Tommy Twit’s mother measures the departure of any bundle from her favorite bundle for Tommy by the sum of the absolute values of the differences. Her favorite bundle for Tommy is (2, 7), that is, 2 cookies and 7 glasses of milk. Tommy’s mother’s indifference curve that passes through the point (c, m) = (4, 5) also passes through

a. the points (4, 7), (2, 5), and (2, 9).

b. the point (2, 7).

c. the points (2, 3), (6, 7), and (4, 9).

d. the point (6, 3).

e. None of the above.

How to solve this question? I thought that it is enough to find a line passing through two points given however then the equation would be $y=9-x$ however the points given does not fit to the equation. Correct answer given in a questionbank is C. I have no additional info regarding this question and i have to admit yes it is badly stated.


The first sentence means that Tommy's mother's utility function over a bundle $(x,y)$ equals \begin{equation*} u(2,7)-u(x,y)=|x-2|+|y-7| \end{equation*} since she measures the disutility of this bundle with respect to the most preferred one by the "sum of the absolute values of the differences".

Therefore the utility that she associates with the point $(4,5)$ equals \begin{equation*} u(4,5)=u(2,7)-(2+2)=u(2,7)-4 \end{equation*}

You are asked to find the indifference curve that passes through the point $(4,5)$, i.e. the set of bundles $(x,y)$ that satisfy \begin{equation*} u(x,y)=u(4,5) \end{equation*} which you can write \begin{equation*} u(2,7)-u(x,y)=u(2,7)-u(4,5)=4 \end{equation*}

The question is therefore: which of the options a), b), c), d) (if any) contain only bundles $(x,y)$ such that $u(2,7)-u(x,y)=4$? You simply have to compute $u(2,7)-u(x,y)$ for all the proposed bundles, given the formula above, and check whether the value equals 4 or not.

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