She is indifferent between bundle (6, 5) and bundle

(12, 3). What is the utility function for goods x and y? Hint: What is the shape of the indifference curve?

A consumer is willing to trade 4 units of x for 1 unit of y when she is consuming bundle (8, 1).

She is also willing to trade in 1 unit of x for 2 units of y when she is consuming bundle (4, 4). She is indifferent between these two bundles. Assuming that the utility function is Cobb–Douglas of the form U(x, y) = x α y β, where α and β are positive constants, what is the utility function for this consumer?

Was there a redundancy of information in part (b)?

If yes, how much is the minimum amount of information required in that question to derive the utility function?