Let Y₁, ..., Y_n (n ≥ 2) be independent observations where Y_i ~ N(βx_i, σ²), i = 1, ..., n, with known constants x_i and σ² > 0. Consider a N(β₀, τ²) prior for the parameter β, where β₀ and τ² > 0 are known constants. Under the squared error loss function, which of the following statements is true?