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A consumer has a quasi-linear utility function u(x 1, x 2 ) = f(x

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?

A consumer consumes two commodities X1 and X2 and the utility function of the consumer is


given by U(X1, X2) = 10X1 ? (X1)2 + X2


The consumer can purchase the required amount of good X 1 at a...


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