ADVANCED MICROECONOMIC THEORY HOMEWORK 1 1. Suppose that a consumer is faced with the following utility function: U Ax y Where A, ẞ and α are constants. a) Does the assumption of monotonic hold for the above-mentioned equation? b) Calculate the Marginal utility of X and Y? c) Determine the MRSx, y d) State and explain what happens as successive units of x are consumed? [2] [2] [2] [2] 2. Consider the utility function U [ x y ]1/ , which is sometimes called the constant elasticity of substitution (CES) utility function. a. Calculate the marginal utilities for X and Y [4] b. Determine whether MUx and MUy are decreasing or not. [2] 3. Draw indifference curves to represent the following types of consumer preferences. [2 for each] a) I like both margarine and jam, and always get the same additional satisfaction from an ounce of margarine as I do from 2 ounces of jam. b) I like hotdogs, but neither like nor dislike coke. c) I like potato chips, but dislike sweets. d) I like apples and oranges, but I only want 3 units of apples for every unit of oranges. 4. Explain the reasons that could result in intransitive preferences for a consumer? /end [3]