A tight prior wins a flat prior yields

Let $Y_1,\dots ,Y_n(n\ge 2)$ be independent observations; $Y_i$ ~ $N(\beta x_i,{\sigma }^2),i=1,\dots ,n$; where $x_1,\dots ,x_n$ and ${\sigma }^2(>0)$ are known constants and $\beta \in \mathbb{R}$ is an unknown parameter. Consider $N({\beta }_0,{\tau }^2)$ prior for the parameter $\beta$, where ${\beta }_0$ and ${\tau }^2(>0)$ are known constants, and $N(\mu ,{\lambda }^2)$ denotes a normal distribution with mean $\mu$ and variance ${\lambda }^2$. Suppose ȳ $=(1/n){\sum }_i$₌${}_1^n{y}_i$ and $\bar{x}=(1/n){\sum }_i$₌${}_1^n{x}_i$ are observed sample means. Under squared error loss function, which of the following statements are true?