11. (4) I'm going to get rid of the budget line to ask a conceptual question. First conrm to your satisfaction that the following utility functions all have the same MRS, y/x, but different marginal utilities of x. (No need to turn this in, but work it through on your own.) Uilxy) = X'5v'5; Uztxy) = x2 f: U3(X,y) = ln x+ in y; These are very different individuals but have the same MRS. Suppose that we give each one the same amount of x and the same amount of y to start with. Would they have any reason to trade (x for y, or y for x) with each other? Explain. Think hard about this. Suppose that you knew these functional forms and you were giving out x and y. If your objective is just to maximize U1 + U; + U3 , how would you allocate x and y? What problems do you see in just adding up utilities like this to get total utility? (This is openended and can support different views.) 12. (2) I explained that l deliberately chose to title this rst major section of the course "consumer theory". This is legitimate; I am indeed teaching consumer theory. What does \"theory" mean here