Assume an endogenous growth model with labor augmenting technology.The production function is Y = F(K,AN), where A = 2(K/N) such that y = 2k.If the savings rate is s = 0.06, the rate of population growth is n = 0.05, and the rate of depreciation is d = 0.04, then the growth rate of real output per capita is
A)1%
B)3%
C)5%
D)6%
E)9%

Question

Quizplus · Accepted Answer

In an endogenous growth model with labor-augmenting technology, the growth rate of real output per capita, $g_y$, can be determined by the formula $g_y = s \cdot \frac{Y}{K} - (n + d)$, where $s$ is the savings rate, $Y/K$ is the output-capital ratio, $n$ is the population growth rate, and $d$ is the depreciation rate. Given $y = 2k$, the output per worker is directly proportional to capital per worker, implying a constant return to scale and thus a constant $Y/K$ ratio. The savings rate $s = 0.06$ (or 6%) is entirely invested, leading to growth. However, the growth rate of real output per capita must also account for the diluting effects of population growth ($n = 0.05$ or 5%) and capital depreciation ($d = 0.04$ or 4%). Since the model specifies $A = 2(K/N)$ and $y = 2k$, implying a direct relationship between capital and output per worker, the growth rate of real output per capita essentially reflects the net effect of investment after accounting for population growth and depreciation. Given the parameters, the correct calculation involves understanding that the growth effect is primarily driven by the efficiency and scale of capital investment relative to the workforce, adjusted for depreciation and population growth. However, without the explicit output-capital ratio ($Y/K$), the direct application of the provided formula is not straightforward, suggesting a need for clarification or additional information to accurately compute $g_y$ using the given parameters. The answer provided assumes an implicit understanding or simplification of the model's dynamics that may not be directly inferred from the given information.

Assume an Endogenous Growth Model with Labor Augmenting Technology