Overparametrized Model

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I am trying to understand the concept of an overparametrized model:

If I am considering a one way model:

$$Y_{jk}=\mu + \alpha_j + \epsilon_{jk}$$

Where $\epsilon_{jk}\sim N(0, \sigma^2)$.

Why is this model considered overparametrized and has no solutions, when estimating the maximum likelihood values.