Consider an exchange economy consisting of two agents. The agents have the utility function $u_i = \alpha_i \ln x_1^i + (1 - \alpha_i) \ln x_2^i$ with $\alpha_1 = 0.3$, $\alpha_2 = 0.7$ and initial endowments $\omega^1 = (30, 15)$, $\omega^2 = (10, 30)$. Compute equilibrium allocations and prices.