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Question: the known values are 9 hourly wage w3 03 y1...

Question details

The known values are:
θ=9
Hourly wage (W)=3
β=0.3
Y1= 20 000
1. (40 MARKS) Bob is deciding how much labour he should supply. He gets utility from con sumption 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: UC. L) = ln(C) + θ ln(L) where the value of was determined by your student number and In(C) denotes the natu- ral logarithm of consumption etc. Given this utility function, Bobs marginal utility from consumption is given by: and his marginal utility from leisure is given by: Bob has 120 hours to allocate between working and leisure time. For every hour that he works he earns a wage of W. The value of this wage was determined by your student number. In addition to any income he gets from wking 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 Bobs budget constraint (b) Suppose Bob is currently spending exactly half his time on leisure L 0, could he raise his utility by increasing or decreasing the number of hours he works? Carefully explain your answer (c) Solve for Bobs optimal choice of hours worked, hours spent on leisure and beer con- sumption. Hint: see the solution to the two good problem at the end of this assignment (d) Suppose Bobs Grandmother now gives him S100 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 Bobs new optimal choices. However you do have to explain why he changes his choices (e) Suppose Bobs 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 Bobs new optimal choices, but you do have to explain why he changes his choices.
2. (30 MARKS) Jane lives for two periods. In the first period of her life she earns income Yi The value of Yi was determined by your student number. In the second period of her life, Jane is retired and does not earn any income. Janes decision is how much of her period one income should she save (S) in order to consume in period two. For every dollar that Jane saves in period one she has (1 r) dollars available to spend in period two, where r is the interest rate. Jane gets utility from consumption in period one (given by Ci) and in period two (given by C2) according to the following utility function: U(C,2)-In(C1 BIn(C2) where the value of B ws determined by your studen number. Given this utility function Janes marginal utility from consumption in period one is given by: au 1 and her marginal utility from consumption in period two is given by ουβ The parameter β describes how impatient Jane is. The lower the value of β the more she prefers consumption in the present (period one) to consumption when retired (period two) (a) What is Janes budget constraint in period one? What is her budget constraint in period (b) Combine these two budget constraints in order to have a single budget constraint that two? relates C and C2 to Janes income and the interest rate. (c) Assume Jane is currently saving exactly 40% of her income in period one. Could she increase her utility by increasing or decreasing the amount she saves? Carefully explain your answer (d) Solve for Janes optimal choice of savings, and how much to consume in periods one and two. Hint: see the solution to the tuo good problem at the end of this assignment.
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