Consider a consumer whose preferences over x1 and x2 are characterized by the following utility function: U(x1, x2) = x 2 1 + x2 a) Does the consumer have convex preferences? Hint: The bundles (1, 9) and (3, 1) lie on the same indifference curve. Consider whether the "average" of these two bundles is preferred to the original bundles.

b) Does the consumer have monotonic preferences? Show this using marginal utilities. Note: If U(x1, x2) is monotonic with respect to only one commodity, state which commodity it is.

c) Derive the marginal rate of substitution as a function of x1 and x2.

d) What is the slope of the indifference curve at the point (4,3)?

5. What type of preferences does this consumer have over x1 and x2 given the following utility functions? Provide a brief rationale for each of your answers.

a) U(x1, x2) = 4x1 + 5x2

b) U(x1, x2) = x 1/2 1 x 1/2 2

c) U(x1, x2) = min{x1, 3x2}

I don't understand how to compute these, I've been going over the formulas given and I can't understand it.