Sen's contribution to global feminism alone seems to justify the prize.
Here are some of my notes from the analysis of Sen's book on famines by Meghnad Desai "Story telling and formalism in economics: the instance of famine", International Social Science Journal August 1987.
Sen's study of famines traces how due to high food prices in a famine there is lower effective demand, that is shrinkng markets, for non food products. He traces this effect on non food agricultural producers in four famines: 1943 Great Bengal Famine, the Ethiopan famine of 1972-4, the Bangladesh famine of 174, the Sahel drought and famine of 1969-74.
Sen also explores the problem of entitlements; that is, it is not enough for groups to migrate where there may be food. Special action is needed to restore entitlements. Sen is especially interested in the development of entitlements which are independent of ownership or any other endowment except birth in a certain community, and wants to show that market transactions are not the only nor the natural set of economic relations: they are one among a variety of arrangements for allocating entitlements.
As for the theoretical point, Desai writes: "In the pure Walrasian case, entitlements are assumed to be secure in a trade independent way, i.e., the possibility of starvation death due to an inability to buy sufficient food in exchange for whatever one to sell is ruled out. The theorist does this to rule out awkward in the formal proof construction, ust as the theory rules out the possibility of the bankruptcy for firms. Such ruling out is not dne with any idea that usch things do not happen in teh real world, but that they are either too unimportant to worry about (they happen rarely or in a neglible proportion of cases) or that they introduce complications which require further elaboration. Thus, for instance, if one were to introduce minimum subsistence for consumers as necessary condition for equilibrium, discontinuities enter and make mathematical proofs difficult.
"But what for general equilibrium theorists is an anomaly or a curiosity to be ruled out is the central problem to be investigated in famines i.e. precisely the fact that minimum subsistence quantities are necessary for survival, but impossible to obtain for a sizeable number of people. The pure economic model of competitive equilibrium cannot handle this any more than than it can handle the phenomenon of involuntary unemployment. To rule it out or to minimize its importance by labelling it an anomaly does not make the problem go away."