The earnings of teens seem to go to their own expenses, rather than family necessities. This was quite evident in the higher personal clothing expenses of employed teens in low-income families in 1997-98 compared with nonemployed teens in such families.
Further, in single-parent families, the employment of a teenager did not have a significant association with changes in any budgetary component. For married-couple families, teen employment had a significant association with increases in spending on food away from home and entertainment, which are not typically considered family necessities.
These data are a product of the BLS Consumer Expenditure Survey program. Additional information is available from "Teenagers: employment and contributions to family spending," by David S. Johnson and Mark Lino, Monthly Labor Review, September 2000.
Bureau of Labor Statistics, U.S. Department of Labor, The Economics Daily, Teens with jobs—where does the money go? at https://www.bls.gov/opub/ted/2000/oct/wk5/art03.htm (visited February 08, 2023).