Irene spends all of her income M on soda and chips. The price of soda is 2 per unit. Irene's utility function is U(s, c) = 5 ln(1 + s) + ln(1 + c).

Hint: throughout the question, you can assume M >=50 and pc <= 8 (these assumptions just rule out the possibility of corner solutions, but do not affect the way we solve the problem).

(a) Derive Irene's demand function for chips (as a function of her income and the price of chips).