Titanium Golf Club
Cross Price Elasticity of Demand?
I'm confused...help!! And write out how you get there too please, don't just give the answer.
Consider the following demand and supply relationships in the market for golf balls: Qd = 90-2P-2T 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.
R = 2 and T = 10
I already figured:
Equilibrium price = 12
Quantity = 46
Price Elasticity of Demand = -.523
Price Elasticity of Supply = -1.304
So my question is:
At the equilibrium values, calculate the cross-price elasticity of demand for golf balls with respect to the price of titanium.
Qd = Qs
Qd = 90 - 2P - 2T
Qs = -9 + 5P - 2.5R
R = 2
T = 10
Qd = 90 - 2P - 2x10 = 70 - 2P
Qs = -9 + 5P - 2.5x2 = 5P - 14
5P - 14 = 70 - 2P
84 = 7P
P = 12
Qs = Qd = 70 - 2x12 = 5x12 - 14 = 46
Exd(T) = (∂Qd/∂T) x (T/Qd)
∂Qd/∂T = -2
T = 10
Exd(T) = -2 x 10 / Qd = -20/46 = -10/23 ≈ -0.43478
Exs(R) = (∂Qs/∂R) x (R/Qs) = -2.5x2/46 ≈ -0.1087
Es = (∂Qs/∂P) x P/Qs = 5x12/46 ≈ 1.3043
Ed = (∂Qd/∂P) x P/Qd = -2x12/46 ≈ -0.5217
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