In a laboratory experiment with supply function competition and private information about correlated costs we study whether cost interdependence leads to greater market power in relation to when costs are uncorrelated in the ways predicted by Bayesian supply function equilibrium. We find that with uncorrelated costs observed behavior is close to the theoretical benchmark. However, with interdependent costs and precise private signals, market power does not raise above the case of uncorrelated costs contrary to the theoretical prediction. This is consistent with subjects not being able to make inferences from the market price when costs are interdependent. We find that this effect is less severe when private signals are noisier.