The world prices of food and energy products have followed similar large swings in recent years. We investigate the long run relationship between these prices using a world Computable General Equilibrium model with detailed representations of food and energy markets. Particular attention is paid to specify macro-economic linkages which have often been overlooked in recent analysis and debate. We find that the omission of these macro-economic linkages has a substantial bearing on this relationship. A positive relationship due to the cost push effect has been identified in most analysis, but we find that the introduction of the real income effect may indeed imply a negative relationship between world food and energy prices. Accordingly, it is crucial to move from a sector-focused analysis to a system wide approach when analyzing the linkages between global energy and food markets.