Problem 2 Consider the following demand and supply relations

Problem 2: Consider the following demand and supply relationships in the market for golf balls: Qd = 90-2P-27, and Qs--9 + 5P-2.5R, where T is the price of titanium, a metal used to make golf clubs, and R is the price of rubber a) If R = 2 and T-10, calculate the equilibrium price and quantity of golf balls. b) At the equilibrium values, calculate the price elasticity of demand and the price elasticity of supply c) At the equilibrium values, calculate the cross-price elasticity of demand for golf balls with respect to the price of titanium. What does the sign of this elasticity tell you about whether golf balls and titanium are substitutes or complements?

Solution

(a)

Qd = 90 - 2P - (2 x 10) = 90 - 2P - 20 = 70 - 2P

Qs = - 9 + 5P - (2.5 x 2) = - 9 + 5P - 5 = - 14 + 5P

In equilibrium, Qd = Qs

70 - 2P= - 14 + 5P

7P = 84

P = 12

Q = 70 - (2 x 12) = 70 - 24 = 46

(b)

Price elasticity of demand = (dQd / dP) x (P / Qd) = - 2 x (12 / 46) = - 0.52

Price elasticity of supply = (dQs / dP) x (P / Qs) = 5 x (12 / 46) = 1.30

(c)

Cross-price elasticity = (dQd / dT) x (T / Qd) = - 2 x (10 / 46) = - 0.43

Since cross-price elasticity is negative, golf balls and titanium are complements.