Question

QUESTION 4 Reshad's preferences over goods 1 and 2 are given by the following utility function: U(q1, q2)q2Select all that applies: O a His preferences satisfy "more is better O b. His preferences fail the transitivity assumption C. His indifference curves are downward sloping His preferences are convex D e. He dislikes good 1 Marginal rate of substitution for his preferences is given by MRS12

Answer 1

Answer 4

The correct options are (a) , (b) , (c) and (d)

Lets check option wise which is correct and which is not.

a)

As q₁ increases U(q₁,q₂) will increase. Hence for q₁ is more is better.

If q₂ increases then (1/(1 + q₂)) will decrease and -((1/(1 + q₂))) will increase and hence for q₂ more is always better.

Hence First option is correct.

b)

Suppose (a₁ , a₂) , (b₁ , b₂) and (c₁ , c₂) are Consumption bundles.

If, a₁ - (1/(1 + a₂)) > b₁ - (1/(1 + b₂)) and b₁ - (1/(1 + b₂)) > c₁ - (1/(1 + c₂)) => a₁ - (1/(1 + a₂)) > c₁ - (1/(1 + c₂))

Hence, Transitivity holds

c) As discussed above that more of both goods are always better. As IC shows combinations of bundles that have same utility. Hence if amount of q₁ increases and hence amount of q 2 should decrease in order to have same utility. So, IC is downward sloping.

Hence this option is correct.

d) Let Utility be 0

U(q₁,q₂) = q₁ - (1/(1 + q₂)) = 0 (Note you can take any c = constant)

=> (1 + q₂) = 1/q₁

=>  q₂ = 1/q₁ - 1

In order to be this function to be convex Second derivative of q₂ wrt q₁ must be positive

As :

Which is positive. Hence IC is convex. SO this option is correct

e) As Discussed above more is better for both goods. Hence he likes both the goods. So this Option is Wrong.

f) Formula:

Hence MRS = (1/(1 + q1)²)/1

Hence This option is wrong

Hence the correct options are (a) , (b) , (c) and (d)