A worker has a total time endowment of 1, which he allocates between

leisure l and labor n. He faces a wage rate w > 0 in the labor market.

He derives utility from both consumption

c and leisure l according to

the following function U(c, l) =

c + l. Use the Lagrange method

to fifind his optimal choices l, n , and c . In particular, how does his

labor supply depend on his wage rate w?