For problems 1, 2, 3, we consider an agent Ann who consumes goods and y and has a utility U(x, y) = x²y. In these problems, Good x costs P₂ and good y costs Py. (1) Ann has I to spend. (a) Write out Ann's utility maximization problem. (b) Find: MU, MUy, and MRS zy- (e) Write out Ann's tangency condition. What is the other equation needed to solve for Ann's demand? (d) Find Ann's demands for x and y as functions of Pz, Py, and I. (Partial credit if you do this only for I = 30, P₂ = 5 and Py = 2.)

The term utility in general refers to the satisfaction earned from usage of a particular product or service. Utility always plays an important role because it influences various important elements like demand & thereby the price of the good or service as…