On Time-to-Build Economies with Multiple-Stage Investments

The paper presents a constructive method for studying dynamic general equilibrium models with time-to-build technology. In the work, the author modifies a seminal work by Kydland and Prescott [1982] by allowing agents to make multi-stage investments. In this framework, consumers decide on how much to consume each period, and how much to invest in future capital, which will yield them income in future periods. Unlike in Kydland and Prescott, agents are allowed to postpone, stop or accelerate the investment by devoting a certain amount of their product to investments, which allows consumers to smooth investment expenses throughout the investment process rather than incur the whole cost at the beginning of the investment, as in Kydland and Prescott. The analysis of the model poses several technical issues, which are tackled in the article. First, the premises of the model exhibit unbounded returns, which makes several dynamic programming arguments invalid. Second, since the imposed assumptions do not exclude boundary solutions, the consumer value function of the underlying problem might not be differentiable, as the standard Benveniste and Scheinkman [1979] argument does not hold. Finally, as the feasible action set is not a lattice, standard monotone comparative statics cannot be introduced in order to bring about the monotonicity results concerning the policy functions in the model. Using dynamic programming methods and monotone operators theory (by Matkowski and Nowak [2009], Quah and Strulovici [2009], and Rincón-Zapatero and Santos [2009]), the author presents a convergent algorithm for the computation of optimal allocations of the model, as well as proposes an economy that decentralizes the allocations in the Arrow-Debreu general equilibrium. Eventually, the author presents some comparative statics results useful for a more general analysis of the problem, and discusses the efficiency of the presented economy.