# ADVANCED MICROECONOMIC THEORY HOMEWORK 1 2017 ```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. 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

b. Determine whether MUx and MUy are decreasing or not.

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

```