Question

Specific factor model: Suppose that there are two sectors in the United States: the food sector, with land as the specific factor, the manufacturing sector, and capital as the specific element. Labor can flow between departments.

1. Suppose a good weather makes several states have a big harvest, which leads to an 8% drop in food prices. Please elaborate and analyze the changes of labor mobility, nominal income and actual income of labor force and factor owners (please show graph).

2. Suppose a typhoon destroys a lot of farmland in Jamaica, so that the land resources in Jamaica are temporarily reduced. And land is a very important specific factor in food production. Jamaica's food and manufactured goods production will be affected by this change.

Please analyze the changes of labor flow, nominal income and actual income of labor force and factor owners in detail and show graph（Assume price do not change）.

Answer 1

1. The equilibrium distrution of labor between food and manufacturing sector will be given by,

Pf × MPLf = Pm × MPLm

Which states that the equilibrium distribution of labor will be such that, value of marginal product of labor in food sector which is equal to price of food multiplied by the marginal product of labor must be equal to value of marginal product labor manufacturing which is equal to price of manufacturing goods multiplied by marginal product of labor in manufacturing.

In the diagram below the curve Pf× MPLf shows the value of marginal product of labor in food sector and the curve PM × MPLm shows the Value of marginal product of labor in manufacturing sector. And the equilibrium distribution is at point A.

Now the price of food falls by 8% so the value of marginal product of labor in food shifts down by 8% due to decrease in price of food by 8%. The new value of marginal product of labor in food sector is given by pf' × MPLf.

As you can see the new equilibrium is at point B where in the new equilibrium distribution the equilibrium wage is lower at w' but notice the wages haven't fallen by exactly 8% due to labor transfer from food sector to manufacturing sector.

You can see the labor mobility, initially there were 0L* amount of labor employed in food sector and L*L amount of labor employed in manufacturing sector. But after the price fall, amount of labor employed in food sector falls to 0L' and the amount of labor employed in manufacturing sector increases to L'L.

As you can see the nominal wage falls from w* to w'. But the fall in nominal wages is less than 8%.

Now let's come to the real wages of labor, since labor wages has fallen the real wage in terms of manufacturing goods has also fallen since price of manufacturing goods hasn't changed, so decrease in wages would mean that labors can now but less of manufacturing goods.

And the real wage in terms of food increases since fall in price of food is more than the decrease in nominal wages.

So the total effect on real wages of labor is ambiguous.

Now let's come to specific factor owners. Since the price of food has fallen the owner of specific factor in the production of food that is land owners are now worse off since their income from the sell of food has fallen more than the fall in wages that they pay to labors. So their net income has fallen.

And the capital owners are now better off since the price of manufacturing goods hasn't changed and the wages has fallen so their income has increased, due to lower wage costs.

2.

Due to the reduction in the land resource in Jamaica the marginal product of labor in food sector will decrease due to the fact that now labors have less land to work on.

So the value of marginal product of labor in food sector will shift down, but this time due to a fall in MPLf. The new marginal product of labor in food sector is given by MPLf' and the price of food Pf remains the same.

In the below diagram the initial equilibrium was at the intersection of Pf × MPL and Pm × MPLm. The initial equilibrium is at point A where the equilibrium wage rate is w*, and the initial distribution of labor in food sector is OL* and the initial distribution of labor in manufacturing sector is L*L.

After the reduction in land resource, the value of marginal product of labor in food sector shifts lower to Pf × MPLf'. And the new equilibrium is at point B where the equilibrium wage rate is w'. Now the labor distribution in food sector falls to OL' and the labor distribution in manufacturing sector increases to L'L.

Now let's come to the income part.

We are given that the price of food and manufacturing goods doesn't change.

We know that the wages have fallen, and prices haven't changed so we can say for sure that the real wages of labor has fallen. Since nominal wages have fallen and the price haven't changed, so now the labors can less amount of food and manufacturing goods.

And the factors owners are now better off. Since the price of good haven't changed and the wages are now lower so they will have to pay less wages to labors and will still get amount of money from the sell of goods. So the specific factor owners are now better off, both capital and land owners.

I hope I was able to help you, thank you.