Mathematical Economics: A Reader

This paper is modeled as a hypothetical first lecture in a graduate Microeconomics or Mathematical Economics Course. We start with 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 we arrive 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 fixed-point theorems and Arrow's impossibility theorem. Several appendices provide a step-wise description of some mathematical concepts often used by economists and a few useful results in microeconomics.Mathematics, Set theory, Utility function, Arrow's impossibility theorem

Network Formation with Endogenous Link Strength and Decreasing Returns to Investment

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

Non-cooperative formation of agent-event networks

We study non-cooperative network formation models with two primitives -- a set of agents and a set of exogenously given events. An event is conceived as any entity around which joint activities can be organized and plays no role beyond serving as a platform to mediate connections between agents. Agents incur costs in subscribing to events but derive benefits from being connected with other agents. This framework differs from most existing models of network formation where agents decide which agents to link with. We first study a benchmark environment and identify the set of strongly efficient and Nash stable architectures. The tension between efficiency and stability in this environment is quite weak because there is no conflict of interest between the agents. Conflict of interest is absent because the underlying preference orderings of agents over the set of feasible networks are such that there is at least one network which is best from the perspective of every agent. The tension that does exist reflects coordination failure among agents. We then consider two extensions which help further clarify the two sources of tension between efficiency and stability. In a model where each event may fail with some exogenously given positive probability, the tension between efficiency and stability arises due to coordination failures. In a model where event subscription costs depend on the identity of agents and events, the tension is either due to conflict of interest or due to coordination failure depending on event subscription costs

Non-cooperative formation of agent-event networks

We study non-cooperative network formation models with two primitives -- a set of agents and a set of exogenously given events. An event is conceived as any entity around which joint activities can be organized and plays no role beyond serving as a platform to mediate connections between agents. Agents incur costs in subscribing to events but derive benefits from being connected with other agents. This framework differs from most existing models of network formation where agents decide which agents to link with. We first study a benchmark environment and identify the set of strongly efficient and Nash stable architectures. The tension between efficiency and stability in this environment is quite weak because there is no conflict of interest between the agents. Conflict of interest is absent because the underlying preference orderings of agents over the set of feasible networks are such that there is at least one network which is best from the perspective of every agent. The tension that does exist reflects coordination failure among agents. We then consider two extensions which help further clarify the two sources of tension between efficiency and stability. In a model where each event may fail with some exogenously given positive probability, the tension between efficiency and stability arises due to coordination failures. In a model where event subscription costs depend on the identity of agents and events, the tension is either due to conflict of interest or due to coordination failure depending on event subscription costs

A primer on mathematical modelling in economics

The Commission on Graduate Education in Economics had raised several concerns regarding the role of mathematics in graduate training in economics (Krueger, 1991; Colander, 1998, 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\u27s 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.<br /

High Prevalence of Antimicrobial Resistance among Clinical Streptococcus pneumoniae Isolates in Asia (an ANSORP Study)

A total of 685 clinical Streptococcus pneumoniae isolates from patients with pneumococcal diseases were collected from 14 centers in 11 Asian countries from January 2000 to June 2001. The in vitro susceptibilities of the isolates to 14 antimicrobial agents were determined by the broth microdilution test. Among the isolates tested, 483 (52.4%) were not susceptible to penicillin, 23% were intermediate, and 29.4% were penicillin resistant (MICs ≥ 2 mg/liter). Isolates from Vietnam showed the highest prevalence of penicillin resistance (71.4%), followed by those from Korea (54.8%), Hong Kong (43.2%), and Taiwan (38.6%). The penicillin MICs at which 90% of isolates are inhibited (MIC(90)s) were 4 mg/liter among isolates from Vietnam, Hong Kong, Korea, and Taiwan. The prevalence of erythromycin resistance was also very high in Vietnam (92.1%), Taiwan (86%), Korea (80.6%), Hong Kong (76.8%), and China (73.9%). The MIC(90)s of erythromycin were >32 mg/liter among isolates from Korea, Vietnam, China, Taiwan, Singapore, Malaysia, and Hong Kong. Isolates from Hong Kong showed the highest rate of ciprofloxacin resistance (11.8%), followed by isolates from Sri Lanka (9.5%), the Philippines (9.1%), and Korea (6.5%). Multilocus sequence typing showed that the spread of the Taiwan(19F) clone and the Spain(23F) clone could be one of the major reasons for the rapid increases in antimicrobial resistance among S. pneumoniae isolates in Asia. Data from the multinational surveillance study clearly documented distinctive increases in the prevalence rates and the levels of antimicrobial resistance among S. pneumoniae isolates in many Asian countries, which are among the highest in the world published to date