An ice-cream lover has a total of $10 to spend one evening. The price of ice-cream is $p per litre.

q∈(0, 10/q)

(a) Find the first-order condition for a utility maximizing quantity of ice-cream. [Hint: the square root function is a power function with exponent 1 2 .]

(b) Solve the first-order condition derived in (a) in order to express the utility maximizing quantity q ∗ as a function of p.

(c) What guarantees that your quantity q ∗ is really a maximum?