Question

12.She has two friends, Michael and Peter and Peter's is given by u(x, ) 4. Anne's utity function is given by u(r\, t2) Michael's utility function is given by u(x, x _ 10+2112 as Anne? And who has indifference curves with similar -1.Who has the same preferences shape as Anne's indifference curves? Explain

Answer 1

Solution:

Anne's utility function is: u(x1,x2) = x1*x2

This means that Anne's utility is increasing in consumption of both goods, x1 and x2.

Among the given utility functions of her two friends, Peter's utility function is negative of that of Anne, implying that Peter's utility is decreasing in both goods' consumption. Thus, the preference of Peter is rather opposite to that of Anne's.

Other friend, Michael, has utility function indicating positive relation in utility level and both goods consumption: the goods are in denominator but there is a negative sign in front, so two negatives making a positive. In other words, utility of Michael is increasing in consumption of both goods.

Thus, Michael has the same preferences as Anne.

The indifference curves, can be noticed by the given utility functions, are similar for Anne and Michael (since consumption can not be negative, ICs for Michael will lie in first quadrant itself). The only difference is that as we move away from origin (towards the north-east direction), the utility or satisfaction level as marked by ICs, increases for Anne while it decreases for Michael (since, Michael's utility decreases in consumption of both the goods).