An individual consumes two goods x and y deriving utility characterised as Cobb Douglas as follows: . Assume that her income is , the price of good x is while the price of good is

(a)Find the marginal utility of x (), then the marginal utility of y () [6 marks]

(b)Given your results in part (a), does the "more is better" assumption hold on the above utility function? [4 marks]

(c)Use the marginal utilities computed to find the marginal rate of substitution (MRS) for this consumer. [5 marks]

Using the MRS you found in part (c), what is the optimal consumption bundle? [Hint: Use the tangency condition. Then, insert your result into the budget line. This should give you the optimal amount of good x and the optimal amount of good y