2. (Endowment Economy) Suppose two goods are leisure (denoted by R) and a composite con- sumption good (denoted by C). The consumer is endowed with 18 hours, and she can decide how many hours to work (L) and rest (R). The consumer has a utility function u(C,R) = C*R3?, and the unit price of the composite consumption good is denoted by p and the hourly wage rate is denoted by w. (a) Derive the consumer's demand functions for R and C by using the Lagrangian optimiza- tion method (not asked in Canvas). (b) Based on (a) or otherwise, find the optimal consumption levels of C' and R when p = 3 and w = 2