with Indn Maid, although I would not have bothered with the "longer than you've walked the earth" part, as that is not relevant.
However, he makes good points. 4 years as a restaurant manager is not 'much knowledge', and in many business areas would be seen as limited, in particular as you do not say where this experience was nor how successful the restaurant was whilst you were it's manager. Stating where allows prospective employers to check back on your claim. If you were not particularly successful, then your claim could be construed as false, and will go against you. If you were successful, then your reputation will be enhanced.
"I am trying to gain...." could be better phrased as "I wish to gain further experience as a business consultant".
"I am recently out of....." should be re-phrased as "I have recently achieved an MBA in Business Management at UCLA's Anderson Business School", and be prepared to tell your grade, (if that is applicable to MBA's), and show your certificate/diploma.
"I am curious...". No. Restaurant owners/managers do not have time for curiosity, but something like, "I am eager to learn more about the restaurant business, and your experience and guidance would be very helpful to me". Do not say you have "ideas to improve the revenue and decrease the cost". You are telling your prospective employer that he is a failure, and you could do better.
Similarly, saying, "I can eradicate any existing inefficiencies your business might have, and improve any existing methods of marketing,day-to-day operation,etc.", tells him you think he is failing. Never appeal to someone's deficiencies, always their strengths.
"Sending a letter to a few small businesses". No-one likes receiving circulars; they tend to be thrown away with the rubbish. If a prospective employer suspects the letter they have received is 'mass produced', they will chuck it out. Find out more about each restaurant/business. Find the Manager's name and address your letter to them personally. Let them know that you are interested in their restaurant/business, and not just any restaurant or business.
Where is your CV?
I hope that helps.
Mark