2.6 — Long Run Industry Equilibrium

# 2.6 — Long Run Industry Equilibrium
## 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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# Firm's *Long Run* Supply Decisions

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# Firm Decisions in the Long Run I

]

- `$\color{orange}{AC(q)_{min}}$` at a market price of $6

- At $6, the firm earns .hi["normal economic profits"] (of 0)

- At any market price *below* $6.00, firm earns **losses**
 - Short Run: firm shuts down if `$p<AVC(q)$`

- At any market price *above* $6.00, firm earns .hi["supernormal profits"] (>0)

]

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# Firm Supply Decisions in the Short Run vs. Long Run

.pull-left[
- .hi-purple[Short run]: firms that shut down `$(q^*=0)$` stuck in market, incur fixed costs `$\pi=-f$`
]

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# Firm Supply Decisions in the Short Run vs. Long Run

.pull-left[
- .hi-purple[Short run]: firms that shut down `$(q^*=0)$` stuck in market, incur fixed costs `$\pi=-f$`

- .hi-purple[Long run]: firms earning losses `$(\pi < 0)$` can .hi[exit] the market and earn `$\pi=0$`
 - No more fixed costs, firms can sell/abandon `$f$` at `$q^*=0$`
]

.pull-right[
.center[
![](https://www.dropbox.com/s/ut01gm60urzbmtl/goingoutofbusiness.jpg?raw=1)
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# Firm Supply Decisions in the Short Run vs. Long Run

.pull-left[
- .hi-purple[Short run]: firms that shut down `$(q^*=0)$` stuck in market, incur fixed costs `$\pi=-f$`

- .hi-purple[Long run]: firms earning losses `$(\pi < 0)$` can .hi[exit] the market and earn `$\pi=0$`
 - No more fixed costs, firms can sell/abandon `$f$` at `$q^*=0$`

- Entrepreneurs not *currently* in market can .hi[enter] and produce, if entry would earn them `$\pi>0$`
]

![:scale 75%](https://www.dropbox.com/s/20ghw4p6te0776x/entry.jpg?raw=1)
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]

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# Firm Supply Decisions in the Short Run vs. Long Run

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# Firm's Long Run Supply: Visualizing

<img src="2.6-slides_files/figure-html/unnamed-chunk-2-1.png" width="504" />
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- Profits are *negative*

- .hi-purple[Short run]: **shut down** production
  - Firm loses more `$\pi$` by producing than by not producing

- .hi-purple[Long run]: firms in industry **exit** the industry
  - *No* new firms will *enter* this industry
]

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# Firm's Long Run Supply: Visualizing

<img src="2.6-slides_files/figure-html/unnamed-chunk-3-1.png" width="504" />
]

- Profits are *negative*

- .hi-purple[Short run]: **continue** production
  - Firm loses *less* `$\pi$` by producing than by *not* producing

- .hi-purple[Long run]: firms in industry **exit** the industry
  - *No* new firms will *enter* this industry
]

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# Firm's Long Run Supply: Visualizing

<img src="2.6-slides_files/figure-html/unnamed-chunk-4-1.png" width="504" />
]

- Profits are *positive*

- .hi-purple[Short run]: **continue** production
  - Firm earning profits

- .hi-purple[Long run]: firms in industry **stay** in industry
  - **New** firms will **enter** this industry
]

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# Production Rules, Updated:

**2. Profit `$\pi=q[p-AC(q)]$`**

**3. Shut down in _short run_ if `$p<AVC(q)$`**

**4. Exit in _long run_ if `$p<AC(q)$`**

]

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# Market Entry and Exit

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# Exit, Entry, and Long Run Industry Equilibrium I

- Now we must combine .hi-purple[optimizing] *individual* firms with *market-wide* adjustment to .hi-purple[equilibrium]

- Since `$\pi = [p-AC(q)]q$`, in the **long run**, profit-seeking firms will:
]

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# Exit, Entry, and Long Run Industry Equilibrium I

- Now we must combine .hi-purple[optimizing] *individual* firms with *market-wide* adjustment to .hi-purple[equilibrium]

- Since `$\pi = [p-AC(q)]q$`, in the **long run**, profit-seeking firms will:
  - .hi-purple[Enter] markets where `$p>AC(q)$`
]

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# Exit, Entry, and Long Run Industry Equilibrium I

- Now we must combine .hi-purple[optimizing] *individual* firms with *market-wide* adjustment to .hi-purple[equilibrium]

- Since `$\pi = [p-AC(q)]q$`, in the **long run**, profit-seeking firms will:
 - .hi-purple[Enter] markets where `$p>AC(q)$`
 - .hi-purple[Exit] markets where `$p<AC(q)$`
]

![](https://www.dropbox.com/s/ut01gm60urzbmtl/goingoutofbusiness.jpg?raw=1)
]
]

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# Exit, Entry, and Long Run Industry Equilibrium II

- .hi-purple[Long-run equilibrium]: entry and exit ceases when .hi-purple[`\$p=AC(q)\$`] for all firms, implying .hi-purple[normal economic profits] of .hi-purple[`\$\pi=0\$`]

]

.pull-right[
.center[
![:scale 100%](https://www.dropbox.com/s/g0cbarnhq81wl8e/breakeven.jpg?raw=1)
]
]

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# Exit, Entry, and Long Run Industry Equilibrium II

- .hi-purple[Long-run equilibrium]: entry and exit ceases when .hi-purple[`\$p=AC(q)\$`] for all firms, implying .hi-purple[normal economic profits] of .hi-purple[`\$\pi=0\$`]

- .hi-purple[Zero Economic Profits Theorem]: **long run economic profits for all firms in a _competitive_ industry are 0**

- Firms must earn an *accounting* profit to stay in business

]

]
]

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# Deriving the Industry Supply Curve

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# The Industry Supply Curve

- .hi[Industry supply curve]: horizontal sum of all individual firms' supply curves
  - recall: `$(MC(q)$` curve above `$AVC_{min})$` (shut down price)

- To keep it simple on the following slides:
  - assume no fixed costs, so `$AC(q)=AVC(q)$`
  - then industry supply curve is sum of individual `$MC(q)$` curves above `$AC(q)_{min}$`

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# Industry Supply Curves (Identical Firms)

<img src="2.6-slides_files/figure-html/unnamed-chunk-5-1.png" width="504" />
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.smallest[
- .red[Industry supply curve] is the horizontal sum of all individual firm's supply curves
  - Which are each firm's marginal cost curve above its breakeven price
]

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# Industry Supply Curves (Identical Firms)

<img src="2.6-slides_files/figure-html/unnamed-chunk-8-1.png" width="504" />
]

]

.smallest[
- .blue[Industry demand curve] (where equal to supply) sets market price, demand for firms
]

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# Industry Supply Curves (Identical Firms)

<img src="2.6-slides_files/figure-html/unnamed-chunk-11-1.png" width="504" />
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- **Short Run**: each firm is earning .hi-green[profits] `$p>AC(q)$`

- **Long run**: induces entry by firm 3, firm 4, `$\cdots$`, firm `$n$`
]
--
.smallest[
- .hi[Long run industry equilibrium]:
]
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# Industry Supply Curves (Identical Firms)

<img src="2.6-slides_files/figure-html/unnamed-chunk-14-1.png" width="504" />
]

]

- **Long run**: induces entry by firm 3, firm 4, `$\cdots$`, firm `$n$`

- .hi[Long run industry equilibrium]: `$p=AC(q)_{min}$`, `$\pi=0$` at `$p=$` $6; supply becomes more **elastic**
]
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# Zero Economic Profits & Economic Rents

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# Back to Zero Economic Profits

.pull-left[
- Recall, we've essentially defined a .hi-purple[firm] as a completely .hi[replicable recipe] (.hi[production function]) of resources

`$$q=f(L,K)$$`

- **"Any idiot"** can enter market, buy required factors, and produce `$q^*$` at market price `$p$` and earn the market rate of `$\pi$`

]

.pull-right[
.center[
![:scale 70%](https://www.dropbox.com/s/zu2c5ijzqvz5sbh/inputoutput.png?raw=1)
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# Back to Zero Economic Profits

- Zero long run economic profit `$\neq$` industry *disappears*, just **stops growing**

- Less attractive to entrepreneurs & start ups to enter than other, more profitable industries

- These are **mature** industries (again, often commodities), the backbone of the economy, just not *sexy*!

]

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# Back to Zero Economic Profits

- All factors being paid their market price
  - i.e. their opportunity cost - the same that they could earn elsewhere in economy

- Firms earning normal market rate of return
  - No *excess* rewards (economic profits) to attract *new* resources into the industry, nor *losses* to bleed resources out of industry
  
]

]
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# Back to Zero Economic Profits

- But we've so far been imagining a market where every firm is *identical*, just a recipe "any idiot" can copy

- What about if firms have *different* technologies or costs?
  
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.pull-right[
.center[
![:scale 70%](https://www.dropbox.com/s/zu2c5ijzqvz5sbh/inputoutput.png?raw=1)
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# Industry Supply Curves (*Different* Firms) I

.pull-left[
.smaller[
- Firms have **different technologies/costs** due to relative differences in:
  - Managerial talent
  - Worker talent
  - Location
  - First-mover advantage
  - Technological secrets/IP
  - License/permit access
  - Political connections
  - Lobbying

- Let's derive .hi-red[industry supply curve] again, and see if this may affact profits
]
]

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# Industry Supply Curves (*Different* Firms) II

<img src="2.6-slides_files/figure-html/unnamed-chunk-17-1.png" width="504" />
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- .red[Industry supply curve] is the horizontal sum of all individual firm's supply curves
  - Which are each firm's marginal cost curve above its breakeven price

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# Industry Supply Curves (*Different* Firms) II

<img src="2.6-slides_files/figure-html/unnamed-chunk-20-1.png" width="504" />
]

]

.smallest[
- .blue[Industry demand curve] (where equal to supply) sets market price, demand for firms
]
--

.smallest[
- .hi[Long run industry equilibrium]: `$p=AC(q)_{min}$`, `$\pi=0$` for .hi-purple[marginal (highest cost) firm] (Firm 2)
]

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# Economic Rents and Zero Economic Profits I

.pull-left[
.center[
![:scale 80%](https://www.dropbox.com/s/rbskabbd2pri9zk/rentvictory.jpg?raw=1)
]
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.pull-right[
- With differences between firms, .hi-purple[**long-run equilibrium** `\$p=AC(q)_{min}\$` of the _marginal (highest-cost)_ firm]
  - If `$p>AC(q)$` for that firm, would induce *more* entry into industry!

]

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# Economic Rents and Zero Economic Profits I

.pull-left[
.center[
![:scale 80%](https://www.dropbox.com/s/rbskabbd2pri9zk/rentvictory.jpg?raw=1)
]
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.pull-right[
- .hi-purple["Inframarginal" (lower-cost)] firms earn .hi[economic rents]
  - returns higher than their opportunity cost (what is needed to bring them into *this* industry)

- Economic rents arise from **relative differences** between firms
  - actually using *different* inputs!

]

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# Economic Rents and Zero Economic Profits III

.pull-left[
.center[
![:scale 80%](https://www.dropbox.com/s/rbskabbd2pri9zk/rentvictory.jpg?raw=1)
]
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.pull-right[
- .hi-purple[Some factors are relatively scarce _in the economy_]
  - (talent, location, secrets, IP, licenses, being first, political favoritism)

- **Inframarginal** firms that use these scarce factors gain a cost-*advantage*

- It would seem these firms earn profits as other firms have higher costs...
  - ...But what will happen to the prices for the scarce factors?

]

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# Economic Rents and Zero Economic Profits IV

.pull-left[
.center[
![:scale 80%](https://www.dropbox.com/s/znztfyevfm2nhrd/jobsiphone.jpg?raw=1)
]
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- Rival firms willing to pay for rent-generating factor to gain advantage

- Competition over acquiring the scarce factors **push up their prices** (i.e. costs to firms)

- .hi-purple[Rents are included in the opportunity cost (price) for inputs]
  - Must pay a factor enough to keep it *out of other uses*

]

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# Economic Rents and Zero Economic Profits IV

.pull-left[
.center[
![:scale 80%](https://www.dropbox.com/s/znztfyevfm2nhrd/jobsiphone.jpg?raw=1)
]
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- **Economic rents `$\neq$` economic profits!**
  - Rents actually *reduce* profits!

- Firm does not earn the rents, they raise firm's costs and squeeze out profits!

- .hi-purple[Scarce factor owners] (workers, landowners, inventors, etc) .hi-purple[earn the rents as higher income for their scarce services] (wages, rents, interest, royalties, etc).

]

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# Recall: Accounting vs. Economic Point of View

- Recall **"economic" point of view**:

- Producing *your* product pulls scarce resources *out of other productive uses* in the economy

- **Profits attract resources** to be pulled out of other uses

- **Losses repel resources** to be pulled away to other uses

- **Zero profits** `$\implies$` resources should stay where they are
  - Optimal use of resources!

]

![](https://www.dropbox.com/s/mb9yaadujqe38fj/disappear.jpg?raw=1)
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# Supply Functions

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# Supply Function

- .hi[Supply function] relates quantity to price

]

<img src="2.6-slides_files/figure-html/unnamed-chunk-23-1.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="2.6-slides_files/figure-html/unnamed-chunk-24-1.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="2.6-slides_files/figure-html/unnamed-chunk-25-1.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="2.6-slides_files/figure-html/unnamed-chunk-26-1.png" width="504" />
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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

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

| | "Elastic" | "Unit Elastic" | "Inelastic" |
|-----------------|-----------|----------------|------------|
| **Intuitively**: | *Large* response | Proportionate response | *Little* response |
| **Mathematically**: | `$\epsilon_{q_s,p} > 1$` | `$\epsilon_{q_s,p} = 1$` | `$\epsilon_{q_s,p} < 1$` |
| | Numerator `$>$` Denominator | Numerator `$=$` Denominator | Numerator `$<$` Denominator |
| **A 1% change in `$p$`** | More than 1% change in `$q_S$` | 1% change in `$q_S$` | Less than 1% change in `$q_S$` |

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# Visualizing Price Elasticity of Supply

<img src="2.6-slides_files/figure-html/unnamed-chunk-27-1.png" style="display: block; margin: auto;" />
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<img src="2.6-slides_files/figure-html/unnamed-chunk-28-1.png" style="display: block; margin: auto;" />
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# Price Elasticity of Supply Formula

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

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

![](2.6-slides_files/figure-html/unnamed-chunk-29-1.png)
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`$$\epsilon_{q,p} = \mathbf{\frac{1}{slope} \times \frac{p}{q}}$$`

- 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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# Price Elasticity of Supply: Examples

.pull-left[
.center[
[![](https://www.dropbox.com/s/97hh5tah2vl9rsd/corona_mask_import.png?raw=1)](https://reason.com/2020/03/31/america-could-import-countless-more-face-masks-if-federal-regulators-would-get-out-of-the-way/)
]
]

.pull-right[
.smallest[
<blockquote class="twitter-tweet">A report by <a href="https://twitter.com/PIIE?ref_src=twsrc%5Etfw">@PIIE</a> found an N-95 respirator mask still faces a 7% U.S. tariff. Remaining US duties include • 5% on hand sanitizer • 4.5% on protective medical clothing • 2.5% on goggles • 6.4-8.3% on other medical headwear By <a href="https://twitter.com/ABehsudi?ref_src=twsrc%5Etfw">@ABehsudi</a> 1/<a href="https://t.co/LcxE0FFlXO">https://t.co/LcxE0FFlXO</a>&mdash; Chad P. Bown (@ChadBown) <a href="https://twitter.com/ChadBown/status/1252602275098492928?ref_src=twsrc%5Etfw">April 21, 2020</a></blockquote> <script async src="https://platform.twitter.com/widgets.js" charset="utf-8"></script> 
]
]

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# Price Elasticity of Supply: Examples

.pull-left[
.center[
[![](../images/fdahandsanitizer.png)](https://reason.com/2020/04/02/the-fda-is-making-it-much-much-harder-for-distilleries-to-produce-hand-sanitizer/)
]
]

.pull-right[
.center[
[![](../images/masksshortage.png)](https://www.flexport.com/blog/why-there-arent-enough-masks-and-how-to-get-more/)
]
]

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# Price Elasticity of Supply: Examples

.pull-left[
.center[
[![](../images/mrhousingelasticity.png)](https://marginalrevolution.com/marginalrevolution/2019/08/the-supply-of-housing-has-become-less-elastic.html)

]
]