Utility and Choice Consider the following utility functions. Assume x1 2 0, X2 2 0. U1 (X1, X2) = (X1 + 4x2)2 U2 (X1, X2) = 5x]x2 U3 (X1, X2) = X1(X2 + 2) U4(X1, X2) = max{x1, x2} Us(X1, X2) = min{3x1 + x2, X1 + 3x2} In your answers, label all intercepts, kinks, coordinates, slopes, and axes. Give an answer to the following two questions for each of the first three utility functions above: 1. Derive an expression for the Marginal Utility of each good. 2. Compute the Marginal Rate of Substitution at the bundle (2,4). Give an answer to the following three questions for each of the five utility functions above: 3. Write an equation for the indifference curve of this consumer passing through the bundle (6, 2). Draw/plot this indifference curve. 4. Does this consumer have convex preferences? Explain briefly with reference to the upper contour sets of the indifference curves (i.e. their at-least-as-good-as sets)