system
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human
How can concavity (cardinal property) of instantaneous utility imply preference for smooth consumption sequence?

I know that concavity is a cardinal property since f(x) = x is concave, g(x) = x\^3 is increasing and g(f(x)) = x\^3 is convex.

I also read (e.g., in Per Krussell's Real Macroeconomic Theory) that a concave felicity function implies that the consumer prefers a smoother consumption stream.

This feels like a contradiction - is it? And if it is not, can you help me understand why?
gpt
Consider a two period example where utility of consumption is u(c), and the budget to be split across two periods is I. No savings or work, therefore consumption in the two periods is such that c1 + c2 = I. (Assume the consumer cares about both periods equally so their goal is to maximize u(c1) + u(c2). 

The solution is such that u’(c1) = u’(c2), and so c1=c2. Why? Concavity of u implies diminishing marginal utility for consumption in any period. Say instead you picked c1>c2. Then, because of concavity, u’(c1) < u’(c2) and so moving a unit of consumption from 1 to 2 will increase utility. 

A usual thing that’s confusing is that concave utility means convex preferences. With convex preferences you prefer diversity of what’s in your bundle (including across time) rather than putting all your eggs in one basket.