Question

This question is belong to Microeconomics.

True/False: based on the information given, state whether you think each statement in quotation marks is true (the statement must hold) or false (there are situations consistent with the information given where the statement does not hold).

If your answer is true, explain why this statement must hold. If your answer is false, you can give an example where the statement does not hold. Explain using no more than 5 sentences.

(a) Suppose Sam's preference over fish and vegetables is rational, continuous, monotone and convex. He discovers an online store that delivers everyday to his house. Package A gives him 10 catties of fish and 30 catties of vegetables per month. Package B gives him 30 catties of fish and 10 catties of vegetables per month. Package C gives him 20 catties and fish and 20 catties of vegetables per month. Sam prefers package A to package B. (!! give a graph with all three bundles)

1. (5 pts) Sam must prefer package C to package A.

2. (5 pts) Sam's marginal rate of substitution at bundle A is greater than or equal to 1.

Answer 1

Answer:

1. Sam must prefer package C to package A. Its False.

Since Sam's preference over fish and vegetables is rational, continuous, monotone and convex and there is no delivery cost and already Sam prefers package A to package B (A>B) which indicates that Sam prefers vegetables to fish. Therefore if Sam prefers package C to package A (C>A) the quantity of vegetables in package C must be greater than the quantity of vegetables in package A but in package C vegetables is less i.e. 20<30. Hence, Sam must not prefer package C to package A.

A graph with all three bundles A, B and C given below:

2. Here the utility curve of Sam is straight line hence the marginal rate of substitution equal to 1.