1. Consider the utility function $U(x, y) = \min \{ax, \beta y\}$
a) Derive the own-price elasticity, income elasticity, and cross-price elasticity of
demand.
2. Consider the utility function $U(x, y) = \min \{2x, 3y\}$, assume that the price of good x is
$p_x$ and the price of good y is $p_y$ and the agent has I dollars to spend.
a) Find the compensated demand function.
b) Use the Slutsky equation to separate income and substitution effect. Explain your
results.