Suppose an individuals utility function is u x 1 1 2 , x 2 1 2 Let p 1 4, p 2 5, and income equal $200 With a general equation and general prices, derive the equal marginal principle Graphically illustrate equilibrium and disequilibrium conditions and how consumers can reallocate their consumption to maximize utility What is the optimal amount of x 1 consumed What is the optimal amount of x 2 consumed What is the marginal rate of substitution at the optimal amounts of x 1 and x 2 As functions of p 1 , p 2 , and m, derive x 1 s demand curve As functions of p 1 , p 2 , and m, derive x 2 s demand curve

Question: Suppose an individuals utility function is u=x 1 1/2 , x 2 1/2 . Let p 1 =4, p 2 =5, and income equal $200.

Suppose an individual’s utility function is u=x₁^1/2, x₂^1/2. Let p₁=4, p₂=5, and income equal $200.
1. With a general equation and general prices, derive the equal marginal principle. Graphically illustrate equilibrium and disequilibrium conditions and how consumers can reallocate their consumption to maximize utility.
2. What is the optimal amount of x₁ consumed?
3. What is the optimal amount of x₂ consumed?
4. What is the marginal rate of substitution at the optimal amounts of x₁ and x₂?
5. As functions of p₁, p₂, and m, derive x₁’s demand curve?
6. As functions of p₁, p₂, and m, derive x₂’s demand curve?

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Consumer Equilibrium with CobbDouglas Utility Utility Function and Budget Constraint The given utility function is ux1 x2 x112 x212 Prices are p1 for x1 and p2 for x2 and income is m The budget constr... View full answer

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