Question

of 2. (30 points) The demand of a product y depends on its own price UP ), and the price another product X (P. The price elasticity of Yis e,ー3.5, and the cross-price elasticity of Y with respect to X is e0.8. (a) Are X and Y substitutes or complements? lete (b) Suppose now P, increases by 2%, and r, decreases by 5%. Will the quantity demanded of Y increase or decrease? By what percent? 3. (20 points) The demand function of cigarettes is linear Q in packs, P is the price/pack in dollars (a) when P $2, what is the elasticity of demand 1,500-25oP where Q is quantity 2 Is the demand elastic or inelastic? (b) What is the price at which the demand for cigarettes has unitary elasticity? (c) Suppose after an anti- cigarettes campaign, the demand function of soft drinks becomes Q 5000-200P2 At the price you identified in (b), what is the elasticity of demand now given the new demand function? Is it elastic or inelastic?

Answer 1

Question 2:
(a) X and Y are complements as cross price elasticity of Y with respect to X is negative given by eyx = -0.8

(b) The price elasticity of Y, ep = -3.5 which means that as price of Y increases, quantity demanded of Y decreases.
Also, they are complements, which means as price of x, Px decreases, quantity demanded of both X and Y increases.

Now, price elasticity of Y, ep = Percentage change in quantity demanded of Y/Percentage change in price of Y
So, Percentage change in quantity demanded of Y = ep*Percentage change in price of Y = (-3.5)*(2%) = -7%

And, cross price elasticity of Y with respect to X, eyx = Percentage change in quantity demanded of Y/Percentage change in price of X
So, Percentage change in quantity demanded of Y = eyx*Percentage change in price of X = (-0.8)*(-5%) = 4%

Thus, total change in quantity demanded of Y = -7% + 4% = -3%

Thus, the quantity demanded of Y will decrease. It will decrease by 3 percent.

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