A consumer's preferences are representable by the following utility function:
u(x,y)= x² + y. (i) Obtain the MRS of the consumer at an arbitrary point (x,y), where x > 0 and y > 0
(ii) Suppose the price of the second good ( y) is 1 , and the price of the first good ( x) is denoted by p>0. If the consumer's income is m>0, obtain the optimal consumption bundle of the consumer (in terms of m and p ). [Caution: make sure you cover cases in which m is relatively low, as well as cases in which m is relatively high.]