Perry consumes cakes and ale. His demand function for cakes is qc = m - 30pc 20pa, where m is his income, pa is the price of ale, pc is the price of cakes, and qc is his consumption of cakes. Percy's income is $100, and the price of ale is $1 per unit. a. Is ale a substitute for cakes or a complement? Explain. b. Write an equation for Percy's demand function for cakes where income and the price of ale are held fixed at $100 and $1. c. Write an equation for Percy's inverse demand function for cakes where income is $100 and the price of ale remains at $1. i. At what price would Percy buy 30 cakes? Use blue ink to draw Percy's inverse demand curve for cakes. d. Suppose that the price of ale rises to $2.50 per unit and remains there. Write an equation for Percy's inverse demand for cakes. i. Use red ink to draw in Percy's new inverse demand curve for cakes.