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Consumer demands strictly positive quantities

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Reference no: EM131246695

A consumer has a quasi-linear utility function u(x1, x2) = f(x1) + x2, where u(x1, x2) is the utility derived from x1 units of good 1 and x2 units of good 2. We assume f(x1) is given by:

f(x1) = 10x1 - (x1)2

The prices of the goods are p1>0 and p2> 0, respectively, and the consumer's income is 0. The consumer chooses a bundle of goods (x1, x2) ≥ 0 to maximize utility u(x1, x2) subject to the budget constraint:

p1x1+ p2x2≤ m

In what follows, we assume the price of good 2 is fixed at p2= 1.

a.) Suppose that prices (p1, p2) and income m are such that the consumer demands strictly positive quantities of both goods. x1 >0 and x2>0. Use the tangency condition MRS= p1/p2 to derive the demand function for good 1. Why is demand for good 1 independent of m?

Reference no: EM131246695

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