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.
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Agent 1: u1 = ln(x1) + (1 - 0.3)ln(x2) = ln(30) + (0.7)ln(15) ≈ 3.4012 + 0.7(2.7081) ≈ 3.4012 + 1.8957 ≈ 5.2969 Agent 2: u2 = ln(x1) + (1 - 0.7)ln(x2) = ln(10) + (0.3)ln(30) ≈ 2.3026 + 0.3(3.4012) ≈ 2.3026 + 1.0204 ≈ 3.3230 Show more…
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