1.   Douglas Cobb has preferences over leisure, L, and consumption, C , described by the        utility function U(L, C) = La CF , with and 0 < a < 1 and 0 < F < 1.  Cobb’s time endowment is T; Cobb’s nonlabor income is V; and Cobb’s wage per unit of time worked is w .

a.   Find Cobb’s reservation wage.

b.   Show that Cobb’s labor supply function is H ∗  = () T − () (), for values of w greater than or equal to Cobb’s reservation wage.

c.   Accurately draw Cobb’s labor supply curve (i.e., the ceteris paribus relationship between H and w), both for V = 0 and for V > 0.

d.   Find an algebraic expression for Cobb’s (uncompensated) wage elasticity of labor supply — i.e., cw  ≡  ∙  — exclusively in terms of the parameters that Cobb   takes as given.

e.   Suppose V > 0.  Analyze, in turn, the effects of ceteris paribus increases in

V, w, a, and F on Cobb’s wage elasticity of labor supply. Interpret your results.

2.   Consider an individual with preferences over weekly leisure, L, and weekly consumption, C , described by an increasing and quasiconcave utility function, U(L, C), with the usual   properties (i.e., UL  > 0, ULL  < 0, UC  > 0, UCC  < 0, and a negative definite Hessian matrix).  Using the definitions of leisure and consumption, one can rewrite utility as a      function of the hourly wage and hours worked per week (and also the time endowment     and weekly nonlabor income) as U(T − H, V + wH).  Suppose that each employer sets    weekly hours and the hourly wage on the job it offers, so that the individual faces a set of offered (H, w) pairs.  In all dimensions other than (H, w), all jobs are identical.

a.   What condition must hold for the individual to find a given (H, w) offer preferable to non-employment?

b.   Use the given properties of U(L, C) to determine the general shape of the individual’s indifference curves over alternative (H, w) combinations, and sketch a graph of these indifference curves (putting H on the horizontal axis).

c.   Use your diagram in (b) to show that, in general, an individual might quit a job     that requires  hours of work per week and pays an hourly wage of  in favor of a lower wage job.  Under what circumstances would an individual be unwilling to quit the current job in favor of a lower wage job?