Utility and Choice Consider the following utility functions. Assume x20,X20. U (x1,x2) = (x2 + 4x2) Uz(X1, X2) = 5x x; U3 (x1,x2) = x1(x2 + 2) U4(x1,x2) = max{x1,x2} U=(x1, x2) = min{3x1 + x2, x1 + 3x2} In your answers, label all intercepts, 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. Draw/plot an indifference curve passing through the bundle (6,2). 4. Does this consumer have convex preferences? Explain briefly. 5. Suppose the consumer is facing prices p = 2, P2 = 1, and has an income of $20. Find the utility maximizing bundle for the consumer. Depending on the utility function, you can use algebra or geometry to find the answer. Utility and Choice Consider the following utility functions. Assume x20,X20. U (x1,x2) = (x2 + 4x2) Uz(X1, X2) = 5x x; U3 (x1,x2) = x1(x2 + 2) U4(x1,x2) = max{x1,x2} U=(x1, x2) = min{3x1 + x2, x1 + 3x2} In your answers, label all intercepts, 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. Draw/plot an indifference curve passing through the bundle (6,2). 4. Does this consumer have convex preferences? Explain briefly. 5. Suppose the consumer is facing prices p = 2, P2 = 1, and has an income of $20. Find the utility maximizing bundle for the consumer. Depending on the utility function, you can use algebra or geometry to find the