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.
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To solve these questions, we need to understand the concept of output growth and how it relates to the factors of production and technology.
Before we begin, it's important to note that the share of capital and labor in national income determines how the total income is divided between these two factors.
To approach this problem, let's break it down step by step:
A. If technology does not increase over time, how much does output grow each year?
To determine the growth rate of output, we need to consider the growth rates of the factors of production, capital, and labor. In this case, the annual growth rates of labor and capital are given as 5% and 3% respectively.
Since technology is assumed to be constant (not increasing or decreasing), it does not directly contribute to output growth. Therefore, we can calculate the output growth based on the growth rates of labor and capital.
To find the growth rate of output, we can use a formula known as the growth accounting equation:
Output growth rate = Labor share × Labor growth rate + Capital share × Capital growth rate
In this case, the labor share is given as 60% (0.60) and the capital share is given as 40% (0.40). The labor growth rate is 5% (0.05) and the capital growth rate is 3% (0.03).
Substituting these values into the formula, we get:
Output growth rate = (0.60 × 0.05) + (0.40 × 0.03)
Output growth rate = 0.03 + 0.012
Output growth rate = 0.042 or 4.2%
Therefore, if technology does not increase over time, the output will grow by approximately 4.2% each year.
B. If technology grows at a 2% rate each year, how much does output grow each year?
In this case, we need to consider the impact of both the growth rates of the factors of production (labor and capital) and the growth rate of technology.
Using the same growth accounting equation as before, we substitute the given values as follows:
Output growth rate = (0.60 × 0.05) + (0.40 × 0.03) + (2% × 100%)
Output growth rate = 0.03 + 0.012 + 0.02
Output growth rate = 0.062 or 6.2%
Therefore, if technology grows at a 2% rate each year, the output will grow by approximately 6.2% each year.
By following these steps and using the growth accounting equation, you can calculate the output growth rate based on different scenarios and input values.