1.8: Factor Markets

# 1.8: Factor Markets
## ECON 326 · Industrial Organization · Spring 2020
### Ryan Safner Assistant Professor of Economics <a href="mailto:safner@hood.edu"> safner@hood.edu</a> <a href="https://github.com/ryansafner/IOs20"> ryansafner/IOs20</a> <a href="https://IOs20.classes.ryansafner.com"> IOs20.classes.ryansafner.com</a>

---

# Returning to Firms

.pull-left[
- Recall a firm uses technology that buys inputs, transforms them, and sells output
`$$q=f(k,l)$$`
  - We classified inputs into the .hi[factors of production]: land, labor, capital

- We *assumed* fixed factor prices
  - show up in total cost `$=wL+rK$`

- Where do they come from? .hi[Factor markets]
]

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

---

# Circular Flow

---

# Supply and Demand in Factor Markets

- The price of a factor is governed by the same market forces as output:

- .hi-red[Supply of Factor]: willingness of factor owners to accept and sell/rent their services to firms
  - landowners, workers, capitalists, resource owners, suppliers

- .hi-blue[Demand for Factor]: willingness of firms to pay for/hire factor services
]

.pull-right[
<img src="1.8-slides_files/figure-html/unnamed-chunk-1-1.png" width="504" style="display: block; margin: auto;" />
]

---

# Factor Market Prices and Opportunity Costs

- .hi[Factor price represents **opportunity cost** of hiring a factor for an alternative use]
  - Firms not only pay for direct use of a factor, but also indirectly for *not using* it in an alternate process!

]

.pull-right[
.center[
![:scale 100%](https://www.dropbox.com/s/mb9yaadujqe38fj/disappear.jpg?raw=1)
]
]
---

# Factor Market Prices and Opportunity Costs

- .green[**Example**]: a producer of hammers buys steel, pays (the opportunity cost) for "taking" the steel away from alternative uses

]

.pull-right[
.center[
![:scale 100%](https://www.dropbox.com/s/mb9yaadujqe38fj/disappear.jpg?raw=1)
]
]

---

# Factor Market Prices and Opportunity Costs

- .green[**Example**]: e.g. salary for a skilled worker must be high enough to keep them at their current firm, and not be attracted to other firms/industries

]

.pull-right[
.center[
![:scale 100%](https://www.dropbox.com/s/mb9yaadujqe38fj/disappear.jpg?raw=1)
]
]

---
# Labor Markets

- We'll focus just on the .hi[market for labor] as an example factor market

- Can do the same for *any* factor market 
  - (e.g. capital, land, materials, etc.)
]

---

# Derived Demand in Factor Markets

.pull-left[
- Demand for factors is a .hi-purple["derived demand"]:
  - Firm only demands inputs to the extent they **contribute to producing sellable output**

- Firm faces a .hi-purple[tradeoff] when **hiring more labor**, as more labor `$\Delta L$` creates:
  1. .hi[Marginal Benefit]: Increases output and thus revenue
  2. .hi[Marginal Cost]: Increases costs
]

---

# Marginal Revenue Product (of Labor)

- Hiring more labor increases output (i.e. labor's .hi-purple[`\$MP_L\$`])
  - Recall: `$MP_L=\frac{\Delta q}{\Delta L}$`, where `$q$` is units of output

- Additional output generates (i.e. labor's .hi-purple[`\$MR(q)\$`])
  - Recall: `$MR(q)=\frac{\Delta R(q)}{\Delta q}$`, where `$R(q)$` is total revenue
--

- Hiring more labor, on the **margin**, generates a **benefit**, called the .hi[marginal revenue product of labor, `\$MRP_L\$`]:
`$$MRP_L=MP_L* MR(q)$$`
  - i.e. the number of new products a new worker makes times the revenue earned by selling the new products

---

# Marginal Revenue Product for *Competitive* Firms

- This is the .hi-blue[Firm's Demand for Labor]:

`$$MRP_L=MP_L* MR(q)$$`

- For a firm in a .hi[competitive (output) market], firm's `$MR(q)=p$`, hence:

`$$MRP_L=MP_L*p$$`
where `$p$` is the price of the firm's *output*

]

---

# Marginal Revenue Product for *Competitive* Firms

`$$MRP_L=MP_L* p$$`

- Marginal benefit of hiring labor, `$MRP_L$` **falls** with more labor used
    - production exhibits **diminishing marginal returns to labor**!

- .hi[Choke price for labor demand]: price too high for firm to purchase any labor

]

---

# A Competitive *Factor* Market

.pull-left[
<img src="1.8-slides_files/figure-html/unnamed-chunk-4-1.png" width="504" style="display: block; margin: auto;" />
]

.pull-right[
<img src="1.8-slides_files/figure-html/unnamed-chunk-5-1.png" width="504" style="display: block; margin: auto;" />
]

- If the .hi[*factor* market is competitive], labor supply for an individual firm is *perfectly elastic* at the market price of labor `$(w^*)$`

---

# A Brief Digression on Economic Rents

---

# Economic Rent I

- Recall .hi-red[market supply] is the **minimum willingness to accept**, the minimum price necessary to bring a resource to market

- But all (equivalent) labor is paid the market wage, `$w^*$` determined by market labor supply and labor demand

]

<img src="1.8-slides_files/figure-html/unnamed-chunk-6-1.png" width="504" style="display: block; margin: auto;" />
]

---

# Economic Rent I

- Some workers would have accepted a job for less than `$w^*$`

- Labor earns .hi[economic rent] in excess of what is needed to bring it into the market (its opportunity cost)

]

<img src="1.8-slides_files/figure-html/unnamed-chunk-7-1.png" width="504" style="display: block; margin: auto;" />
]

---

# Economic Rent II

- Consider a factor (such as land) for which the supply is perfectly inelastic (e.g. a fixed supply)

- Then the **entire value of the land is economic rent**!

- .hi-purple[The *less* elastic the supply of a factor, the *more* economic rent it generates!]

]

<img src="1.8-slides_files/figure-html/unnamed-chunk-8-1.png" width="504" style="display: block; margin: auto;" />
]

---