Consider a worker who maximises utility from consumption, u(c), and leisure, v(1), subject to the following budget constraint: PcW(H-1), (2) where P is the price level, W is the wage rate and H represents the units of time the worker has to allocate between working and leisure. i. Solve the worker's maximisation problem and provide an equation that relates the real wage rate to the optimal allocation between leisure and consumption. ii. Now assume that utility takes the following form: c1-0 u(c) = = (1 - 0) - v (l) = (H - 1) 1+ (3) 1+ Derive marginal utility of consumption and leisure, substitute them into the op- timality condition you derived in (i) and use the budget constraint to solve for 1* and c* (i.e., c* should not appear in your solution for 1* and vice versa). [5]