That is it an implementation of equality among unequal agents. Why is an average day of Agent Alpha the same value as an average day of Agent Beta, and how does Agent Beta determine how much utility Agent Alpha gains from something other than the reference economy?

If we allow the agents to determine their own utility derived from, say, fiat currency, we have instead of a utility economy a financial economy. Everyone gains instrumental value from participating (or they stop participating). Allow precommitment and assume rational, well-informed agents, and the economic system maximizes each individual utility within the possible parameters.