Suppose the consumer's preference is given by c-1 1-o u(c, l) = + In l, o> 0 (1) where c is the consumption and I is the leisure. The consumer's problem is to choose (c, !) to maximize (1) subject to the budget constraint (2) c = w(hl) where w is the real wage and h is the total number of time available. (a) Set up the constrained optimization problem. Write out the Lagrangian and first order conditions. (b) From your calculation in (a), derive an equation that pins down the relationship be- tween optimal choice of working hours n = h - 1 and real wage w. (c) Take derivative on both sides of the equation you get in (b) with respect to w, calculate on. Determine whether the slope of labor supply curve, i.e. is positive or negative. [Hint: your answer should depend on the parameter o.] On* dw