A firm can hire two types of workers: Group A workers will add $200,000 to the firm's revenues over their lifetime, while Group B workers will increase the firm's revenues by $120,000 over their lifetime. The firm cannot distinguish Group A from Group B workers. Instead, the firm knows that 50% of all workers are Group A workers, and 50% are Group B workers. Suppose the firm pays each worker exactly their expected contribution to the firm's revenue. That is, if the firm knew each worker's type, Group A workers would get $200,000 and Group B workers would get $120,000. The differences in the workers' productivity levels are reflected in their costs per year of education. Each year of education costs an A worker $12,500, while each year costs a B worker $25,000. Assume that getting an education does nothing to improve a worker's productivity, but it can function as a signal. Also assume the workers do not discount the future. The firm assumes that a worker is from group A when the worker has studied for at least 3 years, and that the worker is from group B if not. a) How much will the firm pay each worker if it can't tell workers apart? b) Given the 3-year cutoff, will education produce a strong signal? Explain. (Hint: to answer this, compare each type's cost with its benefit of going to school for 3 years.)