Can someone point me in the right direction on how to solve this?
1. Suppose you have an economy with two factors of production (capital and labor), and suppose that capital's share of national income is 40% and that labor's share is 60%. Assume also that the annual growth rates of labor and capital are, respectively, 5% and 3%.
A. If technology does not increase over time, how much does output grow each year?
B. If technology grows at a 2% rate each year, how much does output grow each year.
To solve this problem, we need to understand the relationship between the factors of production (capital and labor) and their respective shares of national income. We also need to consider the growth rates of labor, capital, and technology.
A. If technology does not increase over time, we can assume that the growth rate of output is solely determined by the growth rates of labor and capital. To find the growth rate of output, we need to calculate the weighted average of the growth rates of labor and capital using their respective shares of national income.
1. Start by multiplying the growth rate of labor (5%) by its share of national income (60%):
5% x 0.6 = 0.03
2. Next, multiply the growth rate of capital (3%) by its share of national income (40%):
3% x 0.4 = 0.012
3. Add the weighted growth rates together:
0.03 + 0.012 = 0.042
Therefore, the output grows by a rate of 4.2% each year when technology does not increase.
B. If technology grows at a 2% rate each year, we need to consider its impact on the growth rate of output. In addition to the weighted average of the growth rates of labor and capital, we now need to add the growth rate of technology to find the overall growth rate of output.
1. Start by multiplying the growth rate of labor (5%) by its share of national income (60%):
5% x 0.6 = 0.03
2. Next, multiply the growth rate of capital (3%) by its share of national income (40%):
3% x 0.4 = 0.012
3. Add the weighted growth rates of labor and capital together:
0.03 + 0.012 = 0.042
4. Add the growth rate of technology (2%) to the weighted growth rates:
0.042 + 0.02 = 0.062
Therefore, the output grows by a rate of 6.2% each year when technology grows at a 2% rate.