# The Uses of Interactivity

Bridget Diana & Christopher Makler

SFI

## Outline

• Why interactives?
• Discussion of graphs developed for BH

## Part I: Why Interactives?

• Comparative statics
• Relationships between different graphs
• Causal relationships
• Implications of functional forms
\text{revenue} = r(q) = p(q) \times q
\text{marginal revenue} = {dr \over dq} = {dp \over dq} \times q + p(q)

## Reason 1: Illustrating Comparative Statics

\text{marginal revenue} = {dr \over dq} = {dp \over dq} \times q + p
dr = dp \times q + dq \times p
p
p(q)
q

The total revenue is the price times quantity (area of the rectangle)

\text{marginal revenue} = {dr \over dq} = {dp \over dq} \times q + p
dr = dp \times q + dq \times p
p
p(q)
q
dp
dq

The total revenue is the price times quantity (area of the rectangle)

If the firm wants to sell $$dq$$ more units, it needs to drop its price by $$dp$$

Revenue loss from lower price on existing sales of $$q$$: $$dp \times q$$

Revenue gain from additional sales at $$p$$: $$dq \times p$$

## Reason 2: Showing Relationships between Diagrams

• Relationship of optimal choice in an indifference curve/budget constraint diagram to the demand curve
• Relationship of Edgeworth Box diagram to individual perspectives

## Reason 3: Showing Cause and Effect

• How do price-taking consumers and firms respond to changes in prices in the supply and demand model? How do the equilibrium price and quantity respond to changes in demand/supply shifters?

## Reason 4: Understanding Relationships between Mathematical Formulas and Graphical Representations

• How do indifference curves reflect "utility"?
• How are the parameters of a utility function reflected in the shape of indifference curves?
• How are the parameters of a risk aversion problem reflected in diagrams of expected utility and preferences over lotteries?

## Part III: Interactivity for BH

• Goal: student self-use
• Guiding principles:
• "Playing God" - adjust parameters using controls outside the graph
• "Agent Choice" - move something on the graph
• Heavy on instructions and explanation

By Chris Makler

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