Jeremy is an economics student who loves hamburgers. He could eat any number of them for dinner, but he gets a really bad stomach ache after eating a certain amount. In fact, his utility function for hamburgers is given by:

U(q) =10q = q²/2

where q is the number of hamburgers he eats for dinner (with q ≥ 0).

(a) How many hamburgers can Jeremy eat before he gets a stomach ache (that is, before his utility becomes negative)?

(b) Calculate the optimal number of hamburgers that Jeremy can eat as a function of p, the price per hamburger. (Hint: You have to maximize Jeremy's "net utility". That is, his utility minus the amount he spends on hamburgers.)

(c) Derive Jeremy's inverse demand for hamburgers.

(d) Compute Jeremy's consumer surplus as a function of p.

(e) Show that Jeremy's net utility as a function of p coincides with his consumer surplus