Imelda consumes shoes and a composite of all other goods. For Imelda, the income

Question

Imelda consumes shoes and a composite of all other goods. For Imelda, the income effect of a change in the price of shoes is always zero. Imeldas preferences satisfy all of the usual assumptions (i.e. completeness, nonsatiation, transitivity, and convexity). Initially, Imelda consumes 4 units of shoes and 3 units of other goods. I describe this bundle with the coordinates (4,3).

Let Is denote Imelda’s income elasticity of demand for shoes and Io her income elasticity of demand for other goods. We definitely know that (Select the correct answer, and explain why.):

a) Is <1,Io >1
b) Is <1,Io <1
c) Is >1,Io >1
d) Is >1,Io <1
e) Is =1,Io =1
f) We do not definitely know any of the above.

Explanation / Answer

B is the correct answer. If there are no income effects, then there are only substitution effects. This means demand curves are downward sloping and price elasticities are negative. So, we know that both elasticities are less than 0. Therefore, they are less than 1. This is true unless your professor defines price elasticity as an absolute value. Most don't, but there are a few who do. Check your notes for the formula your professor uses. If he uses the absolute value of price elasticity, then the answer is F because we are not given any information about the shape of the demand curve at (4,3).

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