The high volatility of the world cocoa price makes the millions of African cocoa farmers highly vulnerable to poverty. A large volatility in the value of an agricultural commodity is linked to the inelasticity of its supply or demand. Therefore, we test the hypothesis that the price elasticities of the global cocoa supply and demand are low. We describe the global cocoa market by way of supply, demand and stock sub-models. Our estimates are based on annual global observations covering the years 1963 through 2013, and three estimation methods. We find that the global cocoa supply is extremely price-inelastic: the corresponding short- and long-run estimates are 0.07 and 0.57 respectively. The price elasticity of cocoa demand also falls into the extremely inelastic range: the short- and long-run estimates are -0.06 and -0.34 respectively. Our assessment also shows that the low global cocoa stock levels amplify the price volatility of cocoa.