In this paper, we propose a framework to allocate code rates of component codes in a Plotkin-type unequal error protection (UEP) code. We derive an equivalent noise variance for each component code using structure of the Plotkin construction and Gaussian assumption. Comparing the equivalent noise variance and Shannon limit, we can find a combination of the code rates for the component codes. We investigate three types of code rate combinations and analyse their UEP performance. We also estimate a performance crossing signal to noise ratio (SNR) of the Plotkin-type UEP code. It indicates that which code has better performance for a given SNR. We confirm that the proposed framework is appropriate to obtain a desired UEP capability.