Question

QUESTION 5 Reshad's preferences over goods 1 and 2 are given by the following utility function: Uq1. 42) Reshad's income is $60 and the prices are given by p1-3 and p2-2. Select all that applies: 1+q1 42 41 a. Marginal rate of substitution for his preferences is given by MRS12 When he consumes zero amount of good 1, his MRS is equal to 1. c. It is optimal for him to consume 20 units of good 1. @dㆎt is optimal for him to consume 30 units of good 2. ■ eff the price of good 1 doubles, he will increase his consumption of good 2.

Answer 1

In this case

$MU_{q1}=\frac{\partial U(q_{1},q_{2})}{\partial x}=1$

$MU_{q2}=\frac{\partial U(q_{1},q_{2})}{\partial q_{2}}=-\frac{(-1)}{(1+q_{1})^{2}}=\frac{1}{(1+q_{1})^{2}}$

Marginal Rate of substitution, MRS_{12 is given by}

$MRS_{12}=\frac{MU_{1}}{MU_{2}}=(1+q_{1})^{2}$

Income, I=60

p₁=3

p₂=2

Budget line will be given by

60=3q₁+2q₂

Utility maximization is arrived when

$MRS_{12}=\frac{p_{1}}{p_{2}}=\frac{3}{2}$

$(1+q_{1})^{2}=\frac{3}{2}$

q₁=0.224745

60=3*0.224745+2q₂

q₂=(60-3*0.224745)/2=29.66

a) False

Refer to the derived expression for MRS

b) True

MRS=(1+q1)²=(1+0)²=1

c) False

Refer to optimal bundle arrived for good 1 and good 2

d) True

Refer to optimal bundle arrived for good 1 and good 2

q₂=29.66, we can round it to 30

e) False

Budget line will be given by

60=6q₁+2q₂

Utility maximization is arrived when

$MRS_{12}=\frac{p_{1}}{p_{2}}=\frac{6}{2}$

$(1+q_{1})^{2}=3$

q₁=0.732051

60=6*0.732051+2q₂

q₂=(60-6*0.732051)/2=27.80358