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Consumersurplusproblem

# Consumersurplusproblem - Problem 2.49 old edition 2.50 new...

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Problem 2.49 old edition, 2.50 new edition Original Problem: Someone consumes a single good x and her indirect utility is v ( p, y ) = G A ( p ) + ¯ y η y 1 - η 1 - η , where A ( p ) = Z p 0 p x ( ξ, ¯ y ) dξ. (a) Derive the consumer’s demand for x and show that it has constant income elasticity equal to η . (b) Suppose that the consumer has income equal to ¯ y and the price of x rises from p to p 0 > p . Argue that the change in the consumer’s utility caused by the price change is - Z p 0 p x ( ξ, ¯ y ) dξ < 0 . Interpret this measure. Critical Comment: This problem maintains that there is only one commodity, x . If there is only one commodity then from the budget it follows that x ( p, y ) = y/p and if this is the case, the income elasticity of demand for x can only be 1. Moreover, the indirect utility function proposed in the problem v ( p, y ) = G A ( p ) + ¯ y η y 1 - η 1 - η is not defined in a straightforward way when η = 1. I think this becomes a much more reasonable problem if it is recast something like this.

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