Can anyone please help me to solve this with explanation The

Can anyone please help me to solve this with explanation?

The following graph shows indifference curves and a budget set for a consumer with preferences that are increasing in both goods. State whether the following assertions are true or false, and briefly explain your reasoning 1. B is preferred to A 2. B is chosen over C 3. D is preferred to C 4. u(D)-u(C) (D has the same utility as C) 5. A is the optimal bundle for a consumer with this preference and budget set 6. u(A) > u(B) 7. B> D 9. There exists an affordable bundle which will leave the consumer better off than bundle B 10. There exists an affordable bundle which is preferred to bundle C, for which the quantity of one of the goods in the bundle equals zero 11. Suppose there exists a bundle E for which u(E) 2 u(A), then it must be true that E >C 12. it is not possible for two different indifference curves to cross. Hint: Use Tran sitivity

Solution

1. True, B is prefered to A because bundle B has more number of both goods compare to bundle A and for a ration consumer like in this case, more is better and gives higher utility so bundle B will be preferred over bundle A.

2. False, B cannot be chosen over C because bundle B is not affordable according to the given budget line of the consumer, so the consumer can prefer bundle B over C but cannot choose bundle B.

3. False, D is not preferred to C because both the bundle D and C is on the same indifference curve (IC) so both of the bundle give same level of utility to consumer and the consumer is indifferent between bundle D and bundle C thats why no bundle (D and C) is preferred over one another.

4. True, u(D) = u(C), because both bundle is on the same IC curve and all point on the same IC curve gives same level of utility to the consumer.

5. True, A is the optimal bundle for consumer with this preference and budget set because at point A the budget line is tangent to the IC curve and at this point the slope of IC = slope of budget line i.ee., MRS = Px/Py.

6. False, u(A) is not greater than u(B) because bundle B contains more number of both goods compared to bundle A and more number of goods give more utility so u(B) > u(A). Thats why the statement is false.

7. True, B is strickly preferred over D because if we draw an IC which pass through point B then this IC curve must be higher IC than the IC on which bundle D lies. So the bundle B is strickly preferred over bundle D because it is on the higher IC.

8. False, A is not weekly preferred over bundle C because bundle A is strickly preferred over bundle C as it (bundle A) lies on a higher IC curve.

9. False, there is no affordable bundle exists which leave the consumer better off than bundle B as bundle B is the most preferred and it will leave consumer most better off than any other bundle given in the diagram but even this bundle is not affordable so there is no affordable bundle which leave consumer better off than bundle B.

10. False, there is no such bundle exists which is preferred to bundle C and for which the quantity of one of the goods in the bundle equal zero as this point at which quantity of one good in the bundle is zero is only exists at the vertical and horizontal line where IC touches but there is no IC higher than the IC on which C lies which touches any on the axis. so there is no such bundle exists.

11. True, due to the transivity as bundle E is preferred over A ( because u(E) > u(A)) and we know that bundle A is preferred over bundle C. so automatically bundle E will preferred over bundle C.

12. True, It is not possible for two different indifference curves to crosss because a point on higher IC always gives high utility and preferred over the point on the lower utility so if bundle A is preferred over bundle C because of higher IC and the two IC cross each other at any point than this point at which both IC cross gives same level of utility which is not possible.