Consider the following version of the labour market signalling model we discussed in class. There are two types of workers in the market: low ability workers (Low Type) and high ability (High Type) workers. The group of low ability workers is relatively more numerous, making up 90% of the work force relative to the 10% of the high ability group. Any firm in the market is willing to pay a wage of $60,000 to a Low Type worker and a wage of $120,000 to a High Type worker. However, no firm can directly observe which group a job applicant belongs to (i.e., ability is private information of workers). Assume that there are no outside options, so the value of the outside options is $0. 1. Assume that workers do not have a credible way for signalling their ability to firms. Find the pooled wage both types will receive in this case. 2. Assume now that workers try to use education as a signal of ability. Specifically, the education attainment consists of certificates (C). However, to obtain certificates, Low Type worker must bear a cost of $9000 per certificate, while a High Type worker can achieve certification at the lower cost of $5000 per certificate. Compute the number of certificates each type will obtain to support a separating equilibrium. 3. Are workers better off with a pooled wage? Explain.