The Solow Model 2 – Comparative Statics
Using the Solow Model. What does the model predict when savings rates or other variables change?
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It confused me why the exponent of labor must be 1-the exponet of capital, but then I realized that it is because they are inversely related. Since the exponents are measures of how strongly each factor effects economic activity, and the two factors together make up all of Economic activity then the two exponents together must equal 100% of Economic activity or 1. I realize now that your comment about the doubling of capital and labor leading to a doubling of Economic activity says the same thing, but it's not immediately easy to recognize why the equation works that way.
This is correct. Using "^" for exponentiation and concatenation for multiplication, if the production function is Y=(K^a)(L^b), and we want constant returns to scale, i.e. doubling labor and doubling productivity means doubling output, then cY=(cK)^a(cL)^b. Taking the log of both sides, log(c)+log(Y)= a(log(c)+log(K)) + b(log(c)+log(L))= alog(K)+blog(L) + alog(c)+blog(c)= log(Y) + alog(c)+blog(c), which means that log(c) = alog(c)+blog(c) or that a+b=1
Excelent introduction to Solow model, clear and simple. The anonimous comment above clear it more for me. I maybe would add that Sollow model is an over simplification of the reality who ignore lots of distortions in the real world as government regulations, finantial tricks, subsidies, speculative deceiving, and many other actions related with the use of capital and human resources which is far from the sole will of the investor or government
The sum of the two exponents is equal to one because we have constant returns to scale; meaning that when you double inputs, your outputs double as a result. It may not always be the case. Most probably the instructors will discuss it later