6. According to the Solow model, how would each of the following affect consumption per worker in the long run (that is, in the steady state)? Explain and illustrate your answer graphically.
6a. The destruction of a portion of the nation's capital stock in a war.
6b. A permanent increase in the rate of immigration (which raises the overall population growth rate)?© BrainMass Inc. brainmass.com December 24, 2021, 10:07 pm ad1c9bdddf
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I can only give you the basics of the model and (importantly) the assumptions. I cannot graph the issues or give you answers, but I will give you links for sample graphs. Since the model is so simple, its really not that hard to graph. The key is keeping the variables separate.
First, the variables. The model is simple. The big issue is (new) capital production. Labor is a constant, but knowledge is a variable of itself. It is closely connected with the idea of technological development and the ability to use it.
Q/L is output per worker measured by technology per worker. This is impacted by the stock of capital, its growth, savings, growth in education (or the knowledge to work new capital), the existence of new capital (think of it as high-tech stuff that improves production).
Take a look here for a fairly simple explanation: http://www.pitt.edu/~mgahagan/Solow.htm
And a simple graph: http://www2.econ.iastate.edu/classes/econ302/alexander/Spring2006/SOLOW/SOLOWGROWTHMODEL.htm
Another good one: http://economics.sas.upenn.edu/~vr0j/econ10205/lectures/grow5_solow.pdf
Second, the assumptions. Diminishing returns is a constant issues so long as knowledge (?effective production?) remains the same. Diminishing returns is a problem if the education and technology of a society remains constant. It is eliminated as this education improves.
With the exception of savings, we are not dealing with macroeconomic variables or government policy. We are also not dealing with natural resources or social institutions. This assumes that economics is autonomous. Production is really based on the high tech sector and education.
So for your questions.
1. Destruction through war.
This only matters if we know what kind of capital has been destroyed. If a war has destroyed capital from the ?rust belt,? older, more obsolete factories, then nothing would change. IN fact, like in Germany after World War II, the destruction of the older factories gives investors an excuse to make new ones. Over time, this can help a society.
On the other hand, if the capital is more high tech, then this can set the society back for a long time. So here, we're dealing with quality over quantity.
2. Immigration is a problem, but again, it depends on the type. The average immigrant from Mexico is not well educated. Hence, it increases the diminishing returns factor. In other words, without a highly educated and skilled population, the economic will stagnate. This means that at least, the output per worker will go down since these new arrivals do not have the skills that are required to run an ultra-modern economy.
One of the assumptions of this model is that labor grows at a basic constant rate. This is upset through mass immigration, especially of uneducated and poor people. Over time, this can reverse the trend of production backward, that is, harm production over time because the new capital (the high tech stuff that really matters) is not usable or understandable by immigrants.
What are we talking about? Real inputs are essential, but they are dictated here:
By technology, education, and the constant savings rate that makes investment possible. Without investment (and hence savings) new technology cannot be created and consumption too falls off.
Remember marginal production is always decreasing. This means, just to break even, the society must be constantly improving.
When you graph, keep it simple.
For your left axis, use production.
For the bottom axis, use labor inputs
Your slope will always be those things that make labor inputs more or less productive.
You CAN also use demand. Demand for goods is tightly bound to investment and hence savings. Investment is also bound with high tech production for production to continue to increase and spur demand.
Remember to always match quality to quantity. That's what makes this model interesting.
So when you graph for question 1, you need to make sense out of the sorts of capital that has been destroyed.
For 2, you are dealing with the slope itself, so this might even off or even fall if the new arrivals have no clue how to work the more advanced machines or computer programs. What you are worried about here is how production per worker is going down even if everything else is going up, since the tech quality of the new arrivals is so bad.
This will help you a lot: http://www2.econ.iastate.edu/classes/econ302/alexander/Spring2006/SOLOW/SOLOWGROWTHMODEL.htm
(I already listed this above, but it teaches you how to graph. The big issues are keeping your variables straight.)
Therefore: production=quality of education, capital stock, savings and the creation of high tech capital (and the slow removal of older, obsolete machines)
Demand=investment, savings (of course), and the continual application of knowledge to the capital that exists.
The easy part is that they are both connected.
Just make it logical and you will do fine.