Target group 
Master’s Programme in Economics (Research track). Open to doctoral students in economics. 
Timing 
Annually in the first period 
Learning outcomes 
After the course, the student should
 Understand and be able to reproduce the deterministic version of the RamseyCassKoopman macroeconomic model, in both discrete and continuous time (infinite horizon Lagrangian and Hamiltonian techniques)
 Understand the difference between exogenous and optimal taxation in the above framework, and be able to reproduce both approaches technically
 Be able to solve the models with dynamic programming and value function iteration methods and understand the advantages of the model over the Lagrangian/Hamiltonian structures

Completion methods 
The course consists of lectures (24 hours) and exercise sessions (8 hours), where solutions to the homework assignments are discussed. Participation in lectures and exercise sessions is not mandatory, but completing 40% of the homework assignments is required for taking the exam. There is a written final exam based on the lecture material and the homework assignments. The homework assignments consist of analytical exercises. They familiarise the student with the theory and calculations typically required in applying and extending the models that have been studied in the lecture. 
Prerequisites 
Basic studies in mathematics. In addition, the student is assumed to be familiar with the neoclassical growth model, dynamic optimisation, and household and firm behaviour to the extent covered in a Bachelorlevel macroeconomics course. 
Recommended optional studies 
Any course beyond the Bachelorlevel core courses in microeconomics, macroeconomics and probability supports learning of the course material. 
Contents 
The course first covers the deterministic version of the RamseyCassKoopman growth model, both in discrete and continuous times, and solves it using an infinite horizon Lagrangian/Hamiltonian. The model is then used to study taxation. Two approaches are covered: the case where taxes are exogenously given and when they result from optimisation of the Ramsey planner. Finally, the course introduces dynamic programming and value function iteration methods and compares them with the abovementioned methods in the same model environment 
Study materials and literature 
In addition to the lecture material, selected parts of Recursive Macroeconomic Theory by Ljungqvist and Sargent, 3rd edition (2012, MIT Press; 2nd edition, 2004, available online); Applied Intertemporal Optimization by Wälde (2011, available online); Macroeconomic Theory: A Dynamic General Equilibrium Approach by Wickens, 2nd edition (2012); Introduction to Modern Economic Growth by Acemoglu (2008, available online) that are covered in the course are recommended. 
Activities and teaching methods in support of learning 
Course material is delivered through the course website. The website also contains moderated discussion groups that support learning. Problem sets are designed to support learning of the course material. 
Assessment practices and criteria 
The grade on a scale from 0 (fail) to 5 is based on the points earned in the final exam. At least 40% of the homework assignments must be completed to take the exam 