The high volatility of the world cocoa price makes the millions of cocoa farmers in the developing world 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 with cointegration dynamic supply, demand and price submodels. Our OLS, 2SLS, and SUR estimates are based on annual global observations covering the years 1963 through 2013. We find that the global cocoa supply is extremely price-inelastic: the corresponding short- and long-run estimates are 0.07 and 0.57. 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. Based on these empirical results, we consider the prospects for cocoa price stabilization. The cocoa price volatility was treated with various unsuccessful methods in the past. A possible solution for reducing the price volatility would be the encouragement of crop diversification. This increases the price elasticity of cocoa supply by adjusting the effort and money allocation between the crops, thus decreasing price volatility.