We investigate metabolic interactions between astrocytes and GABAergic neurons at steady states corresponding to different activity levels using a six-compartment model and a new methodology based on Bayesian statistics. Many questions about the energetics of inhibition are still waiting for definite answers, including the role of glutamine and lactate effluxed by astrocytes as precursors for c-aminobutyric acid (GABA), and whether metabolic coupling applies to the inhibitory neurotransmitter GABA. Our identification and quantification of metabolic pathways describing the interaction between GABAergic neurons and astrocytes in connection with the release of GABA makes a contribution to this important problem. Lactate released by astrocytes and its neuronal uptake is found to be coupled with neuronal activity, unlike glucose consumption, suggesting that in astrocytes, the metabolism of GABA does not require increased glycolytic activity. Negligible glutamine trafficking between the two cell types at steady state questions glutamine as a precursor of GABA, not excluding glutamine cycling as a transient dynamic phenomenon, or a prominent role of GABA reuptake. Redox balance is proposed as an explanation for elevated oxidative phosphorylation and adenosine triphosphate hydrolysis in astrocytes, decoupled from energy requirements.