Question

The o-ring model stresses that coordination failure are the causes of poor performance of developing countries. then, we expect that it is a social optimal to edecute everybody even in developing countries. but this doesn't happen in developing countries, why?

Answer 1

The O-Ring model seeks to explain the wage differentials that exist between a developed and developing economy in terms of its wage and productivity.

It can also be applied on the perspective of international migration.It explains why workers may earn so much more when they migrate from a poor country to a rich one, even though their skill remains the same.

Assumptions:

• Production consists of 'n' tasks.
• The tasks can be performed at different levels of skill
• qi is the skill level of the ith worker, which has the following interpretations:

a) probability of completing the task successfully

b) the quality index

• Each task is performed by 1 worker. If there are n tasks in the production process, each work is performed by a single worker.
• 'B' is the output produced per worker when all tasks are performed successfully.

Thus, if there are 'n' number of tasks, then nB is the total output produced in the economy and this is possible when only all the n tasks are completed successfully.

Next, we move on to the O-Ring production function:

where y denotes the expected output

We consider a competitive economy with the producer earning zero profits.

Wage is defined as:

i.e.. wage is a function of q (the quality of a particular worker)

The profit maximization problem of the firm is:

Max

'q'

FOC:

for all n workers, we have an identical solution:

Thus, at optimal level, the skill level of all the workers are the same.

In other words, probability of completing the work is equal for each worker.

The profit function, thus, can be written as:

The idea of equal skill level of workers at optimum is the basic background of skill clustering theorem.

This theorem says that there exists a positive assortative matching in the production process. That is, high skilled workers, will be, in equilibrium, matched with only high skilled workers. Low skilled workers have no other option but to work with low skilled workers. It also says that any combination between high and low skilled workers is sub optimal.

We can prove this by the following:

Consider a vector-

Let us define:

and,

Thus, qH>qL

Define the following:

= profit earned by producers who are producing output with a combination of both high and low skilled workers

=profit earned by producers who are producing output with only high skilled workers

=profit earned by producers who are producing output with only low skilled workers

Hence, we have:

where,

and,

for getting the expressions of and , replace qL with qH and qH with qL respectively.

Now, the skill clustering theorem essentially says that and cannot occur simultaneously. In other words, no heterogeneous level of skill world give optimum profit to the producer.

In order to prove this, suppose ,

then,

Through simplifications, we have:

Since, qL<qH, it means,

which means,

However, we have already assumed that . Hence, cannot give the optimum level of profit.

In other words, production with low and high skilled workers would never be optimum. This completes the proof.

Now, finding the partial derivative of y with respect to the skill level qi

and,

also,

This implies the value of productivity of a worker at a certain level of skill for a certain task 'i' goes up if the other tasks are performed by more skilled workers.

An immediate implication is that if a worker with a certain skill migrates to an area where others have higher skill, then that worker's productivity will be higher. This happens in spite of the fact that his own skill remains unchanged.

This explains why a worker migrating from a developing country to a developed one can earn so much more with the same level of skill.

In light of skill clustering theorem, the profit function of a competitive firm is:

or,

or,

and,

Hence, as q rises, w(q) increases at an increasing rate. Hence, if a worker is skilled, his productivity rises. So , q increases.

As wage is a function of skill, wage rises at an increasing rate as well.

In developing economies, due to the vicious cycle of poverty, people are unskilled. Thus, they earn less wage. They have low productivity and this leads to low per capita income. Low per capita income reinforces the forces of vicious cycle. So, the state of poverty is accentuated.

However, if the worker moves to a developed economy, he gets to have higher productivity as he is working with highly skilled workers there. So his wage increases and he earns higher there.