically and design wise it wasn't very advanced at all and was actually a pre-war design.
Technology and difficulty of manufacture don't always coincide, in fact they often vary inversely. The MG-42, MP-44, MP-40, and P-38 (the pistol) were all easier and cheaper to build and also more up-to-date and effective weapons than the previous generation of small arms.