In this course, you will learn the mathematical methods at the heart of microeconomics and micro-funded macroeconomics. These are basically the optimization methods needed to formalize the rationality of economic agents’ choices. We will start with a review of the linear algebra, vector spaces, and inner product spaces framework needed to be able to use differentiability properties and work with linear and quadratic approximations to get the first and second order conditions characterizing, sufficiently or necessarily, the optimal choices. Then we will cover systematically, in finite-dimensional spaces, the problems of unconstrained optimization, optimization under equality constraints or the problem of Lagrange, optimization under inequality constraints and the Kuhn-Tucker conditions, the sensitivity of the solutions to the parameters of the problem through the Envelope Theorem for all three cases, the interpretation of the multipliers associated to the constraints, the duality properties of linear programs, and finally optimization over an infinite horizon, both using the first order conditions leading to the Euler equation of the problem, and the Bellman functional equation following from the dynamic programming approach.

In this course, you will learn the fundamentals of how to model the behavior of economic agents and their interactions through markets. We will cover the core of the conceptual framework at the heart of most of economics of competitive markets, namely choice theory, consumer’s choices, classical demand theory, choice under uncertainty, the existence of a general equilibrium in and Arrow-Debreu economy of competitive markets and its efficiency properties, the First and Second Welfare Theorems, trading in sequential markets, Radner equilibria in sequential markets economies with financial assets, incompleteness of markets, infinite horizon economies with either “infinitely-lived” agents or dynasties, or with a sequence of overlapping generations of households.

In an increasingly digitalised environment, data availability offers opportunities not only to empirically test theories through statistical analyses, but also to discern behavioural, associative or intrinsic data patterns and enable or even inspire theory development. Familiarity with probabilistic and statistical thinking and exposure to alternative types and sources of data enables researchers and practitioners to broaden their horizons when considering alternatives in diagnosing problems and developing explanations/solutions. Quantitative Research Methods introduces students to a variety of building-block statistical / data analytic techniques and gets them to develop genuine understanding and judgment about when and why to use each of them. The course extends in two semesters: the first semester covers the foundational concepts and techniques for quantitative analysis, while the second builds on this material to introduce and explain the use of an array of essential multivariate methods. On completion of this course, students will be able to work: a) from problem formulation to data extraction/collection and analysis; and b) from existing data to pattern recognition and problem identification. Further to this course, students will be able to develop their knowledge of methodologies further in their area of specialization in the Core Research Skills course.
The course is designed to be accessible to all students regardless of their ability to access any on-campus teaching events that may be offered. Where on-campus events are provided, students are expected to attend but alternative provision will be available for students who are unable to do so for health or similar reasons.