These are the materials I will cover on optimal policy with commitment.

1. The following pertains to the case in which the government has a revenue requirement, it has only distorting taxes available for financing it and there are no nominal frictions.

V.V. Chari, L. Christiano and P. Kehoe, 1991, Optimal Fiscal and Monetary Policy: Some Recent Results, Journal of Money, Credit and Banking, vol. 23, no. 3, August, part 2.

V.V. Chari, L. Christiano and P. Kehoe, 1996, Optimality of the Friedman Rule in Economies with Distorting Taxes, Journal of Monetary Economics.

Pierpaolo Benigno and Michael Woodford, Optimal Taxation in an RBC Model: A Linear-Quadratic Approach, August 16, 2005.

2. The following introduces nominal frictions, but preserves the requirement that the government finance an exogenously given expenditure stream with distorting taxes.

Correia, Isabel, Juan Pablo Nicolini and Pedro Teles, 2001, Optimal Fiscal and Monetary Policy: Equivalence Results, manuscript, Research Department, Bank of Portugal.

Siu, Henry, 2001, Optimal Fiscal and Monetary Policy with Sticky Prices, manuscript, Northwestern University (published in JME)

Schmitt-Grohe, Stefanie and Martin Uribe, 2001, Optimal Fiscal and Monetary Policy Under Sticky Prices, manuscript, University of Pennsylvania (published in JET).

3. The following pertains to the case in which the government has no revenue requirement and cannot manipulate tax rates in a state-contingent way (this is how I interpret the complete absence of taxes in these models), but there are nominal frictions (e.g., sticky prices or sticky portfolios) in the economy. Lecture notes.

Goodfriend, Marvin, and Robert G. King, 2001, The Case for Price Stability, National Bureau of Economic Research Working Paper 8423.

Aubhik Khan, Robert G. King and Alexander Wolman, 2000, Optimal Monetary Policy, Federal Reserve Bank of Richmond Working Paper. This environment comes closest to the one studied in the first homework exercise.

King, Robert G., and Alexander L. Wolman, 1996, Inflation Targeting in a St. Louis Model of the 21st Century, Federal Reserve Bank of St. Louis Review, pp. 83-107.

King, Robert G., and Alexander Wolman, 1999, What Should the Monetary Authority do when Prices are Sticky?, in Taylor, editor, Monetary Policy Rules, published for the NBER by the University of Chicago Press.

Rotemberg, Julio, and Michael Woodford, 1999, Interest Rate Rules in an Estimated Sticky Price Model, in Taylor, editor, Monetary Policy Rules, published for the NBER by the University of Chicago Press.

Dupor, Bill, Optimal Monetary Policy With Nominal Rigidities, Wharton School, University of Pennsylvania. This paper suggests that the optimal monetary policy might involve randomizing the money supply.

Gali, Jordi, New Perspectives on Monetary Policy, Inflation, and the Business Cycle. See section 5.2 for optimal monetary policy with sticky prices.

Erceg, Henderson and Levin, Optimal Monetary Policy with Staggered Wage and Price Contracts. This shows that the case of price stability that is often made in a sticky price environment, evaporates when there are sticky wages.

See also the papers on Mike Woodford's web page, http://www.columbia.edu/~mw2230/, for example, 

Woodford, The Taylor Rule and Optimal Monetary Policy.

Andrew Levin, Alexei Onatski, John C. Williams, and Noah Williams, Monetary Policy Under Uncertainty in Micro-Founded Macroeconomic Models, NBER Working Paper 11523, July 2005.

Gary Anderson, Andrew Levin, and Eric Swanson, October 7, 2004, Higher-Order ‘Perturbation’ Solutions to Dynamic, Discrete-Time Rational Expectations Models: Methods and an Application to Optimal Monetary Policy, manuscript.