Suppose you own a rice that produces two types of apples: High quality \"regular\" rice $x_1$ and low quality
\"broken\" rice $x_2$. The market price for a kilogram of regular rice is higher than that for a kilogram of
broken rice i.e. $p_1 > p_2$. You sell some of your rice locally in Vietnam and you ship the rest to be sold in
on the international market. It costs you an amount c per kilogram of rice to get rice to that market.
Suppose that we model our consumers' tastes as $u(x_1, x_2) = x_1^\alpha x_2^{(1-\alpha)}$.
(a) What has to be true about $\alpha$ in order for $x_1$ to be the regular rice.
(b) Letting consumer income devoted to rice consumption be given by I, derive the consumer's demand
for regular and broken rice as a function of $p_1$, $p_2$, I and c.
(c) What is the ratio of demand for $x_1$ over $x_2$?
d) From your answer to part c), can you tell in which market there will be greater relative demand for
regular versus broken rice -- the local market or the international market?
