2.6 — Long Run Industry Equilibrium

# 2.6 — Long Run Industry Equilibrium

## ECON 306 • Microeconomic Analysis • Fall 2022

### Ryan Safner Associate Professor of Economics <a href="mailto:safner@hood.edu">safner@hood.edu</a> <a href="https://github.com/ryansafner/microF22">ryansafner/microF22</a> <a href="https://microF22.classes.ryansafner.com"> microF22.classes.ryansafner.com</a>

---

# Outline

### [Firm's *Long Run* Supply Decisions](#3)
### [Market Entry and Exit](#14)
### [Deriving the Industry Supply Curve](#20)
### [Economic Rents, Profits, & Competition](#28)
### [Supply Functions](#52)
### [Price Elasticity of Supply](#58)

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# Firm's *Long Run* Supply Decisions

---

# Firm Decisions in the Long Run I

]

- `$\color{orange}{AC(q)_{min}}$` at a market price of $6
  - Firm earns .hi[“normal” economic profits]

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

]
]

---

# 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:
]

---

# 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-turquoise[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

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

---

# 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**
]
---

# Economic Rents, Profits, & Competition

---

# 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 are paid their market price
  - i.e. their .hi-purple[opportunity cost] — what they could earn *elsewhere* in economy

- Firms earn .hi-purple[normal market rate of return]
  - No *excess* rewards (economic profits) to attract *new* resources into the industry, nor *losses* to push 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 **.ul[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 how this may affect 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)
]

.smallest[
- Firm 1 (lower cost) appears to be earning .hi-green[profits]...(we’ll come back to this)
]

---

# Economic Rents and Zero Economic Profits I

.pull-right[
- .hi-purple[**Long-run equilibrium** `\$p=AC(q)_{min}\$` of the _marginal (highest-cost)_ firm]

- .hi-purple[The marginal firm earns normal economic profit (of zero)]
  - Otherwise, 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 are using resources that 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 resources

]

---

# Economic Rent

.pull-right[
- .hi[Economic rent]: a return or payment for a resource above its normal market return (opportunity cost)

- Has no allocative effect on resources, entirely “inframarginal”

- A windfall return that resource owners get for free

]

---

# Sources of Economic Rents

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

]

---

# Firms Using Resources with Economic Rents

.pull-right[
- **Inframarginal** firms that employ these scarce factors gain a .hi-green[short-run profits] from having lower costs/higher productivity

- ...But what will happen to the prices for their scarce factors over time?

]

---

# Economic Rents Examples

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# Economic Rents and Zero Economic Profits

.pull-right[
.smallest[
- In a competitive market, over the long run, **profits are dissipated through competition**
  - Rival firms willing to pay for the scarce factor to gain an advantage

- Competition over acquiring the scarce factors **pushes up their prices**
  - i.e. higher 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

- From the firm’s perspective, over the long-run, .hi-purple[rents are included in the price (opportunity cost) of the scarce factor]
  - Must pay a factor enough to keep it out of other uses

- Firm .ul[does not earn the rents], they raise firm's costs and squeeze profits to zero!

]

---

# Economic Rents Reduce Firms’ Profits Over Long Run

<img src="2.6-slides_files/figure-html/unnamed-chunk-23-1.png" width="504" style="display: block; margin: auto;" />
]

.tri-middle[
<img src="2.6-slides_files/figure-html/unnamed-chunk-24-1.png" width="504" style="display: block; margin: auto;" />
]

.tri-right[
<img src="2.6-slides_files/figure-html/unnamed-chunk-25-1.png" width="504" style="display: block; margin: auto;" />

]

- **Short Run**: firm that possesses scarce rent-generating factors has lower costs, perhaps .green[short-run profits]
]

---

# Economic Rents Reduce Firms’ Profits Over Long Run

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

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

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

]

.smallest[
- **Short Run**: firm that possesses scarce rent-generating factors has lower costs, perhaps .green[short-run profits]

- **Long run**: competition over those factors pushes up their prices, **raising costs to firm**, until its profits go to zero as well
  - Increase in *fixed* cost (scarce factor), raising .orange[AC(q)], which now includes rents (more info [in appendix](resources/appendices/2.6-appendix/#economic-rents))
]

---

# Economic Rents Go To Resource Owners

- .hi-purple[Owners of scarce factors] (workers, landowners, inventors, etc) .hi-purple[earn the rents as higher income for their services] (wages, land rent, interest, royalties, etc).

- Often induces competition to supply alternative factors, which *may* dissipate the rents (to zero)
  - More workers invest in becoming talented, try to create new inventions, build new land, etc.

]

---

# Recall: Accounting vs. Economic Point of View

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

- .hi-turquoise[Profits attract resources]: pulled out of other (less valuable) uses

- .hi-turquoise[Losses repel resources]: pulled away to other (more valuable) uses

- .hi-turquoise[Zero profits keep resources where they are]
  - Implies .hi-purple[society is using resources optimally]
]
]

![](../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-29-1.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-30-1.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
  - Consider the shut-down price...

]

<img src="2.6-slides_files/figure-html/unnamed-chunk-31-1.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-32-1.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

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

.smallest[
| | .hi[“Elastic”] | “Unit Elastic” | .hi[“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 |
| **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://microf22.classes.ryansafner.com/slides/1.7-slides#5)]
---

# Visualizing Price Elasticity of Supply

<img src="2.6-slides_files/figure-html/unnamed-chunk-33-1.png" width="504" style="display: block; margin: auto;" />
]

<img src="2.6-slides_files/figure-html/unnamed-chunk-34-1.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

]

]

---

# 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-35-1.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

]

]

---