Consider a small poor country with a large rural population. Workers in the country can choose to live in the rural area and work in agriculture (which is perfectly competitive with no minimum wage or other distortions), OR, they can choose to migrate to the city and look for work in the formal industrial sector. If they choose to migrate to the city, with probability p they might find a job that pays the minimum wage (w¯ = $5), but there is also a chance (1 − p) that they will not find formal work. If they find no formal work, they either wind up unemployed (earning wU = $0) or employed in the informal sector (earning wI = $2), with equal probability. If they choose to stay in the rural area, they earn the agricultural wage (wA = $3) with certainty. Workers who choose to migrate cannot immediately migrate back.

a) What is the expected value of your earnings if you move to the urban sector and don’t find formal work?