2.7 — External Economies & Industry Supply

# 2.7 — External Economies & Industry Supply
## ECON 306 • Microeconomic Analysis • Spring 2022
### Ryan Safner Assistant Professor of Economics <a href="mailto:safner@hood.edu">safner@hood.edu</a> <a href="https://github.com/ryansafner/microS22">ryansafner/microS22</a> <a href="https://microS22.classes.ryansafner.com"> microS22.classes.ryansafner.com</a>

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# Outline

### [Entry Effects & External Economies](#3)
### [Supply Functions](#27)
### [Price Elasticity of Supply](#33)

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# Entry Effects & External Economies

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# Entry/Exit Effects on Market Price

.pull-left[
.smaller[
- When **all firms produce more/less**; or **firms enter or exit** an industry, this .hi-purple[affects the equilibrium market price]

- Think about basic supply & demand graphs:
  - .hi-purple[Entry]: `$\color{red}{\uparrow}$` .red[industry supply] `$\implies$` `$\uparrow q, \downarrow p$`
  - .hi-purple[Exit]: `$\color{red}{\downarrow}$` .red[industry supply] `$\implies$` `$\downarrow q, \uparrow p$`
]
]

.pull-right[
<img src="2.7-slides_files/figure-html/unnamed-chunk-1-1.png" width="504" style="display: block; margin: auto;" />

]

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# External Economies

- How large this change in price will be from entry/exit depends on industry-wide costs and .hi[external economies]

- **Economies of scale** are *internal* to the firm (a firm's own average cost curve)

- *External* economies have to do with how the size of the *entire* industry affects *all individual firm's costs*
  - These are **externalities** that spill over across all firms in an industry

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# Constant Cost Industry (No External Economies) I

.smallest[
- .hi[Constant cost industry] has *no external economies*, no change in costs as industry output increases (firms enter & incumbents produce more)

- .hi-red[A *perfectly elastic* long-run industry supply curve]

- Determinants:
  - Industry's purchases are not a large share of input markets
  - Often constant marginal costs, insignificant fixed costs

- Examples: toothpicks, domain name registration, waitstaff
]
]

![:scale 50%](https://www.dropbox.com/s/1ejdv6lovob92zr/domainnames.jpg?raw=1)

]
]

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# Constant Cost Industry (No External Economies) II

.pull-left[
<img src="2.7-slides_files/figure-html/base-firm-graph-1.png" width="504" style="display: block; margin: auto;" />
]

.pull-right[
<img src="2.7-slides_files/figure-html/base-market-graph-1.png" width="504" style="display: block; margin: auto;" />
]

.smallest[
- Industry equilibrium: firms earning normal `$\color{#047806}{\pi=0}, \color{blue}{p}=\color{red}{MC(q)}=\color{orange}{AC(q)}$` at points **a**, **A**
]

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# Constant Cost Industry (No External Economies) III

.pull-left[
<img src="2.7-slides_files/figure-html/unnamed-chunk-2-1.png" width="504" style="display: block; margin: auto;" />
]

.pull-right[
<img src="2.7-slides_files/figure-html/industry-demand-increase-1.png" width="504" style="display: block; margin: auto;" />
]

.smallest[
- Industry equilibrium: firms earning normal `$\color{#047806}{\pi=0}, \color{blue}{p}=\color{red}{MC(q)}=\color{orange}{AC(q)}$` at points **a**, **A**

- Consider an increase in .blue[market demand]
]

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# Constant Cost Industry (No External Economies) IV

.pull-left[
<img src="2.7-slides_files/figure-html/firm-demand-increase-1.png" width="504" style="display: block; margin: auto;" />
]

.pull-right[
<img src="2.7-slides_files/figure-html/unnamed-chunk-3-1.png" width="504" style="display: block; margin: auto;" />
]

- Firms charge higher price, produce more output, earn `$\color{#047806}{\pi}$` at point **b**
]

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# Constant Cost Industry (No External Economies) V

.pull-left[
<img src="2.7-slides_files/figure-html/unnamed-chunk-4-1.png" width="504" style="display: block; margin: auto;" />
]

.pull-right[
<img src="2.7-slides_files/figure-html/unnamed-chunk-5-1.png" width="504" style="display: block; margin: auto;" />
]

.smallest[
- **Long run `$(B \rightarrow C)$`**: profit attracts **entry** `$\implies$` .red[industry supply] increases (pushing down price)

- No change in costs to firms in industry, new firms continue to enter until `$\color{#047806}{\pi=0}$` at `$\color{blue}{p}=\color{orange}{AC(q)}$` for firms

- Firms return to point **a**, original price, output, and `$\color{#047806}{\pi=0}$`
]

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# Constant Cost Industry (No External Economies) VI

.pull-left[
<img src="2.7-slides_files/figure-html/unnamed-chunk-6-1.png" width="504" style="display: block; margin: auto;" />
]

.pull-right[
<img src="2.7-slides_files/figure-html/cc-lr-1.png" width="504" style="display: block; margin: auto;" />
]

.smallest[
- .red[Long Run Industry Supply] is perfectly elastic
  - Long run price is not affected in any way by .blue[Market Demand]!
]

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# Increasing Cost Industry (External Diseconomies) I

.smallest[
- .hi[Increasing cost industry] has **external diseconomies**, costs rise for all firms in the industry as industry output increases (firms enter & incumbents produce more)

- .hi-red[An upward sloping long-run industry supply curve]

- Determinants:
  - Finding more resources in harder-to-reach places
  - Diminishing marginal products
  - Greater complexity and administrative costs at larger scales

- Examples: oil, mining, particle physics
]
]

![:scale 50%](https://www.dropbox.com/s/y593zs2tkp7rz21/oilrig.jpg?raw=1)

]
]

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# Increasing Cost Industry (External Diseconomies) II

.pull-left[
<img src="2.7-slides_files/figure-html/unnamed-chunk-7-1.png" width="504" style="display: block; margin: auto;" />
]

.pull-right[
<img src="2.7-slides_files/figure-html/unnamed-chunk-8-1.png" width="504" style="display: block; margin: auto;" />
]

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# Increasing Cost Industry (External Diseconomies) III

.pull-left[
<img src="2.7-slides_files/figure-html/unnamed-chunk-9-1.png" width="504" style="display: block; margin: auto;" />
]

.pull-right[
<img src="2.7-slides_files/figure-html/unnamed-chunk-10-1.png" width="504" style="display: block; margin: auto;" />
]

- Exogenous increase in market demand
]

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# Increasing Cost Industry (External Diseconomies) IV

.pull-left[
<img src="2.7-slides_files/figure-html/unnamed-chunk-11-1.png" width="504" style="display: block; margin: auto;" />
]

.pull-right[
<img src="2.7-slides_files/figure-html/unnamed-chunk-12-1.png" width="504" style="display: block; margin: auto;" />
]

- Firms charge higher `$p^*$`, produce more `$q^*$`, earn `$\pi$`

]

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# Increasing Cost Industry (External Diseconomies) V

.pull-left[
<img src="2.7-slides_files/figure-html/unnamed-chunk-13-1.png" width="504" style="display: block; margin: auto;" />
]

.pull-right[
<img src="2.7-slides_files/figure-html/unnamed-chunk-14-1.png" width="504" style="display: block; margin: auto;" />
]

- **But more industry-wide output increases costs (.red[MC(q)], .orange[AC(q)]) for all firms in industry**

]
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# Increasing Cost Industry (External Diseconomies) VI

.pull-left[
<img src="2.7-slides_files/figure-html/unnamed-chunk-15-1.png" width="504" style="display: block; margin: auto;" />
]

.pull-right[
<img src="2.7-slides_files/figure-html/unnamed-chunk-16-1.png" width="504" style="display: block; margin: auto;" />
]

- Firms charge higher `$p^*$`, producer lower `$q^*$`, earn `$\pi=0$`

]

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# Increasing Cost Industry (External Diseconomies) VII

.pull-left[
<img src="2.7-slides_files/figure-html/unnamed-chunk-17-1.png" width="504" style="display: block; margin: auto;" />
]

.pull-right[
<img src="2.7-slides_files/figure-html/ic-lr-1.png" width="504" style="display: block; margin: auto;" />
]

- .red[Long run industry supply curve] is upward sloping

]

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# Decreasing Cost Industry (External Economies) I

- .hi[Decreasing cost industry] has *external economies*, costs fall for all firms in the industry as industry output increases (firms enter & incumbents produce more)

- A *downward sloping long-run industry supply curve*!

- Determinants:
  - High fixed costs, low marginal costs
  - Economies of scale

- Examples: geographic clusters, public utilities, infrastructure, entertainment

- **Tends towards "natural" monopoly**

]
]

![:scale 50%](https://www.dropbox.com/s/9cgi6o9d5fzyntx/roads.png?raw=1)

]
]

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# Decreasing Cost Industry (External Economies) II

.pull-left[
<img src="2.7-slides_files/figure-html/unnamed-chunk-18-1.png" width="504" style="display: block; margin: auto;" />
]

.pull-right[
<img src="2.7-slides_files/figure-html/unnamed-chunk-19-1.png" width="504" style="display: block; margin: auto;" />
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# Decreasing Cost Industry (External Economies) III

.pull-left[
<img src="2.7-slides_files/figure-html/unnamed-chunk-20-1.png" width="504" style="display: block; margin: auto;" />
]

.pull-right[
<img src="2.7-slides_files/figure-html/unnamed-chunk-21-1.png" width="504" style="display: block; margin: auto;" />
]

- Exogenous increase in market demand

]

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# Decreasing Cost Industry (External Economies) IV

.pull-left[
<img src="2.7-slides_files/figure-html/unnamed-chunk-22-1.png" width="504" style="display: block; margin: auto;" />
]

.pull-right[
<img src="2.7-slides_files/figure-html/unnamed-chunk-23-1.png" width="504" style="display: block; margin: auto;" />
]

- Firms charge higher `$p^*$`, produce more `$q^*$`, earn `$\pi$`

]

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# Decreasing Cost Industry (External Economies) V

.pull-left[
<img src="2.7-slides_files/figure-html/unnamed-chunk-24-1.png" width="504" style="display: block; margin: auto;" />
]

.pull-right[
<img src="2.7-slides_files/figure-html/unnamed-chunk-25-1.png" width="504" style="display: block; margin: auto;" />
]

- **But more production lowers costs `$(MC, AC)$` for all firms in industry**
]

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# Decreasing Cost Industry (External Economies) VI

.pull-left[
<img src="2.7-slides_files/figure-html/unnamed-chunk-26-1.png" width="504" style="display: block; margin: auto;" />
]

.pull-right[
<img src="2.7-slides_files/figure-html/unnamed-chunk-27-1.png" width="504" style="display: block; margin: auto;" />
]

- Firms charge higher `$p^*$`, producer lower `$q^*$`, earn `$\pi=0$`

]

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# Decreasing Cost Industry (External Economies) VII

.pull-left[
<img src="2.7-slides_files/figure-html/unnamed-chunk-28-1.png" width="504" style="display: block; margin: auto;" />
]

.pull-right[
<img src="2.7-slides_files/figure-html/dc-lr-1.png" width="504" style="display: block; margin: auto;" />
]

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# Comparing all Industry Types

.center[
<img src="2.7-slides_files/figure-html/unnamed-chunk-29-1.png" width="504" style="display: block; margin: auto;" />

]
- Constant cost industry
- No external economies
- Increase in industry output has no effect on costs
]

.center[
<img src="2.7-slides_files/figure-html/unnamed-chunk-30-1.png" width="504" style="display: block; margin: auto;" />
]
- Increasing cost industry
- External diseconomies
- Increase in industry output raises all firms’ costs
]

.center[
<img src="2.7-slides_files/figure-html/unnamed-chunk-31-1.png" width="504" style="display: block; margin: auto;" />

]
- Decreasing cost industry
- External economies
- Increase in industry output lowers all firms’ costs

]
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# Supply Functions

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# Supply Function

- .hi[Supply function] relates quantity to price

.bg-washed-green.b--dark-green.ba.bw2.br3.shadow-5.ph4.mt5[
.green[**Example**]: 
`$$q=2p-4$$`
]
- Not graphable (wrong axes)!

]

<img src="2.7-slides_files/figure-html/unnamed-chunk-32-1.png" width="504" style="display: block; margin: auto;" />
]

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# 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**]: 
`$$p=2+0.5q$$`
]
- Graphable (price on vertical axis)!

]

<img src="2.7-slides_files/figure-html/unnamed-chunk-33-1.png" width="504" style="display: block; margin: auto;" />
]

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# Inverse Supply Function

.bg-washed-green.b--dark-green.ba.bw2.br3.shadow-5.ph4.mt5[
.green[**Example**]: 
`$$p=2+0.5q$$`
]

- 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="2.7-slides_files/figure-html/unnamed-chunk-34-1.png" width="504" style="display: block; margin: auto;" />
]

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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="2.7-slides_files/figure-html/unnamed-chunk-35-1.png" width="504" style="display: block; margin: auto;" />
]

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# Price Elasiticity of Supply

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# Price Elasticity of Supply

- .hi[Price elasticity of supply] measures *how much* (in %) quantity supplied changes in response to a (1%) change in price

`$$\epsilon_{q_S,p} = \frac{\% \Delta q_S}{\% \Delta p}$$`

]

]

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# Price Elasticity of Supply: Elastic vs. Inelastic

`$$\epsilon_{q_S,p} = \frac{\% \Delta q_S}{\% \Delta p}$$`

.smallest[
| | .hi[“Elastic”] | “Unit Elastic” | .hi[“Inelastic”] |
|-----------------|-----------|----------------|------------|
| **Intuitively**: | **Large** response | Proportionate response | **Little** response |
| **Mathematically**: | `$\vert \epsilon_{q_s,p}\vert > 1$` | `$\vert \epsilon_{q_s,p}\vert = 1$` | `$\vert \epsilon_{q_s,p} \vert < 1$` |
| | Numerator `$>$` Denominator | Numerator `$=$` Denominator | Numerator `$<$` Denominator |
| **1% change in `$p$` causes** | **More than 1%** change in `$q_s$` | **Exactly 1%** change in `$q_s$` | **Less than 1%** change in `$q_s$` |

]

.footnote[Compare to [price elasticity of demand](https://micros22.classes.ryansafner.com/slides/1.7-slides#5)]
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# Visualizing Price Elasticity of Supply

<img src="2.7-slides_files/figure-html/unnamed-chunk-36-1.png" width="504" style="display: block; margin: auto;" />
]

<img src="2.7-slides_files/figure-html/unnamed-chunk-37-1.png" width="504" style="display: block; margin: auto;" />
]

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# Price Elasticity of Supply Formula

`$$\color{red}{\epsilon_{q,p} = \mathbf{\frac{1}{slope} \times \frac{p}{q}}}$$`
- First term is the inverse of the slope of the inverse supply curve (that we graph)!

- To find the elasticity at any point, we need 3 things:
    1. The price
    2. The associated quantity supplied
    3. The slope of the (inverse) supply curve

]

]

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# Example

.bg-washed-green.b--dark-green.ba.bw2.br3.shadow-5.ph4.mt5[
.green[**Example**]: The supply of bicycle rentals in a small town is given by:

`$$q_S=10p-200$$`
]

1. Find the inverse supply function.

2. What is the price elasticity of supply at a price of $25.00?

3. What is the price elasticity of supply at a price of $50.00?

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# Price Elasticity of Supply Changes Along the Curve

<img src="2.7-slides_files/figure-html/unnamed-chunk-38-1.png" width="504" style="display: block; margin: auto;" />
]

`$$\epsilon_{q,p} = \mathbf{\frac{1}{slope} \times \frac{p}{q}}$$`

- Elasticity `$\neq$` slope (but they are related)!

- Elasticity changes along the supply curve

- Often gets *less* elastic as `$\uparrow$` price `$(\uparrow$` quantity)
  - Harder to supply more

]

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# Determinants of Price Elasticity of Supply I

- .hi[The faster (slower) costs increase with output] `$\implies$` less (more) elastic supply
  - Mining for natural resources vs. automated manufacturing

- Smaller (larger) .hi[share of market for inputs] `$\implies$` more (less) elastic
  - Will your suppliers raise the price much if you buy more?
  - How much competition is there in your input markets?
]
]

]

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# Determinants of Price Elasticity of Supply II

- More (less) .hi[time to adjust] to price changes `$\implies$` more (less) elastic
  - Supply of oil today vs. oil in 10 years

]

]

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