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Show that both goods are essential if tastes can be represented by Cobb- Douglas utility functions.

  1. Show that both goods are essential if tastes can be represented by Cobb- Douglas utility functions.

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Answer #1

Suppose tastes can be represented by a Cobb- Douglas utility functions u(x1,x2) = x1x2(1-) .

Therefore the utility by consuming (0,0) is u(0,0) = 0.

Let consider the utility from a bundle (x1,0) — i.e. a bundle with no x2 consumption. Utility from such a bundle is u(x1,0) = x1 (0) = 0 exactly what it is when the consumer doesn’t consume anything at all.

Thus, x2 is essential. And by similar reasoning, x1 is essential.

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