3.1 — The Supply and Demand Model

# 3.1 — The Supply and Demand Model
## ECON 306 · Microeconomic Analysis · Fall 2020
### Ryan Safner Assistant Professor of Economics <a href="mailto:safner@hood.edu">safner@hood.edu</a> <a href="https://github.com/ryansafner/microF20">ryansafner/microF20</a> <a href="https://microF20.classes.ryansafner.com"> microF20.classes.ryansafner.com</a>

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# Equilibrium

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# 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

]

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# 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%](https://www.dropbox.com/s/j7xenkgo3p71vke/equilibriumbalance.png?raw=1)
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# Equilibrium Analysis: Questions to Answer

- Where do prices come from?

- How do they change?

- How consumers and producers to respond to changes?

]

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# 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
]

.pull-right[
.center[
![:scale 70%](https://www.dropbox.com/s/j7xenkgo3p71vke/equilibriumbalance.png?raw=1)
]
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# *Partial*  Equilibrium Analysis

- We will only look at .hi-purple["*partial* equilibrium"] in a single market

- Changes in *one* market often affect *other* markets, affecting the .hi-purple["*general* equilibrium"]
  - e.g. a change in the 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 70%](https://www.dropbox.com/s/j7xenkgo3p71vke/equilibriumbalance.png?raw=1)
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# Recall: Demand

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# Demand Function

- .hi[Demand function] relates quantity to price

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<img src="3.1-slides_files/figure-html/unnamed-chunk-1-1.png" width="504" />
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# Inverse Demand Function

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

]

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# Inverse Demand Function

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

- 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" />
]

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# 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" />
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# Recall: Supply

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# Supply Function

- .hi[Supply function] relates quantity to price

]

<img src="3.1-slides_files/figure-html/unnamed-chunk-4-1.png" width="504" />
]

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# Inverse Supply Function

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

]

<img src="3.1-slides_files/figure-html/unnamed-chunk-5-1.png" width="504" />
]

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# Inverse Supply Function

- Slope: 0.5

- Vertical intercept called the .hi["Choke price"]: price where `\$q_S=0\$` ($2), just low enough to discourage *any* sales

]

<img src="3.1-slides_files/figure-html/unnamed-chunk-6-1.png" width="504" />
]

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# 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" />
]

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# Market Equilibrium

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# Market Equilibrium

- Market-clearing (equilibrium) price `$(p^*)$`: $6.00

- Market-clearing (equilibrium) quantity exchanged `$(q^*)$`: 4
]

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# Why Markets Tend to Equilibrate

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# Excess Demand I

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

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

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

]

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# Excess Demand II

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

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

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

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

]
]

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# Excess Demand III

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

- `$\color{blue}{Q_d}>\color{red}{Q_s}$`: .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, `$\color{blue}{Q_d}=\color{red}{Q_s}$`
]
]

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# Excess Supply I

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

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

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

]

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# Excess Supply II

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

- `$\color{blue}{Q_d}<\color{red}{Q_s}$`: .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

]
]

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# Excess Supply III

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

- `$\color{blue}{Q_d}<\color{red}{Q_s}$`: .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, `$\color{blue}{Q_d}=\color{red}{Q_s}$`
]
]

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# Why Markets Tend to Equilibrate

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# Comparative Statics

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# Ceterus Paribus I

.pull-left[
.smallest[
- Supply function and demand function relate *quantity* (supplied or demanded) to *price* **only**
  - 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, expectations, etc.

- A supply or demand function (or graph) requires .hi["ceterus paribus"] (all else equal)
]
]
.pull-right[
.center[
![:scale 75%](https://www.dropbox.com/s/pnyb4kyxum5no25/ceterusparibus.png?raw=1)
]

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# 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 1.8](/class/1.8-class) for a reminder.]
]

]

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# Ceterus Paribus II

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

- If the **market price `$(p)$` changes** (perhaps because supply changes), that results in a **change in _quantity demanded_ `$(q_D)$`**
  - We move *along* the existing demand curve

- *Ceterus paribus* has not been violated

]

.pull-right[
.center[
![:scale 75%](https://www.dropbox.com/s/pnyb4kyxum5no25/ceterusparibus.png?raw=1)
]

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# Ceterus Paribus III

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

- If the **something other than price changes** (income, preferences, price of a complement, etc), that results in a **change in _demand_**
  - We need to draw a new demand curve (or demand function)

`$$q_D=12-p$$`

- *Ceterus paribus* has been violated

]

.pull-right[
.center[
![:scale 75%](https://www.dropbox.com/s/pnyb4kyxum5no25/ceterusparibus.png?raw=1)
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# Ceterus Paribus IV

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

]

.pull-right[
.center[
![:scale 75%](https://www.dropbox.com/s/urfaj6q5xgx4nhp/quantitydemandedvsdemand.jpg?raw=1)
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# Increase in Demand

]

]

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# Increase in Demand

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

]

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# Increase in Demand

- Entire demand curve shifts to the *right*

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

]

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# 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[

]

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# 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[

]

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# Decrease in Demand

]

]

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# Decrease in Demand

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

]

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# Decrease in Demand

- Entire demand curve shifts to the *left*

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

]

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# 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
]
]

]

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# 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**
]
]

]

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# Increase in Supply

]

]

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# 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[

]

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# Decrease in Supply

]

]

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# 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[

]

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# Equilibrium Tendencies

![:scale 35%](https://www.dropbox.com/s/hu6jcwr05idub6v/equilibriumball.png?raw=1)
]
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- 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)!
]