If capital’s share of income is 25% and labor’s share of income is 75%, the stocks of both capital and labor increase by 50% (K/K = N/N = 0.5), and there is no technology growth, at what rate will potential output grow? Will the capital-labor ratio increase at all?
To determine the rate at which potential output will grow and whether the capital-labor ratio will increase, we can analyze the given information step by step.
First, let's consider the increase in the stocks of capital and labor. We're told that both capital (K) and labor (N) increase by 50%, which can be expressed as ΔK/K = ΔN/N = 0.5.
Next, let's examine the shares of income. The capital's share of income is 25%, and labor's share is 75%. These percentages represent the portion of total income received by each factor of production.
Using this information, we can calculate the growth rate of potential output. The growth rate of potential output is determined by the weighted average of the growth rates of capital and labor, based on their income shares.
To calculate the weighted average growth rate (g) of potential output, we can use the following formula:
g = (capital share * ΔK/K) + (labor share * ΔN/N)
Substituting the given values:
g = (0.25 * 0.5) + (0.75 * 0.5)
Simplifying the equation:
g = 0.125 + 0.375 = 0.5
Therefore, the rate at which potential output will grow is 0.5 or 50%.
Now let's consider whether the capital-labor ratio will increase. The capital-labor ratio (K/N) measures the amount of capital per unit of labor. If both capital (K) and labor (N) increase by the same percentage, the relative ratio between them remains unchanged.
In this case, since ΔK/K = ΔN/N = 0.5, it means that both capital and labor have increased at the same rate and the capital-labor ratio remains constant. Therefore, the capital-labor ratio does not increase.
In summary, the rate at which potential output will grow is 50%. However, the capital-labor ratio remains unchanged.