A Consumer Has Preferences Given by the Constant Elasticity of Substitution

question 81

Essay

A consumer has preferences given by the constant elasticity of substitution utility function:
U(q₁,q₂)= (q₁.⁵ + q₂.⁵)²
a.Write the Lagrangian for the consumer's maximization problem.
b.Use the Lagrangian to solve for the optimal quantities in terms of the prices and income.

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Definitions:

Least Squares

A mathematical approach used in regression analysis to minimize the sum of the squares of the differences between observed and predicted values.

Regression Line

A line of best fit through a scatter plot of data points, illustrating the relationship between two variables in a linear regression model.

Quadratic Model

A mathematical representation where the relationship between the variables is defined by a second-degree polynomial.

Autoregressive Model

A statistical model for analyzing and forecasting time series data, where future values are assumed to depend linearly on past values.