# 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

#### SFI Presentation

By Chris Makler

# SFI Presentation

- 155