Question

Problem 1:
(a) Prove the statement: Two indifference curves can never intersect.(b) Verify whether the following statement is true or false, and explain.

A choice is rational when an indifference curve is tangent to the budget line.

(c) I am indifferent between consuming bundle 1 (5 cookies and 10 chocolates) and bundle 2 (10 cookies and 5 chocolates). I am also indifferent between bundle 2 and bundle 3 (9 cookies and 15 chocolates). If I also stated that I prefer bundle 3 to bundle 1, what axiom of indifference curve is violated from my last statement? Explain.

Answer 1

a) The property of two indifference curves can never intersect is shown below.

Suppose on indifference curve 1, we have two points A and B, so according to the property of the indifference curve , the consumer would be indifferent between A and B.

And now on indifference curve2, we have B and C as the points which implies consumer is indifferent between B and C. But consumer cannot be indifferent between A and C. So this is a contradiction . Hence indifference curves cannot intersect.

This is shown in the figure above.

b) A rational choice would be when the slope of indifference curve is same as the slope of budget line. This point would give us the maximum utility given the budget. This is because if we are below the budget line , it implies the consumer is not utilising the income completely. If the individual is on budget line but not on the highest indifference curve , it means he is not having maximum utility.

So when the consumer is at the highest indifference curve which is tangent at the budget line, it is the rational choice.

The statement is true.

c)If consumer is indifferent between bundle 1 and bundle 2 and indifferent between bundle 2 and bundle 3, then according to axiom of transitivity, he should also be indifferent between bundle 1 and bundle 3 and not prefer bundle 3 to 1

So axiom of transitivity is being violated.