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) = In(Y) + 3*In(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 $30. How many hours will he choose to work? How many units of Y will he consume? (c) Suppose the wage rate decreases to $10 per hour. How many hours will he choose to work? How many units of Y will 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 7 be so that John would consumes half as many units of Y as in part (b)