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Quasimodo consumes cereals and other things. His utility function for cereals x and money to spend...

Quasimodo consumes cereals and other things. His utility function for cereals x and money to spend on other goods y is given by u(x, y) = 100x − x 2 + y.

(a) Let p denote the price for cereals and y be a numeraire whose price is set equal to 1. What is his demand curve for cereals?

(b) If the price of cereals is $20, how many cereals will he consume? What if the price of cereals is $30?

(c) Suppose that Quasimodo has $2000 in total to spend and the price of cereals has increased from $20 to $30. How much does his income have to increase to make him not complain about the price increase? (In other words, what is the compensating variation?)

(d) What is the change in consumer’s surplus when the price changes from $20 to $30? Compare this number to the answer to (c).

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