Consider the following utility functions. Assume x 0, x 0. U(x, x) = (x...

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Consider the following utility functions. Assume x₁ ≥ 0, x₂ ≥ 0. U₁(x₁, x₂) = (x₁ + 4x₂)² U2(x1,x2) = 5xỉx U3(x1, x₂) = x1(x2 + 2) U₁(x₁, x₂) = max{x₁, x₂} U5(x₁, x₂) = min{3x₁ + x₂, x₁ + 3x₂} In your answers, label all intercepts, kinks, coordinates, slopes, and axes. Give an answer to the following two questions for each of the first three utility functions above: 1. Derive an expression for the Marginal Utility of each good. 2. Compute the Marginal Rate of Substitution at the bundle (2,4). Consider the following utility functions. Assume x₁ ≥ 0, x₂ ≥ 0. U₁(x₁, x₂) = (x₁ + 4x₂)² U2(x1,x2) = 5xỉx U3(x1, x₂) = x1(x2 + 2) U₁(x₁, x₂) = max{x₁, x₂} U5(x₁, x₂) = min{3x₁ + x₂, x₁ + 3x₂} In your answers, label all intercepts, kinks, coordinates, slopes, and axes. Give an answer to the following two questions for each of the first three utility functions above: 1. Derive an expression for the Marginal Utility of each good. 2. Compute the Marginal Rate of Substitution at the bundle (2,4).

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