Time allocation, assignment help

Time allocation, assignment help

Henry is a lawyer with a utility function equal toU=Y+1100L-L^2 .  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) (3pts) Using Lagrangian multiplier techniques, solve for Henry’s optimal level of 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) (3pts) Henry now gets a raise.  His wage is now $150 per hour.  Find Henry’s new optimummathematically and show the change graphically in your original diagram. Be sure to solve forHenry’s new optimal level of leisure, work hours, and income and illustrate your answer onthe graph.d) (2pts) Draw and properly label Henry’s labor supply curve for a wage increase from $100to $150 per hour.