The given statement is not correct. As the price rises, the total expenditure by the family may either increase, decrease or remain same depending upon elastically of demand:
(i) In case of less elastic demand, spending will increase if the price rises (like in case of necessity goods such as salt, medicines, etc.).
(ii) In case of highly elastic demand, spending will decrease if the price rises (like in case of luxury goods such as AC, Curved LED TV. etc.).
(iii) In case of unitary elastic demand, spending will not change with rise in price like in case of normal goods such as scooter, refrigerator, etc.).