Penelope’s ratio of marginal utility for a books to crayons (MUB / MUC) is 3/1, while...

Penelope’s ratio of marginal utility for a books to crayons (MU_B / MU_C) is 3/1, while the price ratio of books to crayons (P_B / P_C) is 1.5/1.0. Which of the following is/are true? Hint: you can approach this question by considering the marginal rate of substitution relative to the price ratio (as presented), or you can cross-multiple to put it into the MU_B / P_B and MU_C / P_C format.

A. Penelope can increase utility by decreasing her consumption of books by 4 units and increasing her consumption of crayons by 6 units.

B. One more book provides Penelope with 3 times the utility of one more box of crayons.

C. Penelope can increase utility by decreasing her consumption of crayons by 1 unit and increasing her consumption of books by 1.5 units.

D. Penelope can increase utility by decreasing her consumption of crayons by 3 units and increasing her consumption of books by 2 units.

Expert Solution

It is given that the ratio of marginal utility for a book to crayons is 3:1.

Let the utility achieved from books be 3x and from box of crayons be x.

The ratio of price of book to the price of crayon is 1.5:1.

According to A if Penelope decreases consumption of books by 4 units and increase consumption of crayons by 6 units , then change in utility will be -12x+6x = -6x. So utility decreases by 6x. So this statement is false.

According to statement B, one more book provides Pennelope with three times the utility of one more box of crayons. We can see that this statement is true.

According to statement C, if Penelope increases consumption of books by 1.5 units and decreases consumption of crayons by 1 unit, the utility will increase. We can see that the change in utility is (4.5-1)=3.5 units. So this statement is true.

According to statement D, Penelope can increase utility by decreasing 3 units of crayons and increasing 2 units of books. The change in utility will be 6x-3x = 3x. So this statement is true.

So statements B, C and D are true.

Rahul Sunny answered 2 years ago

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