Problem 2 (25 points) Kate and William are a couple trying to decide whether or not to move to New York from London. In New York, William would earn $100000 per year for the next 30 years whereas he would earn $y per year in the same time frame in London. Kate's annual salary in New York and London is $z and $130000 respectively, for the next 30 years. (a) If the annual interest rate is 5%, what is the net present value of Kate and William's life-time earnings in New York (as a function of z)? (10 points) (b) How about in London (as a function of y)? (5 points) (c) Suppose it costs $100000 per person to move which is a one-time cost paid in the same period they start working. For what combinations of z and y is William a tied mover? (10 points)