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Change the Humphrey and Lauren example such that Lauren’s utility function is uL(x1,x2) = min{x1, x2}...

Change the Humphrey and Lauren example such that Lauren’s utility function is uL(x1,x2) = min{x1, x2} and Humphrey’s utility function is uH (x1, x2) = 2√x1 + √x2. Their endowments are eL = (4,16) and eH = (2,24).

1)Suppose Humphrey and Lauren are to simply just consume their given endowments. State the definition of Pareto efficiency. Is this a Pareto efficient allocation? As part of answering this question, can you find an alternative allocation of the goods that Pareto dominates the allocation where Humphrey and Lauren consume their respective endowment bundles?

2)As a function of market prices p = (p1,p2), determine Lauren’s and Humphrey’s optimal consumption choices.

3) Determine the market equilibrium price ratio, pˆ = p1/p2. What are Lauren’s and Humprey’s equilibrium consumption bundles.

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