The Bright Future of Economic Growth
How does an increase in both capital and labor affect economic growth?
Given the data that the economy's production function is Y = AK^(0.3)N^(0.7), if both K and N rise by 20% while A remains unchanged, by how much does Y increase?
Impact of Increase in Capital and Labor on Economic Growth
When both capital (K) and labor (N) increase by 20%, with A remaining constant, the resulting increase in economic growth can be calculated using the production function:
Y = A * K^(0.3) * N^(0.7)
Given initial values: K = 2000, N = 100, A = 1, and Y = 246
After the 20% increase: K = 2400, N = 120
Plugging these values into the production function, we find:
Y = 1 * (2400)^0.3 * (120)^0.7
Y = 1 * (10.3 + 28.5)
Y = 38.8The increase in both capital and labor by 20% has resulted in a 15.85% increase in economic growth, as Y now equals 284.8. This demonstrates the positive impact of investing in both factors of production on the overall output of the economy. By fostering growth in capital and labor, countries can enhance their productivity levels and pave the way for a brighter economic future.
By optimizing resources and promoting a conducive environment for investment and innovation, nations can propel their economic growth trajectory upward. This increase in economic output not only drives prosperity but also opens up opportunities for development and advancement across various sectors.
As we continue to witness the positive implications of investing in capital and labor, it reinforces the importance of strategic economic planning and policies that support sustainable growth. With the right approach, countries can harness the full potential of their resources and set the stage for a thriving economy that benefits all members of society.