# Question: price changes 16 points the utility function is given by...

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Price Changes (16 points)

The utility function is given by U(x, y) = xy2 . (a) Write out the demand functions for goods x and y in terms of I, px, and py. (2)

(b) What is the maximum utility the consumer can achieve as a function of I, px, and py? (2)

(c) What is the minimum the consumer needs to spend to achieve a level of utility U as a function of px, and py? (2)

(d) The initial income is $576, initial prices are px = 3 and py = 4. What is the quantity of good x consumed, x0? (2)

(e) Now the price of good x rises to 64/9. What is the new quantity of good x consumed, x 0 ? (2)

(f) What income would the consumer need at the least, in order to be as well off under the new prices as under the old ones? (2)

(g) If the consumer had that amount of money, how much would she consume of good x (call it xˆ)? (2) (h) What are the total, income, and substitution effects of the price change on her demand of x?