Find the price-income and substitution eects

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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?

Reference no: EM131004558

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