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).

1. (a) Derive Irene's demand function for chips (as a function of her income and the price of chips).
2. (b) Are chips an inferior good for Irene? Is the magnitude of the (total) effect of a decrease in price of chips greater or smaller than the corresponding substitution effect.
3. (c) Obtain Irene's inverse demand function for chips when her income is M = 50. Show that this function is decreasing and convex.
4. Is Irene's Engel curve (as defined in our Lecture 5) upward sloping or downward sloping? Explain in detail.