Effect of increasing nitrogen concentration in the synthesis of ammonia For the reversible reaction 
$\ce{N2 + 3H2 &lt;--&gt; 2NH3}$

When $\ce{N2}$ is increased, the the forward reaction is favored, increasing the yield of $\ce{NH3}$ and decreasing the yield of $\ce{H2}$. I read from multiple textbooks that the $\ce{H2}$ decreases in concentration to a greater extent than $\ce{NH3}$ increases in concentration, such that the final concentration of $\ce{NH3}$ is greater than that of $\ce{H2}$. Why is this so?
The final concentration of H$_2$ is lower than the concentration of NH$_3$ because for each NH$_3$ you produce, you need 1.5 H$_2$.  So the rate of consumption of hydrogen is higher than the rate of production of ammonia.

Here you can read about the multiple steps in the synthesis of ammonia, also called the Haber-Bosch Process.  As you mention, by increasing the concentration of nitrogen, you can increase the rate.  The rate limiting step is separation of the nitrogen atoms in N$_2$