Break down and simplify the question. This is what I understood ~ Racquet manufacturers are using old technology. Only professional tennis players are interested and willing to pay for innovation. Therefore, innovation depends on the tennis authorities who set competition standards.

The assumption is pretty clear now. Professional tennis players will only pay for innovations if they are accepted as standard for competitions. They are not interested in innovation otherwise.

C fits perfectly.

Here is my approach to this question. I would like to hear thoughts from others.

Conclusion: Innovation in racquet technology is driven by what authorities for competition will deem acceptable.
To look for an assumption, we basically need a premise which will supports the conclusion.

A. The market for cheap, traditional racquets cannot expand unless the market for technologically advanced racquets also expands.
This does not support the conclusion about what is limiting the racquet technology innovation. Instead, this discusses what will allow the market for racquets to expand.

B. Professional tennis racquets are likely to improve more as a result of technological innovations developed in workshops than as a result of technological innovations developed in major manufacturing concerns.
Again, this discusses how the tech innovation will improve but does not lend any support to how authorities are limiting innovation.

C. Professional tennis players do not generate a strong demand for innovations that fall outside what is officially recognized as standard for purposes of competition.
This choice or statement lends support to the conclusion (or claim) about authorities are limiting innovation.

D. The technological conservatism of tennis racquet manufacturers results primarily from their desire to manufacture a product that can be sold without being altered to suit different national markets.
Outside of the scope of argument. We are not looking for other reasons for tech conservatism.

E. The authorities who set standards for professional tennis racquets do not keep informed about innovative racquet design.
Discusses the 'authorities' but does not tell us how this impacts technology innovation. One might infer from this choice that this is what is causing the authorities to not allow better racquets but there might be other reasons why they dont allow better racquets. Thus, discard this choice also.

Therefore, C is the answer.