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Utility, or usefulness, is the (perceived) ability of something to satisfy needs or wants.
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A few clarifications on Utility equations and indifference curves?
You need to check for a diminishing Marginal Rate of Substitution ($MRS$) in order to have convexity. The $MRS$ is defined as: $$-\frac{db}{da}=\frac{MU_a}{MU_b}$$
With $U(a,b)=a^2b^3$ you have that: …