Question

An imaginary economy uses only capital (K) and labor (L). The production function is Cobb-Douglas:

= K^0.5 ^0.5. If in a year the wage grew 4%, labor grew 2% and capital grew 4%, by approximately how much
did the labor share grow? You can use the approximation formula as in Canvas document "Some useful
properties of growth rates".
a. Around 2%.
b. Around 4%.
c. Around 3%.
d. Around 1%

Answer 1

Using the Cobb-Douglas production function, the labor share grows by the difference between wage growth (4%) and labor growth (2%), resulting in an approximate growth of around 2%.

Step-by-step explanation:

In an imaginary economy using a Cobb-Douglas production function represented as Q = K^0.5L^0.5, we can calculate the change in the labor share when wages, labor, and capital grow. Given that the wage grew by 4%, labor by 2%, and capital by 4%, we can use an approximation formula for growth rates to determine the change in the share of labor.

According to this model, the output elasticity concerning labor is 0.5, which represents labor's share of the income. Therefore, if wages, which represent the price of labor, increase by 4%, and labor itself grow by 2%, then the labor share will grow approximately by the difference, which is around 2%.