Suppose we have two cities: Miami and Atlanta. Individuals expect to live 10 years, face an interest rate of 0% per year. Workers in each city have a yearly labour supply given by h(w) = 8 (e.g., workers always work 8 hours a year). Firms face competitive input and output markets and the yearly production technology of firms in each city is f(E) = 2 E. Firms get $10 per unit produced. Suppose that both Miami and Atlanta have 50 workers and 16 firms. Suppose that there is an immigration wave raising the labour supply of Miami by 50 workers.

1. What is the equilibrium wage and employment before the immigration wave?
2. What is the equilibrium wage and employment before after the immigration wave?
3. Suppose now that workers can move between cities (internal migration) but face moving costs of $2. Do workers want to move from Miami to Atlanta? Do workers want to move from Atlanta to Miami? HINT: compute the present value of income of a worker living in Atlanta and a worker living in Miami.
4. Suppose 5 workers move from Miami to Atlanta. What will be the wage in these two cities after this internal migration? Is the wage difference between Atlanta and Miami bigger or smaller than before internal migration?