Question

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 ʺnecessityʺ (income elasticity between zero and one). Derive the maximum and minimum values for the income elasticity of demand for housing.

Answer 1

To derive the maximum and minimum alues of income elsaticity of demand for housing .

Because Sylvia spend 30% of er budget on food i.e 0.3 on food and 0.7 on housing.

Make a equation that the weighted sum of income ealsticiites will sum to one, i.e:

0.3 E_F + 0.7 E_H = 1.

E_H = (1 - 0.3 E_F ) / 0.7

Now, we know from the question that E_F lies between 0 and 1 , this implies 0<E_F <1.

Therefore, Minimum E_H is When E_F = 1

By putting E_F= 1, we get E_H = (1- 0.3)/0.7 = 0.7/0.7 = 1

Minimum E_H = 1

And Maximum E_H is when E_F = 0

By putting E_F = 0, we get E_H = (1/ 0.7) = 1.43

Maximum E_H = 1.43

Maximum value of income elasticity of housing = 1.43 and minimum values of income elasticity of housing = 1.

1< E_H < 1.43