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Title Essays on Monotone Comparative Statics for Constrained Optimization Problems with Applications
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Publication Date
Date Accessioned
Degree PhD
Discipline/Department Economics
Degree Level doctoral
University/Publisher University of Kansas
Abstract My dissertation consists of three chapters. Chapters 1 and 2 both address extensions to existing monotone comparative statics results for constrained optimization problems using lattice programming techniques. Chapter 3 applies monotone comparative statics results to the question how environmental regulation affects investment in innovation in imperfectly competitive markets. Generally we can distinguish between two types of comparative statics problems. The first type of problem considers the change of the optimal solution to a maximization problem as the objective function changes, the other type considers the change due to a change in the constraint set. Lattice-based comparative statics theorems have been developed for both types of problems in the literature. The strengths of these lattice-theoretic comparative statics results are that they don't depend on the usual smoothness, interiority and concavity assumptions as required by the classical approach based on the Implicit Function Theorem, as well as convexity of the constraint set. Moreover, these comparative statics results also apply in the case of non-unique solutions.Quah (2007) expanded existing results by Milgrom and Shannon (1994) by making them applicable to some non-lattice constraint sets. In the first chapter, I extend existing comparative statics theorems to parametrized objective functions and non-lattice constraint sets. This generalization makes it possible to analyze a variety of economic optimization problems that fall into this class of problems which cannot be addressed using existing lattice-based techniques. I provide examples from consumer theory, producer theory and environmental economics that show the result's broad scope of applications. The second chapter studies monotone comparative statics with respect to price changes in the consumer's utility maximization problem. Most attempts to derive this property rely on aspects of the demand curve, and it has been hard to derive this property using assumptions on the primitive utility function. Using new results on the comparative statics of demand in Quah (2007), I provide simple and easy conditions on utility functions that yield the gross substitutes property. Quah (2007) provides conditions on utility functions that yield normal demand. I add an assumption on elasticity of marginal rate of substitution, which combined with Quah's assumptions yields gross substitutes. I apply this assumption to the family of constant elasticity of substitution preferences. My approach is grounded in the standard comparative statics decomposition of a change in demand due to a change in price into a substitution effect and an income effect. Quah's assumptions are helpful to sign the income effect. Combined with the elasticity assumption, we can sign the overall effect. As a by-product, I also present conditions which yield the gross complements property. Chapter 3 is an application of monotone comparative statics results to the question how environmental regulation affects incentives for R&D investment.…
Subjects/Keywords Economics; Economic theory; comparative statics; consumer problem; environmental regulation; lattice theory; Single Crossing Property; supermodularity
Contributors Sabarwal, Tarun (advisor); Cornet, Bernard (cmtemember); Sicilian, Joseph (cmtemember); Zhang, Jianbo (cmtemember); Pasik-Duncan, Bożenna (cmtemember)
Language en
Rights This item is protected by copyright and unless otherwise specified the copyright of this thesis/dissertation is held by the author.
openAccess
Country of Publication us
Record ID handle:1808/16840
Repository ku
Date Retrieved
Date Indexed 2020-08-13
Issued Date 2014-08-31 00:00:00

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…viii Chapter 1 Extending the Scope of Monotone Comparative Statics Results 1.1 Introduction Comparative statics of constrained optimization problems is a question at the heart of economic analysis. Oftentimes we are not only interested in the…

…optimizers of the problem themselves, but also how they will be affected by changes in exogenous parameters. Generally, we distinguish between two types of comparative statics problems. The first type of problem considers the change of the optimal solution to…

…a maximization problem as the objective function changes, the other type the change due to changes in the constraint set. Comparative statics theorems based on lattice programming methods have been developed for both types of problems. The strengths…

comparative statics results also apply in the case of non-unique solutions. Based on Topkis (1978), Vives (1990) and Milgrom and Roberts (1990) use a lattice-based approach to establish monotone increasing best responses in games…

…with strategic complements 1 under the cardinal assumptions of supermodularity and increasing differences on the objective function when strategy spaces are lattices. Milgrom and Roberts (1990) also focus on monotone comparative statics

…result cannot be applied. Quah (2007) addresses these types of problems and develops comparative statics with respect to changes in non-lattice constraint sets. His result provides necessary and sufficient conditions for nondecreasing solutions…

…set. However, his result does not address comparative statics with respect to parameters in the objective function. In economics, we naturally encounter a variety of questions that involve parameter changes in the objective function, such as changes in…

…problem with Stone-Geary preferences. The question, how income and essential consumption basket changes affect consumer demand, for example, cannot be addressed by existing results. 2 My comparative statics theorem provides necessary and sufficient…

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