Working with the labor-leisure trade-off

Bill faces a wage of $10 per hour (W = $10/hr) and is trying to decide how to best allocate his daily 24 hours between work (which he does not like) and leisure ( which he thoroughly enjoys). We’ll label daily work hours as “H” and his choice of Leisure hours as “L”. Bill has a very successful spouse- Hillary- who generates $500 per day as an attorney. For Bill’s problem, we can consider this $500 per day as “unearned income”, labeled Y*.

A) Please write a formula for Bill’s budget line where “Y” will be Bill’s total available income from both his own work and his unearned income.

B) Please construct Bill’s daily budget line with total income Y on the vertical axis and his hours of leisure, L, on the horizontal axis (this axis has a maximum value of 24 hours).

C) What is the price of Bill’s leisure time?

D) Given the above information, assume that Bill decides to allocate his time by choosing 20 hours of lesuire a day. What would be his available daily income, Y, given this choice? Please show this combination on your diagram above in question B.

E) Bill considers leisure a normal good. Hillary takes a poorly paying job in public service which lowers Bill’s unearned income from $500 per day to only $100 per day. Will he desire to work more or less? Please explain