Suppose that a consumer has preferences over bundles of non-negative amounts of each two goods, x1 and x2, that can be represented by a quasi-linear utility
function of the form
U(x1,x2)=x1 +√x2.
The consumer is a price taker who faces a price per unit of good one that is equal to $p1 and a price per unit of good two that is equal to $p2. An- swer each of the following questions. To keep things relatively simple, focus only on interior solutions in which positive amounts of both commodities are consumed.
1. What is the consumer’s (utility-constrained) expenditure minimisation problem?
What conditions characterise the consumer’s optimal choice of con- sumption bundle for this problem?
What are the consumer’s compensated (Hicksian) demand functions for good one and good two?
Illustrate a representative compensated demand curve for each com- modity.
What is the consumer’s optimal expenditure level, given the minimum- utility constraint? (In other words, what is the consumer’s expenditure function?)
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