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##### [solution] » A consumer has a quasi-linear utility function u(x 1, x 2 ) = f(x

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

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

**f(x _{1}) = 10x_{1} ? (x_{1})^{2}**

**The prices of the goods are p _{1}>0 and p_{2}> 0, respectively, and the consumer?s income is? ? 0. The consumer chooses a bundle of goods (x_{1}, x_{2}) ? 0 to maximize utility u(x_{1}, x_{2}) subject to the budget constraint:**

**p _{1}x_{1}+ p_{2}x_{2}? m **

**In what follows, we assume the price of good 2 is fixed at p _{2}= 1.**

**a.) Suppose that prices (p _{1, }p_{2}) and income m are such that the consumer demands strictly positive quantities of both goods. x_{1} >0 and x_{2}>0. Use the tangency condition MRS= p_{1}/p_{2} 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

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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This question was answered on: * Feb 21, 2020 *

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