Assume an endogenous growth model with labor augmenting technology and a production function of the form Y = F(K,AN), where A = 1.2(K/N) such that y = (1.2)k.If the savings rate is s = 0.15 and the rate of depreciation is d = 0.05, how high does population growth (n) have to be to achieve a growth rate of 10 percent?
A)15%
B)12%
C)10%
D)5%
E)3%

Question

Quizplus · Accepted Answer

In an endogenous growth model with labor-augmenting technology, the steady-state growth rate of output per worker (y) is given by the formula $g_y = sAk^\alpha - (n + d)$, where $s$ is the savings rate, $A$ is the technology parameter, $k$ is capital per worker, $n$ is the population growth rate, and $d$ is the rate of depreciation. Given that $A = 1.2$, $s = 0.15$, and $d = 0.05$, and aiming for a growth rate ($g_y$) of 10% (or 0.10), we can rearrange the formula to solve for $n$.Given the production function $y = (1.2)k$, the growth rate of technology or productivity is not explicitly mentioned, but the effect of technology on output is captured through $A$. Since $A = 1.2(K/N)$ and the growth rate is desired to be 10%, we need to find the value of $n$ that satisfies this condition.The equation simplifies to $0.10 = 0.15 \times 1.2 - (n + 0.05)$. Solving for $n$ gives us $n = 0.15 \times 1.2 - 0.10 - 0.05$, which simplifies to $n = 0.03$ or 3%. This means the population growth rate needs to be 3% to achieve a growth rate of 10% in this model.

Assume an Endogenous Growth Model with Labor Augmenting Technology and a Production