Problem 4 (25 Points) Let us denote John's daily hours of work by H, and his hours of leisure by N = 24 H. Suppose that John's only source of income is wages for hours worked. He derives utility from leisure, N, and from the consumption of a composite good, Y. The price of Y is 1. John's utility function is U(Y, N) = |n(Y) + |n(N). (a) Suppose the wage rate is $30 per hour. Write down John's constraint with Y and N as the choice variables. (b) Continue to assume that the wage rate is 530. How many hours will he choose to work? How many units of Ywill he consume? (c) Suppose the wage rate decreases to $10 per hour. How many hours will he choose to work? How many units of Ywill he consume? (d) Continue to assume that the wage rate is $10, but now assume that John also receives non-labour income T. What should T be so that John would consumes halfas many units of Yas in part (b)