13.B.3' Consider n posirior sclrc~ion version of the model discussed in Section 13.B in which r(.) is a continuous, strictly dcc.rea.sing function of 0. Let the density of workers of type 0 be ,/'(O), with ,/'(O) > 0 for all 0 E [(I, 01. (a) Show that the rnore cupuhle workers are the ones choosing to work at any given wage. (b) Show that if r(l1) > O for all 0, then the resulting competitive equilibrium is Pareto cliicient. (c) Supposc that there exists a i) such that r(0) < 0 for 0 > 8 and r(0) > 0 for 0 < 8. Show that any competitive eq~~ilibrium with strictly positive employment necessarily involves too r?~uc,h employment relat~ve to the Pareto optimal allocation of workers