Question

Problem 4. True or False? Explain your answer X1 = m/pl and x, = ml p, are demand function for some utility maximizing consumer

Answer 1

If there are two goods in the economy, optimal bundle would be the one that maximizes consumer utility as well as satisfies Walrus law (i.e. you consume on the boundary of your budget set and spend all of your income)

Given the following demand functions:

$x_1 = \frac{m}{p_1}$ and $x_2 = \frac{m}{p_2}$

$\Rightarrow p_1x_1 = m$ and $p_2x_2 = m$

Budget constraint is given as:

$p_1x_1 + p_2x_2 = m$

Since this doesn't hold true in our case, the demand function doesn't represent a utility maximizing consumer.

However if the demand functions are modified a bit such that:

$x_1 = \frac{m}{p_1} \hspace{5em} if \hspace{1em} p_1 < p_2, \hspace{1em} 0 \hspace{1em} otherwise$

$x_2 = \frac{m}{p_2} \hspace{5em} if \hspace{1em} p_1 > p_2, \hspace{1em} 0 \hspace{1em} otherwise$

This represents a demand function for utility maximizing consumer (actually it follows perfect substitute preferences)