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The Commission on Graduate Education in Economics had raised several concerns regarding the role of mathematics in graduate training in economics (Krueger, 1991;Colander, 1998Colander, , 2005. This paper undertakes a detailed scrutiny of the notion of a utility function to motivate and describe the common patterns across mathematical concepts and results that are used by economists. In the process one arrives at a classification of mathematical terms which is used to state mathematical results in economics. The usefulness of the classification scheme is illustrated with the help of a discussion of Arrow's impossibility theorem. Common knowledge of the patterns in mathematical concepts and results could be effective in enhancing communication between students, teachers and researchers specializing in different sub-fields of economics. Where Do Economic Agents Operate?Let us consider a standard question in consumer theory -What will be the optimal consumption bundle of an agent given her utility function, the amount of money she plans to spend and the prices of the goods? Formulating this question is a two-step procedure. In the first step we translate the intuitive understanding of the consumer's problem into a mathematical framework. In the second step we implicitly argue that the consumer will choose that feasible bundle which offers her maximum utility.One may say that this question is stated as if the playground is given and we want to predict how the player will play. The crucial thing to note is that mathematics is used, first and foremost, to delineate the precise structure of the playground in which we allow economic agents to operate. Answering how an agent will operate is logically the second step. Economists would summarize the answer to this second question by saying that the agent will optimize given the relevant constraints.We shall be interested in the first step. One of our main goals will be to highlight the common procedure that is used to formulate the playgrounds in which we let economic agents operate. This will allow us to provide a succinct and informative answer to the first question: Where do economic agents operate? In order to answer this question we first need to understand the meaning of a utility function.

We study the formation of networks where agents choose how much to invest in each relationship. The benefit that an agent can derive from a network depends on the strength of the direct links between agents. We assume that the strength of the direct link between any pair of agents is a concave function of their investments towards each other. In comparison with some existing models of network formation where the strength technology is a convex function of investment, we find that (i) the symmetric complete network can dominate the star architecture in terms of total utility; (ii) a dominating symmetric complete network needs not be stable; and, (iii) star and complete networks can be dominated by small-world networks.

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