Question

consider the utility function U(XY) = 3x^2 + 5y. is the assumption that more is better satisfied for both goods?

Answer 1

Yes, it is. Let's demonstrate it with some numbers.
Consider a situation where for the X good we have 3 units and for the Y good 5 units.
With this units the value of the utility function is : \[U \left( 3;5 \right)=3\times3^{2}+5\times5=52\]
Now the X good units are 4 and hold at 5 units the Y good, adn compute again the utility:
\[[U \left( 4;5 \right)=3\times4^{2}+5\times5=73\]
When the consumer has more X good his/her utility is bigger. More X good is better.

Now let's do the same for the Y good. Assume, for example that we have again 3 units for the X good, as in our first situation, but 6 units for Y good. Computing the utility we have:
\[U \left( 3;6 \right)=3\times3^{2}+5\times6=57\]
When the consumer has more Y good his/her utility is bigger. More Y good is better.