A consumer's preferences are given by the following utility function:
$u(x,y) = 4x + y$
a. Assume $P_x = 10$, $P_y = 1$, and $I = 30$. What is the quantity demanded of x and y?
$x^*(10, 1, 30) = 5$
$y^*(10, 1, 30) = -20$
\frac{P_x}{4}
b. Now, suppose we don't know $P_x$, $P_y$, or $I$. If $\frac{P_x}{4} > P_y$ what is the quantity demanded for x and y?
$x^*(P_x, P_y, I) = 0$
$y^*(P_x, P_y, I) = \frac{I}{P_y}$
$P_x$
c. Suppose we don't know $P_x$, $P_y$, or $I$. If $\frac{P_x}{4} < P_y$ what is the quantity demanded for x and y?
$x^*(P_x, P_y, I) = \frac{I}{P_x}$
$y^*(P_x, P_y, I) = 0$
