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.

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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