Why solving the model for a benevolent social planner gives an efficient allocation? Probably this question is really dumb - and I'm sorry if it is - but why solving the model for a benevolent social planner, gives an efficient allocation?

What's the criteria for this efficiency?

I'm asking this because in several NK models in macro, when we're comparing the 'desirability' of simple rules, we take as efficient the allocation obtained from solving the model as stated above.

Any help would be appreciated.
I think the general proof is in this paper.

Thinking in a simple exchange Edgeworth Box, a competitive economy involves prices, which mediate the relationship between consumers relative valuation of goods - the marginal rate of substitution. A (benevolent) social planner does not need those prices, as goods will not be traded in the market, but simply allocated to whom it "corresponds", based on the same optimality conditions. Such equilibrium is simply found by equalising consumers marginal rate of substitution. 

In other words:


equilibrium in competitive economy through exchange/markets:


$$ MRS^1_{X,Y} = \frac{P_x}{P_y} = MRS^2_{X,Y} $$


equilibrium via allocation from benevolent social planner:


$$ MRS^1_{X,Y} = MRS^2_{X,Y} $$

(the formulas above can be trivially extended to $n$ consumers and goods)