1. Caty consumes only goods X and Y . Her utility function is: U(X; Y ) = min{X; Y}. We are given that PX = 3; PY = 6, and Caty's income is 18.

Calculate Caty's optimal consumption bundle, (X, Y). (Hint: Since Caty's indif-ference curves are not smooth and \curvy", we cannot use MRS = MRT to solve for the optimal bundle. Draw a diagram to see where Caty's optimal bundle must be on her IC. How do you characterize this bundle mathematically?)

2. John consumes only goods X and Y . His utility function is: U(X, Y ) = X + 2Y . We aregiven that PX = 3; PY = 3, and John's income is 30.

(a) Calculate the slopes of John's budget constraint and his indierence curves, as viewedwith Y as the vertical axis and X as the horizontal axis

(b) Calculate John's optimal consumption bundle, (X, Y). (Hint: Since John's indif-ference curves are not smooth and \curvy", we cannot use MRS = MRT to solve for the optimal bundle. Draw a diagram to see where the John's optimal bundle must be on his IC. How do you characterize this bundle mathematically?)