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

Hint: throughout the question, you can assume M>or=50 and pc

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

(b)Are chips an inferior good for Irene? Is the magnitude of the (total) eect of a decrease in price of chips greater or smaller than the corresponding substitution eect?

(c)Obtain Irene's inverse demand function for chips when her income isM=50.Show that this function is decreasing and convex.

(d)Is Irene's Engel curve (as defined in our Lecture 5) upward sloping or downward sloping?Explain in detail.