In place of the generation of a carbene via the reaction of sodium hydroxide and chloroform, you would like to try the Simmons-Smith reaction; however, your boss has declined this reaction due to the cost of reagents. After some research you discover that the Simmons-Smith reaction rate and yield can be improved by the use of ultrasonication and your lab group already has one. Do you think this would improve the carbene generation in the phase transfer catalyst reaction you performed in lab

The generation of carbene from sodium hydroxide and chloroform and the Simmon-Smith reactions are the two distinct processes. The cost of the reagent di-iodomethane is also very much as mentioned in the question. Though the rate and the productivity of the Simmons-Smith reaction can get better with the help of sonification treatment, it cannot reduce the cost associated with it.  

The application of the sonification treatment to the Simmons-Smith reaction, however, can better the production of carbenes in the phase-transfer catalyst reactions. With the spontaneous transferring of the produced carbenes to the organic phase, one can always witness a reduction in the concentration of carbene in the aqueous phase in which the reaction between the di-iodomethane and zinc-copper alloy give rise to the carbenes. In the process, equilibrium is mediated towards the generation of more carbenes.