4.5 — Factor Markets II: Capital

# 4.5 — Factor Markets II: Capital
## 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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# Outline

### [Labor Market for Competitive Firm](#12)

### [Labor Market for a Monopoly](#30)

### [Monopsony Power](#34)

### [Monopoly Power in Labor Markets: Unions](#54)

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# What is Capital?

- A note on how we used capital `$K$` earlier this semester...

- Assumed capital (essentially machines) has a market price `$“r”$`, the “rental rate of capital”
  - Most firms purchase machines outright, rather than rent them per period (e.g. per hour)
  - But like any input, we consider the (opportunity) cost of using a marginal unit of an input as its market price if it were exchanged on the market
  - Hence, consider the price of capital the market rate to rent a machine for an hour

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# What is Capital?

- Exact nature & definition remains controversial to economists to this day

- “Capital” is:
  - hard to define or (especially) aggregate
  - necessarily bound up with time and uncertainty

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# What Is Capital?

.smallest[
- Economists (and others) often talk about different *types* of capital
  - .hi-turquoise[Physical capital]: tools, machines, specialized equipment, software, that makes labor more productive
  - .hi-turquoise[Human capital]: skills, training, education, experience embodied in a person that makes their labor more productive
  - .hi-turquoise[Financial capital]: access to immediate cash to finance investment for production

- Social scientists also talk about “political capital,” “social capital,” etc...
]
]

![:scale 40%](../images/mind.png)

![:scale 40%](../images/moneyloan.png)
]
]

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# What Is Capital?

- .hi-turquoise[Capital is *not an original factor*]
  - It’s land & labor combined in the past (i.e. someone had to make the shovel, the factory, etc. with land & labor)

- .hi-turquoise[Capital goods are not directly consumed]
  - Used in the production of other goods

- .hi-turquoise[Capital inherently consists of a time element]
  - Makes labor more productive
  - Capital as “stored labor time”
  - Capital comes from **savings**, and earns **interest**

]
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.pull-right[
.center[
![](../images/capitalresolved.png)
]
]

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# What Is Capital?

.pull-left[
.smallest[
- For our purposes today, let’s not think of capital as *physical* capital, but as financial capital
  - All types of capital have the following financial aspect

- Capital is about .hi-purple[the diversion of present consumption towards future consumption]
  - Capital comes from savings, and is used for investments that firms (and households) use to increase their (production for) consumption
  - The return that owners of capital get for providing capital to firms is .hi[interest]

]
]

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# What Is Capital?

- Historically, the idea came from farmers

- During harvest time, can consume all produce today, or save some for next year
  - The more you save today, the less you can eat now, but the more you will have in the future
  - The more you consume today, the less you will have in the future

]

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# Capital Markets

- Firms (and households) get money for investment today by participating in .hi[capital markets]

- The funds in capital markets come from individual savings
]

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# The Time Value of Money

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# Present vs. Future Goods

- In discussing capital, we are comparing .hi-purple[present goods] with .hi-purple[future goods]

- Futures: claims on goods to be delivered at a future date
  - corn futures, oil futures, etc.

- Financial assets: bonds, lottery winnings, loans

- Real goods: immature orchard of fruit trees; durable goods that yield output later

]

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# Present vs. Future Goods

- .hi-purple[Interest rate is a price of future goods in terms of present goods]
  - How much individuals will pay to receive income now vs. later

- .hi-purple[Investment in capital]: present consumption can be saved to buy/build machinery that can increase future income flows

]

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# Present vs. Future Goods

.pull-left[
- Consider goods-bundles consumed now vs. consumed at later date
  - i.e. not apples vs. oranges, but apples and oranges **today** vs. apples and oranges **next year**

- .hi-purple[Agent's objective]: optimize time-profile of consumption, **maximize net present value**

]

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# Present vs. Future Goods

.smallest[
- .hi-purple[Time Value of Money]: same nominal amount of money.magenta[†] is worth different amounts over time

`$$\begin{align*}
PV &= \frac{FV}{(1+r)^n}\\
FV &= PV(1+r)^n\\ \end{align*}$$`

- `$PV$`: present value
- `$FV$`: future value
- `$r$`: interest rate
- `$n$`: number of time periods
]

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# Present vs. Future Goods

- .hi-green[Example]: what is the present value of getting $1,000 one year from now at 5% interest?

`$$\begin{align*}
PV &= \frac{FV}{(1+r)^n}\\
PV &= \frac{1000}{(1+0.05)^1}\\
PV &= \frac{1000}{1.05}\\
PV &= \$952.38\\ 
\end{align*}$$`

]

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

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# Present vs. Future Goods

- .hi-green[Example]: what is the *future* value of $1,000 lent for one year at 5% interest?

`$$\begin{align*}
FV &= PV(1+r)^n\\
FV &= 1000(1+0.05)^1\\
FV &= 1000(1.05)\\
FV &= \$1050\\
\end{align*}$$`

]

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

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# Rule of 72

- A good rule of thumb: number of years for your principal to double:

`$$\frac{72}{r}$$`
- This is known as the .hi-purple[rule of 72].magenta[1]

.footnote[.magenta[1] Different people use other numbers, like 70. The point is more to make mental calculations easily rather than accurately.]
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# Rule of 72

- If interest rate is 2%, your money doubles in `$\frac{72}{2}=36$` years

- If interest rate is 3%, your money doubles in `$\frac{72}{3}=24$` years

- If interest rate is 4%, your money doubles in `$\frac{72}{4}=18$` years

- If interest rate is 6%, your money doubles in `$\frac{72}{6}=12$` years

- Interest rate is very important price! Makes all the difference whether it is 1% vs. 2%!

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# Compounding Interest

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# Historical Interest Rates

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