Introduction9To clarify these ideas, and other to follow, we list the following set of primarydimensions used in economics:(1)Money [M](2)Resources or quantity [Q](3)Time [T](4)Utility or satisfaction [S]Apples has, say, dimension [Q1] and bananas [Q2]. We cannot add an apple toa banana (we can of course add the number of objects, but that is not the samething). Thevalueof an apple has dimension [M] and the value of a banana hasdimension [M], so we can add the value of an apple to the value of a banana. Theyhave the same dimension. Our reference to [Q1] and [Q2] immediately highlights aproblem, especially for macroeconomics. Since we cannot add apples and bananas,it is sometimes assumed in macroeconomics that there is asingleaggregate 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)Ifa∈[M] andb∈[M] thena±b∈[M](2)Ifa∈[M] andb∈[T] thenab∈[MT] anda/b∈[MT−1](3)Ify
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