Question

The output of a certain economy is given by the production function:

Q = A.K¹/³ . L²/³
If technology is growing at a rate of 1% per year, and the capital stock by 3% per year, what will be the growth rate of output in this economy?

Answer 1

The growth rate of output in the economy is 2% per year.

Step-by-step explanation:

To calculate the growth rate of output in this economy, we need to use the production function Q = A*K^(1/3) * L^(2/3), where Q is the output, A is the level of technology, K is the capital stock, and L is the labor input. Given that technology is growing at a rate of 1% per year and the capital stock is growing at a rate of 3% per year, we can calculate the growth rate of output as follows:

1. For technology: 1% growth rate means A increases by 1% per year.
2. For capital stock: 3% growth rate means K increases by 3% per year.

We can substitute these growth rates into the production function and calculate the growth rate of output as follows:

1. Growth rate of output = Growth rate of A + (1/3)*(Growth rate of K) + (2/3)*(Growth rate of L)
2. Growth rate of output = 1% + (1/3)*(3%) + (2/3)*(0%)
3. Growth rate of output = 1% + 1% + 0%
4. Growth rate of output = 2%

Therefore, the growth rate of output in this economy is 2% per year.