RBC models

Hello,
I’m an older guy doing some adjunct work trying to get up to speed on the latest theories. The RBC theory is driving me bats! The RBC models seem extremely complex. I think I can get the basic point across to students with a much simpler model than the ones I’m coming across. But I’d appreciate the opinion of the group!
I think a model as simple as:
• C=Consumption
• L=Labor
• A= Technology
C=A*L Output is a function of technology and labor and all output is consumed. No savings, no capital. Super simple as I said. The agent produces as much as possible as efficiently as possible, which is entirely dependent on A and the exogenous labor force. Given L changes in C must be due to A. A is determined by random shocks!
Does this sum up the main point of RBC?
Thanks!