The demand curve for a product X is given as: Q_d = 75 - 12Px + 15Ps; where Px is the price of product X and Ps is the price of a related good S.

Let the price of this related good S be $3.

(a) Is the related good S a substitute good or a complement good to product X? Explain your reasoning.

(b) If Px is = $6, what is the quantity demanded?

(c) If Px decreases to $2, what is the new quantity demanded?

(d) If Px = $2, what is the own-price elasticity of demand?

(e) If Px = $2, what is the cross-price elasticity of demand?