Consider the economy of Lewisville, which is just beginning to industrialize. The economy was entirely reliant on corn production until now. There are 100 identical families each farming their own land. Each family has 6 members who participate equally in farm work and share the output. Each farm has a small land area and can employ up to 3 full time workers, each of whom produce 1 unit of corn each. Beyond 3 workers, additional workers generate no additional farm output. Hence farm output c=min{3,x} where x is the number of workers on the farm. In response to an industrialization policy adopted by the government, new factories have recently started opening up in Lewisville. Each new factory produces shirts using labor, and the marginal product of labor in each factory is 10-y, where y is the number of workers. Workers are free to move between farm and factory with no migration or transport costs. Factories are owned by entrepreneurs who maximize profits. They save 10% of their profits and invest these profits to build new factories, which start the following year. Each new factory requires a set up cost equal to 32 shirts. Lewisville trades with the rest of the world and is too small to affect world prices. Hence, shirt and corn prices are fixed: the price of corn relative to shirts is 4, and each shirt can thus be sold at a price of 0.25 units of corn.
(a) Before the factories arrive, what is the average product of labor (corn output/worker) in each farm? What is the marginal product of labor? What proportion of the economy’s labor force is surplus?
(b) In year 1, 20 new factories arrive. With wages in agriculture set to the average product of labor and free mobility between sectors, what will the wage rate in the industrial sector be in units of shirts? How many workers will each factory employ in year 1? [Hint: Wage_I = APL_A * P_A (where P_A is price of corn relative to shirts).]
(c) What is total employment in industry in year 1?
(d) Will there be surplus labor in agriculture in year 1?
(e) How many factories will there be in year 2 given that each factory earns of a profit of 32 (=1/2*y*(10-W_I)) in year 1?
(f) Will there be surplus labor in agriculture in year 2?
(g) Suppose the government introduces a tax credit that increases the savings rate to 0.45. How many more years will it take for all surplus labor to transition out of agriculture?