"Transfer Resistor"-official name of ___?

The assumption $\alpha_{ac}\approx 1$ and KVL yield the solution: $\begin{aligned} \alpha_{ac}&=\frac{I_C}{I_E}\approx 1 &&&\Rightarrow &&&& V_{out} &=R_CI_C\approx R_CI_E = R_C\frac{V_{in}}{R_{in}} &&&\Rightarrow &&&&\frac{V_{out}}{V_{in}}&\approx\frac{R_C}{R_{in}}=\frac{1000}{20}=\boxed{50} \end{aligned}$