Teresa likes to consume chocolate and yogurt. Her utility function is given by U(x, y) = x0.5y0.5where x and y are the quantities of chocolate and yogurt she consumes. Suppose that her income is $10 and the initial prices for both of the goods is $1. Due to a tropical storm in West Africa, the global price of chocolate suddenly rises to $4. Consider that the price of yogurt is unchanged.

d) Find xs, which is the optimal value of x when the consumer has enough income to reach the level of utility ¯Uwith the new price levels. (Hint: find the income that allows Teresa to reach the utility level ¯Uwith the new price ratio.)

e) Find the Price, Income and Substitution Eects.

f) Now graph (x*,y*), (x',y') and (xs, ys)

g) Extra (not required): think about how the optimal quantities of yogurt change when the price of chocolate changes. What is the intuition behind this result? Does it apply to any utility functions?