Sylvia allocates her monthly income between Food and Housing. Her budget share spent on food in a given month is always 30%, and for Sylvia, food is a "necessity" (income elasticity between zero and one)
Derive the maximum and minimum values for the income elasticity of demand for housing.
The weighted (by budget share) sum of income elasticities will sum to one. Thus to derive bounds for income elasticity of housing, we use the following equation:
.3?F + .7?H = 1
Rearrange this equation:
?H = (1 - .3?F)/.7
We are told that food is a necessity (0 < ?F < 1 ) which tells us the range of ?H:
minimum ?H = 1
maximum ?H = 1.43
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