For each of the following utility functions for goods x and y 2.1. calculate the marginal of utility for x; 2.2. calculate the marginal utility for y; 2.3. calculate the marginal rate of substitution; 2.4. graph two indifference curves; identify which one yields higher utility; 2.5. using the definition of convex preferences, verify whether the preferences are convex. Choose two bundles that belong to the same indifference curve. Label them a and b. Define a third bundle that mixes one half of each of the previous ones. Label it c. Evaluate whether it is at least as good as both a and b. 1. u(x, y) = (x 2)2 (y 3)2 2. u(x, y) = x2 + 2xy + y2 3. u(x, y) = x + y 4. u(x, y) = x2 + y2