Suppose that education does not affect workers productivity, but it is more costly for low-ability

workers to obtain the education. If firms cannot distinguish between different workers they

must pay them all the wage equal to the expected productivity. If they can distinguish between

workers with different abilities, they pay each worker their marginal product of labour and make

zero profits. 70% of workers in the population have low ability. The productivity of low-ability

workers is YL = 20000, and the productivity of high-ability workers is YH = 50000. The cost of

education to high-ability workers is CH (S) = S , and the cost of education to low-ability workers4

isCL =S.

1. Suppose firms cannot observe workers education. What wage will they offer to a high-

   ability worker? What is the optimal level of schooling for the high-ability worker? Why?

2. Suppose that firms can observe workers educational attainment and believe that workers with the level of schooling above some benchmark S are high-ability workers. For what values of S high-and low-ability workers choose different levels of educational attainment (separating equilibrium)?

3. Whatwillbetheoptimallevelofschoolingforhigh-andlow-abilityworkersinaseparating equilibrium?

4. Draw indifference curves of high- and low-ability workers and the values of S that sustain the separating equilibrium.

5. For what levels of S will all workers optimally choose to obtain positive schooling S(pooling equilibrium). What will be the wage offered to high-ability workers?

6. Supposethatthegovernmentreformstheschoolsystemtopromoteeducationamonglow- ability workers and decreases the cost of education for low-ability workers to CL = S .

   2

   For what range of educational requirements the separating equilibrium is sustained? Is it different from 2.2? Why?