Question

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? [1 point]

(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? [1 point]

Answer 1

(a) When each family has six members equally participating in the agricultural operation and 6 > 3, total corn production is 3, mean labor production is 3/6 = 0.5 in the year 0.

Marginal product: In year 0, the minimum labor force is 0, as it would have no impact on farm production to eliminate one worker.

Surplus: 3 surplus employees are present, and thus the surplus job ratio is 3/6 = 0.5 in year 0.

b The wage rate is the average job value i.e 0.5 units of corn, times 2 i.e the corn price as shirts.
This is 1 shirt per employee employed.
A factory wants to employ employees until the marginal revenue is equal to the wage rate. If a factory's marginal revenue is expressed in shirt units, Marginal product= 9-y
Growing plant will therefore employ employees up to
9-y = 1
So, y = 8.

(c) Total factory employment
= 20 * y
= 20 * 8 = 160

(d) Certainly! As marginal product of labor is 0 in year 1.

N.B: Due to Chegg's rules and regulation could submit only first four answers.