Introduction 9 To clarify these ideas, and other to follow, we list the following set of primary dimensions used in economics: (1) Money [ M ] (2) Resources or quantity [ Q ] (3) Time [ T ] (4) Utility or satisfaction [ S ] Apples has, say, dimension [ Q 1] and bananas [ Q 2]. We cannot add an apple to a banana (we can of course add the number of objects, but that is not the same thing). The value of an apple has dimension [ M ] and the value of a banana has dimension [ M ], so we can add the value of an apple to the value of a banana. They have the same dimension. Our reference to [ Q 1] and [ Q 2] immediately highlights a problem, especially for macroeconomics. Since we cannot add apples and bananas, it is sometimes assumed in macroeconomics that there is a single aggregate good, which then involves dimension [ Q ]. For any set of primary dimensions, and we shall use money [ M ] and time [ T ] to illustrate, we have the following three propositions: (1) If a ∈ [ M ] and b ∈ [ M ] then
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