Consider the utility function U(x, y) = 1 – [(1-x)^2]/2 + ln (x) + ln (y), where x, y 0. Fix a utility level U bar 0.

Consider the utility function U(x, y) = 1 – [(1-x)^2]/2 + ln (x) + ln (y), where x, y > 0. Fix a utility level U bar > 0.

(A) Show that there exists a function that describes the indifference curve through U bar.

(B) Fix U bar = 1, and the point (x, y) = (1, 1) on the corresponding curve. Compute MRS at this point.