Question

Coca-Cola Co has determined that the price elasticity of demand for a case of Diet Coke for California residents is E_CA =  –2.0, while the price elasticity of demand for West Virginia residents is E_WV = –3.5. Assume that the marginal cost is constant at MC = $5 and that Coca-Cola can successfully segment the market and prevent arbitrage. To maximize profit, Coca-Cola should set the price for a case of Diet Coke in California at P_CA = $  _______  and in West Virginia at P_WV = $ _______  

Answer 1

Lerner Index = -1 / Elasticity of demand = (P - MC) / P

(1) In California,

-1 / -2 = (PCA - 5) / PCA

1/2 = (PCA - 5) / PCA

PCA = 2 x PCA - 10

PCA = $10

(2) In West Virginia,

-1 / -3.5 = (PWV - 5) / PWV

1/3.5 = (PWV - 5) / PWV

PWV = 3.5 x PWV - 17.5

2.5 x PWV = 17.5

PWV = $7