According to Bergson-Samuelson social welfare function approach, social welfare is maximized when _____ .
The social indifference curve is tangent to the utility possibility curve
The social indifference curve is tangent to the utility possibility curve option is correct.
The Bergson–Samuelson social welfare function W = W(U1, U2,…, Un) ranks alternative distributions of individual utilities. Its level curves in utility space are social indifference curves. The utility possibility frontier (UPF) is the outer envelope of all Pareto-efficient utility combinations attainable from the economy’s resources and technology.
Social welfare is maximised at the point where the highest attainable social indifference curve just touches the UPF, i.e. where they are tangent. At tangency the marginal social rate of substitution between the utilities of any two individuals equals the marginal rate of transformation of one person’s utility into another’s along the UPF — the Bergson–Samuelson optimum, sometimes called the “bliss point”.
Intersections mean the social indifference curve cuts inside the UPF, so a higher indifference curve is still reachable. The production possibility frontier lives in commodity space, not utility space, and is therefore the wrong frontier for maximising a welfare function defined over utilities.
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