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?