Distribution of Ability and Earnings in a Hierarchical Job Assignment Model

We examine the mapping of the distribution of ability onto earnings in a hierarchical job assignment model. Workers are assigned to a continuum of jobs in fixed proportions, ordered by sensitivity to ability. The model implies a novel marginal productivity interpretation of wages. We derive comparative statics for changes in technology and in the distribution of ability. We find conditions under which a more unequal distribution of ability maps onto a more/less unequal distribution of earnings. We also analyze an assignment model with variable proportions and find that in the Cobb-Douglas case, a rise in the inequality of ability always narrows the range of earnings