2.6 — Long Run Industry Equilibrium

# 2.6 — Long Run Industry Equilibrium
## ECON 306 • Microeconomic Analysis • Spring 2021
### Ryan Safner Assistant Professor of Economics <a href="mailto:safner@hood.edu">safner@hood.edu</a> <a href="https://github.com/ryansafner/microS21">ryansafner/microS21</a> <a href="https://microS21.classes.ryansafner.com"> microS21.classes.ryansafner.com</a>

---

# Outline

### [Firm's *Long Run* Supply Decisions](#3)
### [Market Entry and Exit](#14)
### [Deriving the Industry Supply Curve](#20)
### [Zero Economic Profits & Economic Rents](#28)
### [Supply Functions](#46)
### [Price Elasticity of Supply](#52)

---

# Firm's *Long Run* Supply Decisions

---

# 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)

]

---

# 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 `$\pi=-f$`
]

---

# 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 `$q^*=0$`
]

---

# 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%](../images/entry.jpg)
]
]

---

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

]

---

# Firm's Long Run Supply: Visualizing

<img src="2.6-slides_files/figure-html/unnamed-chunk-2-1.png" width="504" style="display: block; margin: auto;" />
]

- 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
]

---

# Firm's Long Run Supply: Visualizing

<img src="2.6-slides_files/figure-html/unnamed-chunk-3-1.png" width="504" style="display: block; margin: auto;" />
]

- 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
]

---

# Firm's Long Run Supply: Visualizing

<img src="2.6-slides_files/figure-html/unnamed-chunk-4-1.png" width="504" style="display: block; margin: auto;" />
]

- 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
]

---

# 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 `$p<AC(q)$`**

]

---

# Market Entry and Exit

---

# 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:
]

---

# 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 `$p>AC(q)$`
]

---

# 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 `$p<AC(q)$`
]

![](../images/goingoutofbusiness.jpg)
]
]

---

# 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\$`]

]

---

# 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

]

]
]

---

# Deriving the Industry Supply Curve

---

# 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 `$AC(q)_{min}$`

---

# Industry Supply Curves (Identical Firms)

<img src="2.6-slides_files/figure-html/unnamed-chunk-5-1.png" width="504" style="display: block; margin: auto;" />
]

.tri-middle[
<img src="2.6-slides_files/figure-html/unnamed-chunk-6-1.png" width="504" style="display: block; margin: auto;" />
]

.tri-right[
<img src="2.6-slides_files/figure-html/unnamed-chunk-7-1.png" width="504" style="display: block; margin: auto;" />

]

.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
]

---

# Industry Supply Curves (Identical Firms)

<img src="2.6-slides_files/figure-html/unnamed-chunk-8-1.png" width="504" style="display: block; margin: auto;" />
]

.tri-middle[
<img src="2.6-slides_files/figure-html/unnamed-chunk-9-1.png" width="504" style="display: block; margin: auto;" />
]

.tri-right[
<img src="2.6-slides_files/figure-html/unnamed-chunk-10-1.png" width="504" style="display: block; margin: auto;" />

]

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

---

# Industry Supply Curves (Identical Firms)

<img src="2.6-slides_files/figure-html/unnamed-chunk-11-1.png" width="504" style="display: block; margin: auto;" />
]

.tri-middle[
<img src="2.6-slides_files/figure-html/unnamed-chunk-12-1.png" width="504" style="display: block; margin: auto;" />
]

.tri-right[
<img src="2.6-slides_files/figure-html/unnamed-chunk-13-1.png" width="504" style="display: block; margin: auto;" />

]

- **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]:
]
---

# Industry Supply Curves (Identical Firms)

<img src="2.6-slides_files/figure-html/unnamed-chunk-14-1.png" width="504" style="display: block; margin: auto;" />
]

.tri-middle[
<img src="2.6-slides_files/figure-html/unnamed-chunk-15-1.png" width="504" style="display: block; margin: auto;" />
]

.tri-right[
<img src="2.6-slides_files/figure-html/unnamed-chunk-16-1.png" width="504" style="display: block; margin: auto;" />

]

- **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**
]
---

# Zero Economic Profits & Economic Rents

---

# 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 `$(L,K)$` at prices `$(w,r)$`, produce `$q^*$` at market price `$p$` and earn the market rate of `$\pi$`

]

---

# 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*!

]

---

# Back to Zero Economic Profits

- All factors being paid their market price
  - i.e. their .hi-purple[opportunity cost] - what that they could earn *elsewhere* in economy

- Firms earning .hi-purple[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
  
]

]
]

---

# 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?
  
]

---

# 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
]
]

---

# Industry Supply Curves (*Different* Firms) II

<img src="2.6-slides_files/figure-html/unnamed-chunk-17-1.png" width="504" style="display: block; margin: auto;" />
]

.tri-middle[
<img src="2.6-slides_files/figure-html/unnamed-chunk-18-1.png" width="504" style="display: block; margin: auto;" />
]

.tri-right[
<img src="2.6-slides_files/figure-html/unnamed-chunk-19-1.png" width="504" style="display: block; margin: auto;" />

]

- .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

---

# Industry Supply Curves (*Different* Firms) II

<img src="2.6-slides_files/figure-html/unnamed-chunk-20-1.png" width="504" style="display: block; margin: auto;" />
]

.tri-middle[
<img src="2.6-slides_files/figure-html/unnamed-chunk-21-1.png" width="504" style="display: block; margin: auto;" />
]

.tri-right[
<img src="2.6-slides_files/figure-html/unnamed-chunk-22-1.png" width="504" style="display: block; margin: auto;" />

]

.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)
]

---

# Economic Rents and Zero Economic Profits I

.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!

]

---

# Economic Rents and Zero Economic Profits I

.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!

]

---

# Economic Rents and Zero Economic Profits III

.pull-right[
- .hi-purple[Some factors are relatively scarce _in the whole economy_]
  - (talent, location, secrets, IP, licenses, being first, political favoritism)

- **Inframarginal** firms that use these scarce factors gain an *advantage*

- It would seem these firms earn profits, as they have loewr costs...
  - ...But what will happen to the prices for the scarce factors over time?

]

---

# Economic Rents and Zero Economic Profits IV

- 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 of using the factor!

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

]

---

# Economic Rents and Zero Economic Profits V

- **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).

]

---

# Recall: Accounting vs. Economic Point of View

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

- **Profits attract resources**: pulled out of other (less valuable) uses

- **Losses repel resources**: pulled away to other (more valuable) uses

- **Zero profits** `$\implies$` resources stay where they are
  - .hi-purple[Optimal social use of resources]!
]
]

![](../images/disappear.jpg)
]
]

---

# Supply Functions

---

# 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="2.6-slides_files/figure-html/unnamed-chunk-23-1.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**]: 
`$$p=2+0.5q$$`
]
- Graphable (price on vertical axis)!

]

<img src="2.6-slides_files/figure-html/unnamed-chunk-24-1.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**]: 
`$$p=2+0.5q$$`
]

- 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="2.6-slides_files/figure-html/unnamed-chunk-25-1.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="2.6-slides_files/figure-html/unnamed-chunk-26-1.png" width="504" style="display: block; margin: auto;" />
]

---

# Price Elasiticity of Supply

---

# Price Elasticity of Supply

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

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

]

]

---

# 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 `$q_S$` |

---

# Visualizing Price Elasticity of Supply

<img src="2.6-slides_files/figure-html/unnamed-chunk-27-1.png" width="504" style="display: block; margin: auto;" />
]

<img src="2.6-slides_files/figure-html/unnamed-chunk-28-1.png" width="504" style="display: block; margin: auto;" />
]

---

# 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

]

]

---

# 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?

---

# Price Elasticity of Supply Changes Along the Curve

<img src="2.6-slides_files/figure-html/unnamed-chunk-29-1.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

]

---

# 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?
]
]

]

---

# 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

]

]

---

# Price Elasticity of Supply: Examples

.pull-left[
.center[
[![](../images/corona_mask_import.png)](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> 
]
]

---

# 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/)
]
]

---

# 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)

]
]