Group of Visualisations

CES Indifference Curves

Introduction

General Objective

The CES utility function allows us to represent both substitutes as well as complements. For the case of two goods, this visualisation shows how an individual consumer’s indifference curves react to changes in the values of the parameters that define a constant elasticity of substitution (CES) utility function.

Equations

The following equations drive the visualisation in this group.

CES Utility

where $U$ is utility, $q_1$ is the quantity of good 1, $q_2$ is the quantity of good 2, $\alpha_{1}$ is the share parameter of good 1, $\alpha_{2}$ is the share parameter of good 2, and $\rho$ characterises substitution between $q_1$ and $q_2$ .

Since we only have two goods and $\alpha_{1}$ and $\alpha_{2}$ are the respective share parameters, we require $\alpha_{1}+\alpha_{2}=1$ . The elasticity of substitution, which we use as a parameter below, is given by $\sigma=\frac{1}{1-\rho }$ . Note that this value is constant.

CES Indifference Curve

To get the equation for the indifference curve, we set

where $k$ is a constant. Hence, the indifference curve is given by:

Note that by requiring $U(q_{1},q_{2})=k$ we have $dU=0$ , i.e. no change in utility.

How to Use This Visualisation

The visualisation in this group offers the following modes of interaction.

The following values can be changed

Meaning of the icons

Refresh

Refresh the visualisation. It will reload with all its initial values as described below.

Select a Parameter or Variable

Select one of the parameters $\alpha_1$ , $\sigma$ or $k$ or the variable $q_1$ in order to change its value and display the effects of the respective changes.

Increase Value

Increase the value of the selected parameter ( $\alpha_1$ , $\sigma$ or $k$ ) or variable ( $q_1$ ). By keeping the button pressed, the value will continue to increase incrementally.

Decrease Value

Decrease the value of the selected parameter ( $\alpha_1$ , $\sigma$ or $k$ ) or variable ( $q_1$ ). By keeping the button pressed, the value will continue to decrease incrementally.

Change Value

Set the value of the selected parameter ( $\alpha_1$ , $\sigma$ or $k$ ) or variable ( $q_1$ ) by using a slider. This allows for faster changes than by using the plus and minus buttons.

Select a View

Choose between two different selections of coordinate systems.

Display Details

Display a brief description as well as the equations driving the visualisation.

Visibilities

Toggle the visibilities of the graphical elements described below.

Combinations of coordinate systems

Available Focuses

The visualisation offers two focuses:

Indifference curves

A single coordinate system showing two indifference curves. We display two indifference curves to highlight the effects of changes in the values of parameters. The visibility of the initial indifference curve can be toggled.

Indifference curves with bar charts

This focus displays the same coordinate system and graphs as in (1) above on the left side, while adding bar charts that represent both the initial and current values of the parameters of CES utility.

CES Indifference Curves

Introduction

General Objective

Equations

The following equations drive the visualisation in this group.

CES Utility

CES Indifference Curve

How to Use This Visualisation

The visualisation in this group offers the following modes of interaction.

The following values can be changed

Meaning of the icons

Refresh

Select a Parameter or Variable

Increase Value

Decrease Value

Change Value

Select a View

Display Details

Visibilities

Combinations of coordinate systems

Available Focuses

Indifference curves

Indifference curves with bar charts

Initialisation

Description

Parameter Values

Highlighted Variable Value

Initial Visibilities

CES Indifference Curves

Introduction

General Objective

Equations

The following equations drive the visualisation in this group.

CES Utility

CES Indifference Curve

How to Use This Visualisation

The visualisation in this group offers the following modes of interaction.

The following values can be changed

Meaning of the icons

Refresh

Select a Parameter or Variable

Increase Value

Decrease Value

Change Value

Select a View

Display Details

Visibilities

Combinations of coordinate systems

Available Focuses

Indifference curves

Indifference curves with bar charts

Initialisation

Description

Parameter Values

Highlighted Variable Value

Initial Visibilities

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