Irene spends all of her incomeMon 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).

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 isM= 50. Show that this function is decreasing and convex.
4. (d)Is Irene's Engel curve (as defined in our Lecture 5) upward sloping or downward sloping? Explain in detail.