Final answer:
The Edgeworth box models welfare economic theory by showing the distribution of resources and their effect on individual utility, making alternative (ii) the correct answer.
Step-by-step explanation:
The Edgeworth box is a tool used in microeconomic theory to display and analyze the distribution of resources and the concept of efficiency in the context of a two-person economy. The box is used to model welfare economic theory by showing how different distributions of goods or resources can affect the welfare or utility of the individuals involved. The correct answer to the question is therefore D: Only alternative (ii) is true.
Welfare social functions can be represented with the Edgeworth box only in the sense that they relate to theories of welfare economics, but the box itself does not model social welfare functions explicitly. Additionally, non-welfare economic theories are not directly modeled by the Edgeworth box, as it focuses on welfare and utility maximization.