4. Consider a variation of the signaling model of Spence (1973) we discussed in class. There are workers whose types are either H or L, with half the population of each type. Both types have a reservation utility of zero. A worker can acquire an education at the cost c(eH)=e2 or c(eL)=e3; depending on their type. The output (productivity) of an L worker is y(L;e)=3e. The output for an H type is y(H;e)=5e. There are two firms that bid for the workers' services after observing the education level (so the firms pay the workers their marginal productivity). The worker overall utility is their wage minus the cost of education. A) Find a separating BNE when the workers' types are unknown. (You need to find the education level and wage of the two types. Hint: What would be each worker optimal level of education when their type is known?) 4. Consider a variation of the signaling model of Spence (1973) we discussed in class. There are workers whose types are either H or L, with half the population of each type. Both types have a reservation utility of zero. A worker can acquire an education at the cost c(eH)=e2 or c(eL)=e3; depending on their type. The output (productivity) of an L worker is y(L;e)=3e. The output for an H type is y(H;e)=5e. There are two firms that bid for the workers' services after observing the education level (so the firms pay the workers their marginal productivity). The worker overall utility is their wage minus the cost of education. A) Find a separating BNE when the workers' types are unknown. (You need to find the education level and wage of the two types. Hint: What would be each worker optimal level of education when their type is known?)