Constant Elasticity Of Substitution Utility Function Research Articles

The Nonlinear Model of Intersectoral Linkages of Kazakhstan for Macroeconomic Decision-Making Processes in Sustainable Supply Chain Management

We provide a nonlinear model of intersectoral balance with constant elasticity of substitution (CES) production functions of industries and CES utility function of final consumer for the study of intersectoral linkages in the Kazakhstan economy. The model is formalized in terms of the primal problem of resource allocation and the corresponding Fenchel dual problem which solution gives costs of inputs of industries in a supply network. We identify the model with the actual data of the Input-Output tables of Kazakhstan and estimate the elasticity of substitution of production factors for the aggregated industry complexes. With the help of developed framework, we evaluate the inter-industry financial flows in the aggregated supply network for the period 2013–2020 and compare the results with the actual data of Kazakhstan. The developed framework can be used to support decision-making processes in sustainable supply chain management in a situation of the government economic policy change and external shocks. Using the developed framework, we evaluate the risks for Kazakhstan’s supply chains in scenario of sharp weakening of the national currency.

The Optimal Urban Scale from Different Perspectives and under Different Development Goals Based on the CES Utility Function

To analyze the differences in the optimal urban scale of a country, a government, and residents under different urban development goals and to provide a reference for urban development, an urban development model is constructed based on the constant elasticity of substitution (CES) utility function. The objective function includes four indicators: the economic level, the traffic level, environmental quality, and living conditions. The urban development model is constructed by integrating an urban road planning model, bus route planning model, land use model, and four-stage traffic sharing and traffic allocation model. Based on the setting of different development goals, this model is used to calculate the urban utility value perceived by each stakeholder at different urban scales. Through comparative analysis, we determine the following: (1) When the urban development goals are different, the optimal urban scale of residents and the government differs greatly, and the optimal scale of the country differs very little. (2) When facing the same development goal, the optimal urban scales of the three stakeholders are not the same. However, the three stakeholders are closely related to urban development. Therefore, the selection of the optimal urban scale should comprehensively consider the interests of the three stakeholders.

General Equilibrium in a Heterogeneous-Agent Incomplete-Market Economy with Many Consumption Goods and a Risk-Free Bond

We study a pure-exchange incomplete-market economy with heterogeneous agents. In each period, the agents choose how much to save (i.e., invest in a risk-free bond), how much to consume, and which bundle of goods to consume while their endowments are fluctuating. We focus on a competitive stationary equilibrium (CSE) in which the wealth distribution is invariant, the agents maximize their expected discounted utility, and both the prices of consumption goods and the interest rate are market-clearing. Our main contribution is to extend some general equilibrium results to an incomplete-market Bewley-type economy with many consumption goods. Under mild conditions on the agents' preferences, we show that the aggregate demand for goods depends only on their relative prices and that the aggregate demand for savings is homogeneous of degree in prices, and we prove the existence of a CSE. When the agents' preferences can be represented by a CES (constant elasticity of substitution) utility function with an elasticity of substitution that is higher than or equal to one, we prove that the CSE is unique. Under the same preferences, we show that a higher inequality of endowments does not change the equilibrium prices of goods, and decreases the equilibrium interest rate. Our results shed light on the impact of market incompleteness on the properties of general equilibrium models.

Household utility maximization with life insurance: a CES utility case

We investigate the optimal consumption, portfolio, and life insurance decisions problem of a liquidity constrained household whose preference is given by the CES (constant elasticity of substitution) utility function. By applying the martingale and duality method, we obtain the closed-form solution for the household’s value function and optimal strategies. We provide a rigorous proof for the optimality of the strategies. We exhibit comparative static results of the optimal decisions with respect to the elasticity of substitution between consumption and leisure.

Investigations to the price evolutions of goods exchange with CES utility functions

The price evolutions of goods exchange in multi-agent market are investigated by employing the kinetic theory. Assume that a closed market consists of two groups (A and B) of agents, who have the same preferences for goods. The constant elasticity of substitution (CES) utility function which contains Cobb–Douglas utility function and Leontief utility function, is used to describe the agent’s preferences. A system of linear Boltzmann type equation is given to describe the probability distributions of goods for agents of the two groups, in which the agents are allowed to adopt certain trading strategies to maximize their utility and improve their wealth conditions. We assume that agents in group A put all their goods into the market for maximum utility, while agents in group B aim to acquire maximal utility from goods exchange by suitably selecting the percentage of goods which are exchanged. The effects of different trading strategies on commodity price and wealth distribution are discussed. The results show that the trading strategies of agents in group B have effectively improved their wealth status under certain assumptions. Also, a general system of nonlinear Boltzmann equation for the probability distributions of goods is given to describe the pricing issues of goods exchange for agents. The numerical experiments of nonlinear Boltzmann equations demonstrate how the trading strategies and preferences of agents modify the price of goods.

Solving the consumer’s utility-maximization problem with CES and Cobb-Douglas utility function via mathematical inequalities

This paper presents a new, non-calculus approach to solving the consumer’s utility–maximization problem with constant elasticity of substitution (CES) utility function, as well as with Cobb-Douglas utility function in case of \(n\ge 2\) commodities. Instead of using the Lagrange multiplier method or some other method based on differential calculus of several variables which might give complicated terms and equations difficult to handle, the utility–maximization problems are solved by using Jensen’s inequality and weighted arithmetic-geometric mean (weighted AM–GM) inequality. In comparison with calculus methods, such approach does not require checking first and second order conditions.

Proportional response dynamics in the Fisher market

We show that the proportional response dynamics, a utility based distributed dynamics, converges to the market equilibrium in the Fisher market with constant elasticity of substitution (CES) utility functions. By the proportional response dynamics, each buyer allocates his budget proportional to the utility he receives from each good in the previous time period. Unlike the tâtonnement process and its variants, the proportional response dynamics is a large step discrete dynamics, and the buyers do not solve any optimization problem at each step. In addition, the goods are always cleared and assigned to the buyers proportional to their bids at each step. Despite its simplicity, the dynamics converges fast for strictly concave CES utility functions, matching the best upper-bound of computing the market equilibrium via the solution of a global convex optimization problem.