Analysis of Bob's Budget Constraint and Optimal Choices in Time Allocation and Beer Consumption

QUESTION 1
(a) Bob has 120 hours to allocate between working and leisure time. If Bob devotes L hours
of his time to leisure. He therefore take
(120-L) hours to work
Bob’s budget constraint. Every hour he works he earns a wage of W but he works for
(120-L)hours
And therefore the total amount he received is
$(120-L)W where W=5
$(120-L)5
He also get $10 from grandmother. So his total income
(120-L)5 +10
Again we realize that beer is $1 per unit. So his total expenditure on beer is
( (120-L)5+10)units and L is the leisure time
Which is Bob’s budget constraint.
(b) Bob is currently spending exactly half his time on leisure L=60
We know that utility is the total satisfaction received from consuming a good or service.
Hence he can raise his utility by increasing the number of hours he works. This is

because when he take many hours working his income also increases this is because its
income is directly proportional to the amount he spend on beer hence increase its utility.
On the other hand, if he decreases the number of hours his working this will ensure that
his income reduces and hence the amount that he will spend on beer consumption will be
low leading to decrease in utility.
(c) To solve for Bob’s optimal choice of hours worked, hours spent on leisure and beer
consumption. We have that Bob’s optimal choice of hours spent on leisure and beer
consumption satisfies
MRS= L/θC
=L/5C
where L is the leisure time and C is the consumption of beer and the value of θ is
determined by student number which is 5. Suppose we assume that he spend L hours on
leisure then he spend (120-L) hours working which implies that he spend (120-L)hours
consuming beer. Hence we have that
QP/QB =L/(120-L)
(d) Bob’s Grandmother now give him $100 instead of $10. Therefore his amount that he
spend on beer consumption would increase this is simply because his income has
increased. Furthermore, the number of hours he takes as leisure would also rise because
most of the time he will take consuming beer instead of working because of the increase
of income due to Grandmother’s addition of $100.

(e) Bob’s hourly wage rate increase by $1 will mean that the number of units of beer being
consumed would rise this is due to increase on the hourly wage. The number of hours he
take as leisure would reduce this is simply because he would like to work hence
spending many hours working due to increase on hourly wage. Moreover, his labour
supply would rise because he spend most of hours working due to hourly wage increase
and this make it possible for him to change his choices (Driscoll, 2003).
QUESTION 2
(a) Jane’s budget constraints in period one. The utility function U(c1,c2 )=ln(c1) + βln (c2)
Jane’s marginal utility from consumption in period one is given by
MUC1=∂U/∂C1=1/C1
And her marginal utility from consumption in period two is given by
MUC2=∂U/∂C2=β/C2
And so his marginal rate of substitution is
MRS=C2/C1β where β is determined by student
number and its value is 0.1
MRS=C2/0.1C1
Jane has an income of Y1=100,000 according to the student number. 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.
Y1=1C2
And her budget constraint in period two is
Y1 = 0.1(1+r)C1 where Y1=10000