Time Allocation: Henry is a lawyer with a utility function equal to U=Y+1100L-L2. He works with a law firm on an hourly basis. They pay him $100/hour. He has allocated himself a work-hour time budget of a maximum of 2000 hours per year.

a) (2pts)UsingLagrangianmultipliertechniques,solveforHenry'soptimallevelof work hours and leisure hours per year (out of his 2000 possible work hours).

b) (2pts) Illustrate Henry's optimal time allocation in a diagram with income per month on the y-axis and leisure hours on the x-axis.

c) (2pts) Henry now gets a raise. His wage is now $150 per hour. Find Henry's new optimum mathematically and show the change graphically in your original diagram. Be sure to solve for Henry's new optimal level of leisure, work hours, and income and illustrate your answer on the graph.

d) (2pts)Draw and properly label Henry's labor supply curve for a wage increase from $100 to $150 per hour.