Suppose an individual has an endowment of T units of time that she can devote to labor supply (L) or leisure (R), so T=L + R. There is one consumption good in the economy, denoted C, of which she has no endowment. Her endowment bundle is thus (eR, eC)=(T, 0). Let the price of the consummption good be one, and the wage w.

-Show that if the individual has Cobb-Douglas preferences over leisure and consumption bundles, then her labor supply is independent of the wage (i.e, her choice of R and L does not depend on w).