3.1 — The Supply and Demand Model

# 3.1 — The Supply and Demand Model

## ECON 306 • Microeconomic Analysis • Spring 2023

### Ryan Safner Associate Professor of Economics <a href="mailto:safner@hood.edu">safner@hood.edu</a> <a href="https://github.com/ryansafner/microS23">ryansafner/microS23</a> <a href="https://microS23.classes.ryansafner.com"> microS23.classes.ryansafner.com</a>

---

# Outline

### [Equilibrium](#3)
### [Recall: Demand](#10)
### [Recall: Supply](#15)
### [Market Equilibrium](#21)
### [Why Markets Tend to Equilibrate](#23)
### [Comparative Statics](#31)

---

# Equilibrium

---

# Recall: 2 Major Models of Economics as a “Science”

## Optimization

- Agents have .hi[objectives] they value

- Agents face .hi[constraints]

- Make .hi[tradeoffs] to maximize objectives within constraints

## Equilibrium

- Agents .hi[compete] with others over **scarce** resources

- Agents .hi[adjust] behaviors based on prices

- .hi[Stable outcomes] when adjustments stop

]

---

# Recall: Optimization and Equilibrium

.pull-left[
- If people can *learn* and *change* their behavior, they will always switch to a higher-valued option

- If there are no alternatives that are better, people are at an *optimum*

- If everyone is at an optimum, the system is in *equilibrium*
]

![:scale 70%](../images/equilibriumbalance.png)
]
]

---

# Equilibrium Analysis & Price Theory

- Where do prices come from?

- *How* do they *change*?

- How consumers and producers to *respond* to changes?

- What *predictions* can we make about what we will see in the world?
]

---

# Equilibrium Analysis

.pull-left[
- An .hi[equilibrium] is an allocation of resources such that no individual has an incentive to alter their behavior

- In markets: .hi-purple[“market-clearing”] prices where quantity supplied equals quantity demanded
]

---

# *Partial*  Equilibrium Analysis

.pull-left[
.smallest[
- We will only look at .hi-purple[“*partial* equilibrium”] for a single market

- Changes in *one* market often affect *other* markets, affecting the .hi-purple[“*general* equilibrium”]
  - .hi-green[Example]: change in price of *corn* will affect the market for wheat, soybeans, flax, cereal, sugar, candy, ethanol, gasoline, automobiles, etc...
  - think of all of the *complements*, *substitutes*, upstream and downstream goods in production...
  - General equilibrium is too complicated for undergraduate courses...
]
]
.pull-right[
.center[
![:scale 100%](../images/stockprices.jpg)
]
]

---

# Recall: Demand

---

# Demand Function

- .hi[Demand function] relates quantity to price

.bg-washed-green.b--dark-green.ba.bw2.br3.shadow-5.ph4.mt5[
.green[**Example**]: 
`$$q=10-p$$`
]
- Not graphable (wrong axes)!

]

<img src="3.1-slides_files/figure-html/unnamed-chunk-1-1.png" width="504" style="display: block; margin: auto;" />
]

---

# Inverse Demand Function

- .hi[*Inverse* demand function] relates price to quantity
    - Take demand function and solve for `$p$`

.bg-washed-green.b--dark-green.ba.bw2.br3.shadow-5.ph4.mt5[
.green[**Example**]: 
`$$p=10-q$$`
]
- Graphable (price on vertical axis)!

]

---

# Inverse Demand Function

- .hi[*Inverse* demand function] relates price to quantity
    - Take demand function and solve for `$p$`

.bg-washed-green.b--dark-green.ba.bw2.br3.shadow-5.ph4.mt5[
.green[**Example**]: 
`$$p=10-q$$`
]

- Vertical intercept (.hi-purple["Choke price"]): price where `\$q_D=0\$` ($10), just high enough to discourage *any* purchases

]

<img src="3.1-slides_files/figure-html/unnamed-chunk-2-1.png" width="504" style="display: block; margin: auto;" />
]

---

# Inverse Demand Function

- Read two ways:

- Horizontally: at any given price, how many units person wants to buy

- Vertically: at any given quantity, the .hi[maximum willingness to pay (WTP)] for that quantity
    - This way will be very useful later

]

<img src="3.1-slides_files/figure-html/unnamed-chunk-3-1.png" width="504" style="display: block; margin: auto;" />
]

---

# Recall: Supply

---

# Supply Function

- .hi[Supply function] relates quantity to price

.bg-washed-green.b--dark-green.ba.bw2.br3.shadow-5.ph4.mt5[
.green[**Example**]: 
`$$q=2p-8$$`
]
- Not graphable (wrong axes)!

]

<img src="3.1-slides_files/figure-html/unnamed-chunk-4-1.png" width="504" style="display: block; margin: auto;" />
]

---

# Inverse Supply Function

- .hi[*Inverse* supply function] relates price to quantity
    - Take supply function, solve for `$p$`

.bg-washed-green.b--dark-green.ba.bw2.br3.shadow-5.ph4.mt5[
.green[**Example**]: 
`$$p=4+0.5q$$`
]
- Graphable (price on vertical axis)!

]

<img src="3.1-slides_files/figure-html/unnamed-chunk-5-1.png" width="504" style="display: block; margin: auto;" />
]

---

# Inverse Supply Function

.bg-washed-green.b--dark-green.ba.bw2.br3.shadow-5.ph4.mt5[
.green[**Example**]: 
`$$p=4+0.5q$$`
]

- Slope: 0.5

- Vertical intercept called the .hi["Choke price"]: price where `\$q_S=0\$` ($4), just low enough to discourage *any* sales

]

<img src="3.1-slides_files/figure-html/unnamed-chunk-6-1.png" width="504" style="display: block; margin: auto;" />
]

---

# Inverse Supply Function

- Read two ways:

- Horizontally: at any given price, how many units firm wants to sell

- Vertically: at any given quantity, the .hi[minimum willingness to accept (WTA)] for that quantity

]

<img src="3.1-slides_files/figure-html/unnamed-chunk-7-1.png" width="504" style="display: block; margin: auto;" />
]

---

# Market Equilibrium

---

# Market Equilibrium

- .hi-purple[Market-clearing (equilibrium) quantity exchanged] `$\color{#6A5ACD}{(q^\star)}$`: 4 units
]
]

.pull-right[
<img src="3.1-slides_files/figure-html/unnamed-chunk-8-1.png" width="504" style="display: block; margin: auto;" />
]

---

# Why Markets Tend to Equilibrate

---

# Excess Demand I

.bg-washed-green.b--dark-green.ba.bw2.br3.shadow-5.ph4.mt5[
.smallest[
.green[**Example**]: Consider *any* price below $6, such as $5:

- `$\color{blue}{Q_d=5} \quad \color{red}{Q_s=2}$`

- `$\color{blue}{Q_d}>\color{red}{Q_s}$`: .hi[excess demand]

- A .hi[shortage] of 3 units
]
]

]

.pull-right[
<img src="3.1-slides_files/figure-html/unnamed-chunk-9-1.png" width="504" style="display: block; margin: auto;" />
]

---

# Excess Demand II

.bg-washed-green.b--dark-green.ba.bw2.br3.shadow-5.ph4.mt5[
.smallest[
.green[**Example**]: Consider *any* price below $6, such as $5:

- `$\color{blue}{Q_d=5} \quad \color{red}{Q_s=2}$`

- `$\color{blue}{Q_d}>\color{red}{Q_s}$`: .hi[excess demand]

- A .hi[shortage] of 3 units
]
]

- For 2 units, some buyers are willing to pay more than $5

]
]

.pull-right[
<img src="3.1-slides_files/figure-html/unnamed-chunk-10-1.png" width="504" style="display: block; margin: auto;" />
]

---

# Excess Demand II

---

# Excess Demand III

.bg-washed-green.b--dark-green.ba.bw2.br3.shadow-5.ph4.mt5[
.smallest[
.green[**Example**]: Consider *any* price below $6, such as $5:

- `$\color{blue}{Q_d=5} \quad \color{red}{Q_s=2}$`

- `$\color{blue}{Q_d}>\color{red}{Q_s}$`: .hi[excess demand]

- A .hi[shortage] of 3 units
]
]

- At higher prices, sellers willing to sell more!

- Until .hi-purple[equilibrium], no pressure for change, `$\color{blue}{Q_d}=\color{red}{Q_s}$`
]
]

.pull-right[
<img src="3.1-slides_files/figure-html/unnamed-chunk-11-1.png" width="504" style="display: block; margin: auto;" />
]

---

# Excess Supply I

.bg-washed-green.b--dark-green.ba.bw2.br3.shadow-5.ph4.mt5[
.smallest[
.green[**Example**]: Consider *any* price above $6, such as $7:

- `$\color{blue}{Q_d=2} \quad \color{red}{Q_s=8}$`

- `$\color{blue}{Q_d}<\color{red}{Q_s}$`: .hi[excess supply]

- A .hi[surplus] of 6 units
]
]

]

.pull-right[
<img src="3.1-slides_files/figure-html/unnamed-chunk-12-1.png" width="504" style="display: block; margin: auto;" />
]

---

# Excess Supply II

.bg-washed-green.b--dark-green.ba.bw2.br3.shadow-5.ph4.mt5[
.smallest[
.green[**Example**]: Consider *any* price above $6, such as $7:

- `$\color{blue}{Q_d=2} \quad \color{red}{Q_s=8}$`

- `$\color{blue}{Q_d}<\color{red}{Q_s}$`: .hi[excess supply]

- A .hi[surplus] of 6 units
]

]
.smallest[
- Buyers will not buy more than 2 units

- For 2 units, some sellers willing to accept less than $8

]
]

.pull-right[
<img src="3.1-slides_files/figure-html/unnamed-chunk-13-1.png" width="504" style="display: block; margin: auto;" />
]

---

# Excess Supply II

---

# Excess Supply III

.bg-washed-green.b--dark-green.ba.bw2.br3.shadow-5.ph4.mt5[
.smallest[
.green[**Example**]: Consider *any* price above $6, such as $7:

- `$\color{blue}{Q_d=2} \quad \color{red}{Q_s=8}$`

- `$\color{blue}{Q_d}<\color{red}{Q_s}$`: .hi[excess supply]

- A .hi[surplus] of 6 units
]
]
.smallest[
- Sellers will **lower their asking prices** against one another, lowering the price

- At lower prices, buyers willing to buy more!

- Until .hi-purple[equilibrium], no pressure for change, `$\color{blue}{Q_d}=\color{red}{Q_s}$`
]
]

.pull-right[
<img src="3.1-slides_files/figure-html/unnamed-chunk-14-1.png" width="504" style="display: block; margin: auto;" />
]

---

# Why Markets Tend to Equilibrate

---

# Comparative Statics

---

# Ceterus Paribus I

.pull-left[
.smallest[
- Supply function and demand function *only* relate **quantity** (supplied or demanded) to **price**
  - Describes how buyers/sellers respond to changes in market price

- Certainly there are many *other* factors that influence how much a buyer or seller will purchase at a particular price!
  - income, preferences, prices of other goods, costs, expectations, etc.

- A supply or demand function (or graph) requires .hi[“ceterus paribus”] (all else equal)
]
]
.pull-right[
.center[
![:scale 75%](../images/ceterusparibus.png)
]

]

---

# Recall (for example), Demand I

`$$q_x^D = q_x^D(m, p_x, p_y)$$`

- How does **demand for x** change?

1. .hi-purple[Income effects] `$\left(\frac{\Delta q_x^D}{\Delta m}\right)$`: how `$q_x^D$` changes with changes in income
2. .hi-purple[Cross-price effects] `$\left(\frac{\Delta q_x^D}{\Delta p_y}\right)$`: how `$q_x^D$` changes with changes in prices of *other* goods (e.g. `$y)$`
3. .hi-purple[(Own) Price effects] `$\left(\frac{\Delta q_x^D}{\Delta p_x}\right)$`: how `$q_x^D$` changes with changes in price (of `$x)$`
]
]

# Recall (for example), Demand II

.pull-left[
.smallest[
- A change in one of the .hi-purple["determinants of demand"] will **shift** demand curve!
  - Change in **income** `\$m\$`
  - Change in **price of other goods** `\$p_y\$` (substitutes or complements)
  - Change in **preferences** or **expectations** about good `\$x\$`
  - Change in **number of buyers**

- Shows up in (inverse) demand function by a **change in intercept (choke price)**!

- Again, see my [Visualizing Demand Shifters](https://ryansafner.shinyapps.io/Demand/)
]
.source[See [Class 1.5](/content/1.5-content) for a reminder.]
]

]

---

# Ceterus Paribus II

- Consider our demand function:
`$$q_D=10-p$$`

- If the .hi-turquoise[market price changes] (perhaps because supply changes), that results in a .hi-turquoise[change in _quantity demanded_]
  - We move **along** the existing demand curve

- *Ceterus paribus* has not been violated

]

]

---

# Ceterus Paribus III

- Consider our demand function:
`$$q_D=10-p$$`

- If the .hi-turquoise[something *other* than price changes] (income, preferences, price of a complement, etc), that results in a .hi-turquoise[change in _demand_]
  - A whole *new* demand function/graph:

`$$q_D=12-p$$`

- *Ceterus paribus* has been violated

]

]

---

# Ceterus Paribus IV

- .hi-purple[There is a big difference between a change in "quantity demanded" and a change in "demand"!]

]

]

---

# Increase in Demand

]

]

---

# Increase in Demand

- Entire demand curve shifts to the *right*
]
]

]

---

# Increase in Demand

- Entire demand curve shifts to the *right*

- At the original market price, a **shortage!** `$(q_D > q_S)$`
]
]

]

---

# Increase in Demand

- Entire demand curve shifts to the *right*

- At the original market price, a **shortage!** `$(q_D > q_S)$`

- Some buyers willing to pay more at this quantity
]
]
.pull-right[

]

---

# Increase in Demand

- Entire demand curve shifts to the *right*

- At the original market price, a **shortage!** `$(q_D > q_S)$`

- Some buyers willing to pay more at this quantity

- Buyers raise bids, inducing sellers to sell more

- Reach new equilibrium with:
  - **higher market-clearing price**
  - **larger market-clearing quantity exchanged**
]
]
.pull-right[

]

---

# Decrease in Demand

]

]

---

# Decrease in Demand

- Entire demand curve shifts to the *left*
]
]

]

---

# Decrease in Demand

- Entire demand curve shifts to the *left*

- At the original market price, a **surplus!** `$(q_D < q_S)$`
]
]
.pull-right[

]

---

# Decrease in Demand

- Entire demand curve shifts to the *left*

- At the original market price, a **surplus!** `$(q_D < q_S)$`

- Some sellers willing to accept less at this quantity
]
]

]

---

# Decrease in Demand

- Entire demand curve shifts to the *left*

- At the original market price, a **surplus!** `$(q_D < q_S)$`

- Some sellers willing to accept less at this quantity

- Sellers lower asks, inducing buyers to buy more

- Reach new equilibrium with:
  - **lower market-clearing price**
  - **smaller market-clearing quantity exchanged**
]
]

]

---

# Increase in Supply

]

]

---

# Increase in Supply

- Entire supply curve shifts to the *right*
]
]

]

---

# Increase in Supply

- Entire supply curve shifts to the *right*

- At the original market price, a **surplus!** `$(q_D < q_S)$`
]
]

]

---

# Increase in Supply

- Entire supply curve shifts to the *right*

- At the original market price, a **surplus!** `$(q_D < q_S)$`

- Some sellers willing to accept less at this quantity
]
]
.pull-right[

]

---

# Increase in Supply

- Entire supply curve shifts to the *right*

- At the original market price, a **surplus!** `$(q_D < q_S)$`

- Some sellers willing to accept less at this quantity

- Sellers lower asks, inducing buyers to buy more

- Reach new equilibrium with:
  - **lower market-clearing price**
  - **larger market-clearing quantity exchanged**
]
]
.pull-right[

]

---

# Decrease in Supply

]

]

---

# Decrease in Supply

- Entire supply curve shifts to the *left*
]
]

]

---

# Decrease in Supply

- Entire supply curve shifts to the *left*

- At the original market price, a **shortage!** `$(q_D > q_S)$`
]
]
.pull-right[

]

---

# Decrease in Supply

- Entire supply curve shifts to the *left*

- At the original market price, a **shortage!** `$(q_D > q_S)$`

- Some buyers willing to pay more at this quantity
]
]
.pull-right[

]

---

# Decrease in Supply

- Entire supply curve shifts to the *left*

- At the original market price, a **shortage!** `$(q_D > q_S)$`

- Some buyers willing to pay more at this quantity

- Buyers raise bids, inducing sellers to sell more

- Reach new equilibrium with:
  - **higher market-clearing price**
  - **smaller market-clearing quantity exchanged**
]
]
.pull-right[

]

---

# Equilibrium Tendencies

![:scale 35%](../images/equilibriumball.png)
]
]

- Equilibrium is a *tendency* we can *predict* with our models

- Buyers and sellers raise and lower their bids and asks to adjust to competition from other buyers and sellers, moving the market price

- *Ceterus paribus*, market prices will settle on an equilibrium given existing conditions

- But conditions are always changing (and so are prices)!
]