Question

Problem 2 Suppose that Prof. Wu faces three consumption bundles A-1 apples,3 bananas), . B (3 apple, 2 bananas), . C (4 apples, 2 bananas) Assume that Prof. Wu prefers C to B and he is indifferent between Λ and B 1) If Prof. Wu is rational, what additional conditions you need to impose on Prof. Wu's pref erences? Explain why after adding those conditions, we can say Prof. Wu is rational 2) Depict the three consumption bundles on a graph. Then draw two indifference curves that are consistent with Pr()f. Wu's preferences. The thre(: с(nsımptin bundles need to be ()n these indifference curves you dravw 3) Suppose that the price for one apple is $1 and the price for one banana is $1 and Prof. Wu has $5 in his pocket to spend on food. Draw Prof. Wu's budget line. What would Prof. Wu choose among the three consumption bundles if he is rational? Explain

Answer 1

Solution:

Consumption bundles faced by Prof. Wu: A = (1 apple, 3 bananas), B = (3 apples, 2 bananas) and C = (4 apples, 2 bananas)

We are also given that Prof. Wu is indifferent between A and B, and prefers C to B.

1) Since, Prof. Wu is rational, he has to satisfy the conditions of rationality. Rational preferences are the one which satisfy both the conditions, condition of completeness and condition of transitivity.

Under completeness, Prof. Wu can always compare any 2 given consumption bundles. That is whenever faced with 2 consumption choices, he can always decide whether he prefers either one over the other or is indifferent between the two. We already know from the question that how the prof. compares bundles A and B, and how he compares bundles B and C. Completeness property tells that the prof can also always compare bundles A and C.

Under transitivity, we mainly refer to the consistency of preferences. Like under completeness we claimed that prof can compare A and C, under transitivity we can figure out the order of comparison. So, given any 3 bundles choices, if we know how any 2 of the pairs are compared by a person, with principle of transitivity we can always learn the comparison of the third remaining pair. So, for consistency, if Prof. Wu prefers C over B and is indifferent between B and A, it must be that he prefers C over A. In notations, this means

If (C (curly) > B) and (B ~ A), then (C (curly) > A).

2) Since, Prof. Wu is indifferent between bundles A and B, they both must lie on the same indifference curve. Correspondingly, since bundle C is preferred to bundle B (and bundle A as well), bundle C must lie lie on an indifference curve lying higher (in direction of 1st quadrant, that is up and right to the origin) to the one carrying bundles A and B.

Following is the required graph:

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3) We are given price of an apple, Pa = $1 and price of banana, Pb = $1, income to be spend on food, M = $5, and denoting apples by Ap and bananas by Ba

So, the budget line becomes: Pa*Ap + Pb*Ba = M

1*Ap + 1*Ba = 5

Ap + Ba = 5

Taking apples on the horizontal axis and bananas on the vertical axis, Ap/5 + Ba/5 = 1, gives us horizontal intercept as 5 and vertical intercept as 5.

To maximize the satisfaction, Prof. Wu will always consume ON the budget line. So, among the three consumption bundles and given the budget line, it will choose the bundle where Ap and Ba are such that Ap + Ba = 5 (so, subject to the budget constraint).

Among the given 3 bundles, this equation/condition is satisfied only when bundle B is chosen (Ap = 3, Ba = 2, and Ap + Ba = 3 + 2 = 5). So, Prof. Wu would choose bundle B.