So the cobbs douglas demand system indicates that the consumption of the capitalist class can be modeled as C=(1+r)K where r represents net profit for that time period, K represents capital stock of that time period and C represents consumption

What I want to know is, how do you properly incorporate the law of diminishing marginal utility into this?

So let's say the capitalist class has a constant population, or at least very little growth. An increase in production from one period to the next means more goods are produced. These goods will be consumed by both the laboring class, who spends the whole wage, and the capitalist class who spends a portion of profit on consumption. However, as the capitalist class consumes more, shouldn't individuals within that class experience decreasing marginal utility for general levels of consumption? As the class has a constant population, wouldn't that mean consumption would eventually drop off? So like, as they consume more, they get less and less utility from consumption and therefore at a certain point no longer want to consume?

I don't see that in the consumption function, as it does not account for past consumption.

Am I missing something? Where is diminishing marginal utility incorporated in the cobbs douglas demand system?