Percy consumes cakes and ale. His demand function for cakes is qc = m - 30pc + 20pa, where pa is the price of ale, and 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? (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 respectively. (c) Write an equation for Percy's inverse demand function for cakes where income is $100 and the price of ale remains at $1.
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