# Irrespective of the amount of cheese doodles and pretzels that Sam consumes, his marginal rate of substitution of cheese doodles for pretzels is 2. Also, irrespective of the amount of cheese...

Irrespective of the amount of cheese doodles and pretzels that Sam consumes, his marginal rate of substitution of cheese doodles for pretzels is 2. Also, irrespective of the amount of cheese doodles and pretzels that Sally consumes, her marginal rate of substitution of cheese doodles for pretzels is 3. Initially Sam and Sally are allocated 10 cheese doodles and 10 pretzels each. How is this not Pareto optimal and why would an allocation that gave Sam all of the cheese doodles and Sally all of the pretzels would make both of them better off.

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### 3 Answers

Irrespective of the amount of cheese doodles and pretzels that Sam consumes, his marginal rate of substitution of cheese doodles for pretzels is 2. This implies that Sam gains the same level of utility from either consuming 2 cheeze doodles or one pretzel.

On the other hand Sally's marginal rate of substitution of cheese doodles for pretzels is 3. This implies that Sally derives the same level of utility from 3 cheese doodles or one pretzel.

Initially, if Sam and Sally are allocated 10 cheese doodles and 10 pretzels each, the level of utility that Sam derives in terms of cheese doodles is 20 + 10 = 30. For Sally, this figure is 30 + 10 = 40. This gives the total level of utility as 30 + 40 = 70.

On the other hand, if Sam is given all the cheese doodles and Sally is given all the pretzels, their level of utility in terms of cheese doodles is 40 and 60 respectively. The total level of utility now is increased to 40 + 60 = 100.

This is the reason why the latter allocation of cheese doodles and pretzels would make both of them better off.

Irrespective of the amount of cheese doodles and pretzels that Sam consumes, his marginal rate of substitution of cheese doodles for pretzels is 2. This implies that Sam gains the same level of utility from either consuming 2 cheeze doodles or one pretzel.

On the other hand Sally's marginal rate of substitution of cheese doodles for pretzels is 3. This implies that Sally derives the same level of utility from 3 cheese doodles or one pretzel.

Initially, if Sam and Sally are allocated 10 cheese doodles and 10 pretzels each, the level of utility that Sam derives in terms of cheese doodles is 20 + 10 = 30. For Sally, this figure is 30 + 10 = 40. This gives the total level of utility as 30 + 40 = 70.

On the other hand, if Sam is given all the cheese doodles and Sally is given all the pretzels, their level of utility in terms of cheese doodles is 40 and 60 respectively. The total level of utility now is increased to 40 + 60 = 100.

This is the reason why the latter allocation of cheese doodles and pretzels would make both of them better off.

Marginal rate of substitution of X for Y is defined as the maximum amount of Y that a person is willing to give up to obtain an additional unit of X. Therefore, your first paragraph is entirely wrong. MRS of cheese doodles for pretzels implies that a person derives the same level of utility from consuming either one cheese doodle or 2 pretzels. Following this definition, I reasoned like you and concluded that the question has a wrong answer.

I am sorry. The formatting seems to be messed up in the question above. I'll try to repeat correctly in this comment.

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I am browsing my microeconomics textbook test bank, but I find the given answer for the following problem suspicious.

Problem: Irrespective of the amount of cheese doodles and pretzels that Sam consumes, his marginal rate of substitution of cheese doodles for pretzels is 2. Also, irrespective of the amount of cheese doodles and pretzels that Sally consumes, her marginal rate of substitution of cheese doodles for pretzels is 3. Initially Sam and Sally are allocated 10 cheese doodles and 10 pretzels each. Which of the following statements are true?

Answer: The allocation is not Pareto optimal. An allocation that gave Sam all of the cheese doodles and Sally all of the pretzels would make both of them better off.

At first glance, the answer seems implausible since Sally derives more utility from consuming cheese doodles relative to utility gained from consuming pretzels than Sam. I did a sketch of the Edgeworth box that seems to confirm my suspicion. After the suggested reallocation, Sally is on an indifference curve that corresponds to a lower level of utility than the initial one. Am I right or did I misunderstand the question completely?"