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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...

7. 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.

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