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utility functions and budget constraints

A households utility is given by:
u(C, 1 − L) = C^0.5 + (1 − L)^0.5
where C is the total household consumption and L is the labor supply of the child. 0<L<1 and L+e=1, where e is education.
The household budget constraint is:
C=Y=Ya+wL
where Y is total household income, Ya is adult income and is assumed to be fixed, w is the wage children recieve, and L is defined as above.

-How can you go about finding L*? normally it is where the budget constraint and utility functions slopes are equivalent, but I am confused with the budget constraint and exactly what (1 - L) is supposed to be

Solution Summary

Given the utility function & the budget constraint, the maximizing condition is determined.

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