Antonio's utility function for the goods X and Y is U(X,Y)= 2( \(\sqrt(X)\) + \((Y)\) ).

A. What is the MRSxy? What is the MRSyx?

B. Is this a well behaved utility functions?

C. If M=$1800 and both goods cost $1 per unit, what is the optimal bundle? Now suppose the price of good X rises to $2.

D. What is the new optimal bundle?

E. What is the compensating variation for this price change?

F. Decompose the uncompensated effect of the increase in price into substitution and income effects

H. If you used the uncompensated demand curve to calculate the change in consumer surplus, would your calculation be too high or too low?

I. Provide a graph showing the initial outcome, the outcome after price change, the income effect, the substitution effect, and the uncompensated effect of the price change