Question

Bob is deciding how much labour he should supply. He gets utility from consumption of beer (given by C) and from leisure time (given by L), which he spends hanging out with his friend Doug. This utility is given by the following utility function: U(C, L) = ln(C) + 10 ln(L). Given this utility function, Bob’s marginal utility from consumption is given by: MUC = ∂U ∂C = 1 C and his marginal utility from leisure is given by: MUL = ∂U ∂L = θ L Bob has 120 hours to allocate between working and leisure time. For every hour that he works he earns a wage of 9 per hour. In addition to any income he gets from working Bob also gets $10 from his Grandmother. He spends all of his income (that is, what he gets from working plus the $10 from Grandma) on beer which costs $1 per unit. (a) If Bob devotes L hours of his time to leisure, how many hours does he work? Write out Bob’s budget constraint. (b) Suppose Bob is currently spending exactly half his time on leisure L = 60, could he raise his utility by increasing or decreasing the number of hours he works? Carefully explain your answer. (c) Solve for Bob’s optimal choice of hours worked, hours spent on leisure and beer consumption. Hint: see the solution to the two good problem at the end of this assignment. (d) Suppose Bob’s Grandmother now gives him $100 instead of $10. What would expect would happen to his consumption of beer, the number of hours he takes as leisure and his labour supply? You do not have to solve for Bob’s new optimal choices. However, you do have to explain why he changes his choices. (e) Suppose Bob’s hourly wage rate increases by $1. What would expect would happen to his consumption of beer, the number of hours he takes as leisure and his labour supply? Again, you do not have to solve for Bob’s new optimal choices, but you do have to explain why he changes his choices.