Cost curve of the firm

# Cost curve of the firm
## Week 5
### Krisna Gupta
### 8 March 2021 (updated: 2021-03-07)

---

## Recap on last week

- Elasticities matter, as they dictate how surpluses are distributed in a market.

- It is important also for the government.

- Demand elasticity varies depending on preference and the state of the good
  - substitute vs complement, luxury vs normal, etc
  - usually hard to change market preferences.
  - preference can be estimated but it is beyond the cover of this course.
  
---

## Today's cover
  
- Supply curve is a bit different: 
  
  - Cost can be easier to guess.
  - Easier to make framework.
  - Has an important implication to the market.

- What we will learn today is:

- The production function.
  - Types of cost.
  - Implication to the supply curve and the market.
  
---

# The Production Function

---

## The production function

- A firm is an organization that produces goods and services.

- To produce, it uses inputs and transform them into a final product and then sell it to the market.

- This relationship:

$$
input \xrightarrow{magic!} output
$$

&nbsp; &nbsp; &nbsp;  &nbsp;  &nbsp;is called **production function**

---

## Reminder: What is a function?

- Function is a mathematical expression to show a relationship between two or more variables.

- Let `$X$` be input and `$Y$` be output, a production function is:

$$
Y=f(X)
$$

- How labor makes rice is sometimes not the main emphasize for economist.

- We care more on how much `$X$` is needed to make `$Y$`.

---

## The production function

- Let there be a hypothetical **rice** farmer named Kensi.

- Kensi own a hectare of **land**. In the short run, Kensi can't increase his number of land.

- However, Kensi can hire a **labour** to work at his farm.

- In this case, the inputs are land and labour, while the output is rice.

---

## Fixed and variable input

- We call land a **fixed input**, an input which can't be changed.

- We call labour a **variable input** because Kensi can hire or fire labour anytime.

- It is important to distinguish the two, because a producer can adjust variable input to adjust demand.
  - In good times, hire more labour. In bad times, fires.
  
---

## Short and long run

- Fixed input won't probably be fixed for long.

- buying and selling new land may take time, but it is doable.
  - However, when there's a quick shock to demand, it is not easy to adjust it.
  
- For example, the price for surgical mask at one point rose to 150k IDR a box, but it is now settled back to around 30k IDR a box.
  - In the short run, fixed input can't keep up.
  
- TSMC and Samsung need time to build new factories.

---

## Short and long run

- How long is 'long run'? depends on how quickly the fixed input can adjust.

- In the case of masks, it catched up to the demand shock in less than a year. Hand sanitizer is even faster.

- In the case of chip, the new capacity for TSMC will operate somewhere in 2022, while Samsung needs even longer time.

- Knowing how long is the demand shock is also important.
  - forecasting demand is a useful skill to have.
  
---

## The hypothetical farmer

- Kensi can't change his arable land, but can change how much labour he employs.

.pull-left[
<table class="table table-striped" style="font-size: 20px; margin-left: auto; margin-right: auto;">
 <thead>
  <tr>
   <th style="text-align:center;"> Quantity 
 of 
 labour L 
 (workers)  </th>
   <th style="text-align:center;"> Quantity of 
 rice Q 
 (ton) </th>
   <th style="text-align:center;"> MPL </th>
  </tr>
 </thead>
<tbody>
  <tr>
   <td style="text-align:center;"> 0 </td>
   <td style="text-align:center;"> 0 </td>
   <td style="text-align:center;"> - </td>
  </tr>
  <tr>
   <td style="text-align:center;"> 1 </td>
   <td style="text-align:center;"> 19 </td>
   <td style="text-align:center;"> 19 </td>
  </tr>
  <tr>
   <td style="text-align:center;"> 2 </td>
   <td style="text-align:center;"> 36 </td>
   <td style="text-align:center;"> 17 </td>
  </tr>
  <tr>
   <td style="text-align:center;"> 3 </td>
   <td style="text-align:center;"> 51 </td>
   <td style="text-align:center;"> 15 </td>
  </tr>
  <tr>
   <td style="text-align:center;"> 4 </td>
   <td style="text-align:center;"> 64 </td>
   <td style="text-align:center;"> 13 </td>
  </tr>
  <tr>
   <td style="text-align:center;"> 5 </td>
   <td style="text-align:center;"> 75 </td>
   <td style="text-align:center;"> 11 </td>
  </tr>
  <tr>
   <td style="text-align:center;"> 6 </td>
   <td style="text-align:center;"> 84 </td>
   <td style="text-align:center;"> 9 </td>
  </tr>
  <tr>
   <td style="text-align:center;"> 7 </td>
   <td style="text-align:center;"> 91 </td>
   <td style="text-align:center;"> 7 </td>
  </tr>
  <tr>
   <td style="text-align:center;"> 8 </td>
   <td style="text-align:center;"> 96 </td>
   <td style="text-align:center;"> 5 </td>
  </tr>
</tbody>
</table>
]

.pull-right[
- MPL is short for **Marginal Product of Labour**
`$$MPL=\frac{\Delta Q}{\Delta L}$$`
- MPL shows how much Q increase if we increase L by 1.
]

---

## Total product curve

![](week5_files/figure-html/rice1-1.png)

---

## Marginal product

- In general, **marginal product** of an input is the additional quantity of output produced by using one more additional unit of that input.

- In our case, we have MPL of every one more additional worker. But if that data is not possible, we can just use the formula in general

- for example, if Kensi have only two data points: one where he work alone and one when he hire 7 workers.

---

## Marginal product

| worker | production |
| ------ | ---------- |
| 1 | 19 |
| 8 | 96 |

$$
MPL=\frac{\Delta Q}{\Delta L}=\frac{96-19}{8-1}=11
$$

- In our case, MPL decreases as the number of worker increases: 
  - it is better to have a smooth data point.
  - We call this a **diminishing return to labour**

---

## Marginal product curve

![](week5_files/figure-html/rice2-1.png)

---

## Diminishing return to an input

- When you have 1 hectare of land, 1 worker can only work so much before he gets tired.

- It is sensible to hire one more person to work on a larger area. This will lead to a huge gain in harvest.

- If the land area is fixed, as we introduce more people, each person will have to work in a smaller area.

- Too much people become inefficient.

- In an office setting: imagine if you add workers without adding the number of computers.

---

## Marginal product and the fixed input

- If Kensi would like to scale up production, increasing only labour will be inefficient.

- Kensi can start planning to increase its land to 2 hectare by buying or renting his  neighbour's land, for example.

- Suppose it takes one year for Kensi to buy one more hectare of land, what's his TP and MPL would look like one year later?

---

### TP shifts up with additional land

![](week5_files/figure-html/beras1-1.png)

---

### MPL is still diminishing, but higher

![](week5_files/figure-html/beras2-1.png)

---

## Marginal product

- The crucial point of the diminishing marginal product concept is *ceteris paribus*.

- if you increase labour AND land, then MPL will look like it goes up.
  
- Hence, when we measure MP of an input, it must be the case that **everything else is held fixed**.

- Production function can be a bit more complex.

1 programmer in 12 months `$\not\rightarrow$` 12 programmers in 1 month.
  
---

# Cost

---

## From production function to profit

- Kensi understand how his farm work. He would like to profit from his farm.

- If Kensi can't control the selling price (rice is competitive), he needs to know how to control his own cost.

- He has to know at least two things:
  - **fixed cost** (FC), the cost of his land, and
  - **variable cost** (VC), the cost of labour.

---

## Kensi's hypothetical cost

- Suppose Kensi's land's rent price is 200 k IDR, while the wage rate in his neighbourhood is 100k IDR.

<table class="table table-striped" style="font-size: 20px; margin-left: auto; margin-right: auto;">
 <thead>
  <tr>
   <th style="text-align:center;"> point </th>
   <th style="text-align:center;"> L 
 (workers) </th>
   <th style="text-align:center;"> Q 
 (ton) </th>
   <th style="text-align:center;"> FC </th>
   <th style="text-align:center;"> VC </th>
   <th style="text-align:center;"> TC=FC+VC </th>
  </tr>
 </thead>
<tbody>
  <tr>
   <td style="text-align:center;"> A </td>
   <td style="text-align:center;"> 0 </td>
   <td style="text-align:center;"> 0 </td>
   <td style="text-align:center;"> 200 </td>
   <td style="text-align:center;"> 0 </td>
   <td style="text-align:center;"> 200 </td>
  </tr>
  <tr>
   <td style="text-align:center;"> B </td>
   <td style="text-align:center;"> 1 </td>
   <td style="text-align:center;"> 19 </td>
   <td style="text-align:center;"> 200 </td>
   <td style="text-align:center;"> 100 </td>
   <td style="text-align:center;"> 300 </td>
  </tr>
  <tr>
   <td style="text-align:center;"> C </td>
   <td style="text-align:center;"> 2 </td>
   <td style="text-align:center;"> 36 </td>
   <td style="text-align:center;"> 200 </td>
   <td style="text-align:center;"> 200 </td>
   <td style="text-align:center;"> 400 </td>
  </tr>
  <tr>
   <td style="text-align:center;"> D </td>
   <td style="text-align:center;"> 3 </td>
   <td style="text-align:center;"> 51 </td>
   <td style="text-align:center;"> 200 </td>
   <td style="text-align:center;"> 300 </td>
   <td style="text-align:center;"> 500 </td>
  </tr>
  <tr>
   <td style="text-align:center;"> E </td>
   <td style="text-align:center;"> 4 </td>
   <td style="text-align:center;"> 64 </td>
   <td style="text-align:center;"> 200 </td>
   <td style="text-align:center;"> 400 </td>
   <td style="text-align:center;"> 600 </td>
  </tr>
  <tr>
   <td style="text-align:center;"> F </td>
   <td style="text-align:center;"> 5 </td>
   <td style="text-align:center;"> 75 </td>
   <td style="text-align:center;"> 200 </td>
   <td style="text-align:center;"> 500 </td>
   <td style="text-align:center;"> 700 </td>
  </tr>
  <tr>
   <td style="text-align:center;"> G </td>
   <td style="text-align:center;"> 6 </td>
   <td style="text-align:center;"> 84 </td>
   <td style="text-align:center;"> 200 </td>
   <td style="text-align:center;"> 600 </td>
   <td style="text-align:center;"> 800 </td>
  </tr>
  <tr>
   <td style="text-align:center;"> H </td>
   <td style="text-align:center;"> 7 </td>
   <td style="text-align:center;"> 91 </td>
   <td style="text-align:center;"> 200 </td>
   <td style="text-align:center;"> 700 </td>
   <td style="text-align:center;"> 900 </td>
  </tr>
  <tr>
   <td style="text-align:center;"> I </td>
   <td style="text-align:center;"> 8 </td>
   <td style="text-align:center;"> 96 </td>
   <td style="text-align:center;"> 200 </td>
   <td style="text-align:center;"> 800 </td>
   <td style="text-align:center;"> 1000 </td>
  </tr>
</tbody>
</table>

---

## Total cost curve for Kensi's farm

![](week5_files/figure-html/kensi1-1.png)

---

## Total product curve vs total cost curve

- Both are upward sloping

- however, as production increase, TP is getting flatter, while TC is increasingly steeper.

- Using more labour increases additional TC but decreases additional TP.

---

# Intermezzo

Since the land is owned by Kensi, does it make sense to put the rent price as his fixed cost?

yes because **opportunity cost** is also a cost: Kensi can rent his land to someone else.

---

# Two key concepts:

### Marginal cost & average cost

---

### Liv's fancy footwear

.s[Liv is a learning entrepreneur. She start her fancy footwear business in New York with this cost structure:]

---

## Marginal cost

- **Marginal cost** (MC) is the change in **total cost** generated by producing one additional unit of output.

$$
MC = \frac{\text{Change in }TC}{\text{change in }Q}=\frac{\Delta TC}{\Delta Q}
$$
- Let's add MC on Liv's fancy footwear cost structure

---

### Liv' fancy footwear cost structure

.pull-left[
<table class="table table-bordered table-striped table-responsive" style="font-size: 20px; margin-left: auto; margin-right: auto;">
 <thead>
  <tr>
   <th style="text-align:center;"> Q </th>
   <th style="text-align:center;"> FC </th>
   <th style="text-align:center;"> VC </th>
   <th style="text-align:center;"> TC </th>
   <th style="text-align:center;"> MC </th>
  </tr>
 </thead>
<tbody>
  <tr>
   <td style="text-align:center;"> 0 </td>
   <td style="text-align:center;"> 108 </td>
   <td style="text-align:center;"> 0 </td>
   <td style="text-align:center;"> 108 </td>
   <td style="text-align:center;"> 0 </td>
  </tr>
  <tr>
   <td style="text-align:center;"> 1 </td>
   <td style="text-align:center;"> 108 </td>
   <td style="text-align:center;"> 12 </td>
   <td style="text-align:center;"> 120 </td>
   <td style="text-align:center;"> 12 </td>
  </tr>
  <tr>
   <td style="text-align:center;"> 2 </td>
   <td style="text-align:center;"> 108 </td>
   <td style="text-align:center;"> 48 </td>
   <td style="text-align:center;"> 156 </td>
   <td style="text-align:center;"> 36 </td>
  </tr>
  <tr>
   <td style="text-align:center;"> 3 </td>
   <td style="text-align:center;"> 108 </td>
   <td style="text-align:center;"> 108 </td>
   <td style="text-align:center;"> 216 </td>
   <td style="text-align:center;"> 60 </td>
  </tr>
  <tr>
   <td style="text-align:center;"> 4 </td>
   <td style="text-align:center;"> 108 </td>
   <td style="text-align:center;"> 192 </td>
   <td style="text-align:center;"> 300 </td>
   <td style="text-align:center;"> 84 </td>
  </tr>
  <tr>
   <td style="text-align:center;"> 5 </td>
   <td style="text-align:center;"> 108 </td>
   <td style="text-align:center;"> 300 </td>
   <td style="text-align:center;"> 408 </td>
   <td style="text-align:center;"> 108 </td>
  </tr>
  <tr>
   <td style="text-align:center;"> 6 </td>
   <td style="text-align:center;"> 108 </td>
   <td style="text-align:center;"> 432 </td>
   <td style="text-align:center;"> 540 </td>
   <td style="text-align:center;"> 132 </td>
  </tr>
  <tr>
   <td style="text-align:center;"> 7 </td>
   <td style="text-align:center;"> 108 </td>
   <td style="text-align:center;"> 588 </td>
   <td style="text-align:center;"> 696 </td>
   <td style="text-align:center;"> 156 </td>
  </tr>
  <tr>
   <td style="text-align:center;"> 8 </td>
   <td style="text-align:center;"> 108 </td>
   <td style="text-align:center;"> 768 </td>
   <td style="text-align:center;"> 876 </td>
   <td style="text-align:center;"> 180 </td>
  </tr>
  <tr>
   <td style="text-align:center;"> 9 </td>
   <td style="text-align:center;"> 108 </td>
   <td style="text-align:center;"> 972 </td>
   <td style="text-align:center;"> 1080 </td>
   <td style="text-align:center;"> 204 </td>
  </tr>
  <tr>
   <td style="text-align:center;"> 10 </td>
   <td style="text-align:center;"> 108 </td>
   <td style="text-align:center;"> 1200 </td>
   <td style="text-align:center;"> 1308 </td>
   <td style="text-align:center;"> 228 </td>
  </tr>
</tbody>
</table>
]

.pull-right[.s[
- For the first fancy footwear produced, liv's `$\Delta$`Q is 1, while her `$\Delta$`TC is 120-108=12

- The second fancy footwear, her `$\Delta TC=156-120=36$` and so on.

- In our case, we have complete one fancy footwear incremental. In the real world, you might not have this kind of data.

- But the principle is the same.
]]

---

## Liv's fancy footwear

![](week5_files/figure-html/grafikliv1-1.png)
]

- An additional pair of fancy footwear from 1 to 2 costs an additional $36

- The additional cost is $180 from 7 pairs to 8 pairs
]]

---

## Liv's fancy footwear

![](week5_files/figure-html/grafikliv2-1.png)
]

.pull-right[ .s[
- The marginal cost is also upward sloping.
  - in this case, the cost structure is designed to be **diminishing in return**
  
- It means, the additional bobba needs more input as the fancy footwear increases.

- recall that the TP curve in Kensi's case is flattening because of this.

]]

---

## Average Total Cost (ATC)

- There is also **average total cost**, or simply **Average Cost**

$$
ATC=\frac{TC}{Q}
$$

- ATC is important because it tells the cost of each fancy footwear given the current state of production.

- Be careful, `$ATC \neq MC$`

- Which one would Liv use to set the price?

---

### Liv's fancy footwear cost structure

<table class="table table-bordered table-striped table-responsive" style="font-size: 20px; margin-left: auto; margin-right: auto;">
 <thead>
  <tr>
   <th style="text-align:center;"> Q </th>
   <th style="text-align:center;"> FC </th>
   <th style="text-align:center;"> VC </th>
   <th style="text-align:center;"> TC </th>
   <th style="text-align:center;"> MC </th>
   <th style="text-align:center;"> AFC </th>
   <th style="text-align:center;"> AVC </th>
   <th style="text-align:center;"> ATC </th>
  </tr>
 </thead>
<tbody>
  <tr>
   <td style="text-align:center;"> 0 </td>
   <td style="text-align:center;"> 108 </td>
   <td style="text-align:center;"> 0 </td>
   <td style="text-align:center;"> 108 </td>
   <td style="text-align:center;"> 0 </td>
   <td style="text-align:center;"> Inf </td>
   <td style="text-align:center;"> NaN </td>
   <td style="text-align:center;"> Inf </td>
  </tr>
  <tr>
   <td style="text-align:center;"> 1 </td>
   <td style="text-align:center;"> 108 </td>
   <td style="text-align:center;"> 12 </td>
   <td style="text-align:center;"> 120 </td>
   <td style="text-align:center;"> 12 </td>
   <td style="text-align:center;"> 108.00 </td>
   <td style="text-align:center;"> 12 </td>
   <td style="text-align:center;"> 120.00 </td>
  </tr>
  <tr>
   <td style="text-align:center;"> 2 </td>
   <td style="text-align:center;"> 108 </td>
   <td style="text-align:center;"> 48 </td>
   <td style="text-align:center;"> 156 </td>
   <td style="text-align:center;"> 36 </td>
   <td style="text-align:center;"> 54.00 </td>
   <td style="text-align:center;"> 24 </td>
   <td style="text-align:center;"> 78.00 </td>
  </tr>
  <tr>
   <td style="text-align:center;"> 3 </td>
   <td style="text-align:center;"> 108 </td>
   <td style="text-align:center;"> 108 </td>
   <td style="text-align:center;"> 216 </td>
   <td style="text-align:center;"> 60 </td>
   <td style="text-align:center;"> 36.00 </td>
   <td style="text-align:center;"> 36 </td>
   <td style="text-align:center;"> 72.00 </td>
  </tr>
  <tr>
   <td style="text-align:center;"> 4 </td>
   <td style="text-align:center;"> 108 </td>
   <td style="text-align:center;"> 192 </td>
   <td style="text-align:center;"> 300 </td>
   <td style="text-align:center;"> 84 </td>
   <td style="text-align:center;"> 27.00 </td>
   <td style="text-align:center;"> 48 </td>
   <td style="text-align:center;"> 75.00 </td>
  </tr>
  <tr>
   <td style="text-align:center;"> 5 </td>
   <td style="text-align:center;"> 108 </td>
   <td style="text-align:center;"> 300 </td>
   <td style="text-align:center;"> 408 </td>
   <td style="text-align:center;"> 108 </td>
   <td style="text-align:center;"> 21.60 </td>
   <td style="text-align:center;"> 60 </td>
   <td style="text-align:center;"> 81.60 </td>
  </tr>
  <tr>
   <td style="text-align:center;"> 6 </td>
   <td style="text-align:center;"> 108 </td>
   <td style="text-align:center;"> 432 </td>
   <td style="text-align:center;"> 540 </td>
   <td style="text-align:center;"> 132 </td>
   <td style="text-align:center;"> 18.00 </td>
   <td style="text-align:center;"> 72 </td>
   <td style="text-align:center;"> 90.00 </td>
  </tr>
  <tr>
   <td style="text-align:center;"> 7 </td>
   <td style="text-align:center;"> 108 </td>
   <td style="text-align:center;"> 588 </td>
   <td style="text-align:center;"> 696 </td>
   <td style="text-align:center;"> 156 </td>
   <td style="text-align:center;"> 15.43 </td>
   <td style="text-align:center;"> 84 </td>
   <td style="text-align:center;"> 99.43 </td>
  </tr>
  <tr>
   <td style="text-align:center;"> 8 </td>
   <td style="text-align:center;"> 108 </td>
   <td style="text-align:center;"> 768 </td>
   <td style="text-align:center;"> 876 </td>
   <td style="text-align:center;"> 180 </td>
   <td style="text-align:center;"> 13.50 </td>
   <td style="text-align:center;"> 96 </td>
   <td style="text-align:center;"> 109.50 </td>
  </tr>
  <tr>
   <td style="text-align:center;"> 9 </td>
   <td style="text-align:center;"> 108 </td>
   <td style="text-align:center;"> 972 </td>
   <td style="text-align:center;"> 1080 </td>
   <td style="text-align:center;"> 204 </td>
   <td style="text-align:center;"> 12.00 </td>
   <td style="text-align:center;"> 108 </td>
   <td style="text-align:center;"> 120.00 </td>
  </tr>
  <tr>
   <td style="text-align:center;"> 10 </td>
   <td style="text-align:center;"> 108 </td>
   <td style="text-align:center;"> 1200 </td>
   <td style="text-align:center;"> 1308 </td>
   <td style="text-align:center;"> 228 </td>
   <td style="text-align:center;"> 10.80 </td>
   <td style="text-align:center;"> 120 </td>
   <td style="text-align:center;"> 130.80 </td>
  </tr>
</tbody>
</table>
---

## Liv's cost structure

.pull-left[
<table class="table table-bordered table-striped table-responsive" style="font-size: 20px; margin-left: auto; margin-right: auto;">
 <thead>
  <tr>
   <th style="text-align:center;"> Q </th>
   <th style="text-align:center;"> TC </th>
   <th style="text-align:center;"> AFC </th>
   <th style="text-align:center;"> AVC </th>
   <th style="text-align:center;"> ATC </th>
  </tr>
 </thead>
<tbody>
  <tr>
   <td style="text-align:center;"> 0 </td>
   <td style="text-align:center;"> 108 </td>
   <td style="text-align:center;"> Inf </td>
   <td style="text-align:center;"> NaN </td>
   <td style="text-align:center;"> Inf </td>
  </tr>
  <tr>
   <td style="text-align:center;"> 1 </td>
   <td style="text-align:center;"> 120 </td>
   <td style="text-align:center;"> 108.00 </td>
   <td style="text-align:center;"> 12 </td>
   <td style="text-align:center;"> 120.00 </td>
  </tr>
  <tr>
   <td style="text-align:center;"> 2 </td>
   <td style="text-align:center;"> 156 </td>
   <td style="text-align:center;"> 54.00 </td>
   <td style="text-align:center;"> 24 </td>
   <td style="text-align:center;"> 78.00 </td>
  </tr>
  <tr>
   <td style="text-align:center;"> 3 </td>
   <td style="text-align:center;"> 216 </td>
   <td style="text-align:center;"> 36.00 </td>
   <td style="text-align:center;"> 36 </td>
   <td style="text-align:center;"> 72.00 </td>
  </tr>
  <tr>
   <td style="text-align:center;"> 4 </td>
   <td style="text-align:center;"> 300 </td>
   <td style="text-align:center;"> 27.00 </td>
   <td style="text-align:center;"> 48 </td>
   <td style="text-align:center;"> 75.00 </td>
  </tr>
  <tr>
   <td style="text-align:center;"> 5 </td>
   <td style="text-align:center;"> 408 </td>
   <td style="text-align:center;"> 21.60 </td>
   <td style="text-align:center;"> 60 </td>
   <td style="text-align:center;"> 81.60 </td>
  </tr>
  <tr>
   <td style="text-align:center;"> 6 </td>
   <td style="text-align:center;"> 540 </td>
   <td style="text-align:center;"> 18.00 </td>
   <td style="text-align:center;"> 72 </td>
   <td style="text-align:center;"> 90.00 </td>
  </tr>
  <tr>
   <td style="text-align:center;"> 7 </td>
   <td style="text-align:center;"> 696 </td>
   <td style="text-align:center;"> 15.43 </td>
   <td style="text-align:center;"> 84 </td>
   <td style="text-align:center;"> 99.43 </td>
  </tr>
  <tr>
   <td style="text-align:center;"> 8 </td>
   <td style="text-align:center;"> 876 </td>
   <td style="text-align:center;"> 13.50 </td>
   <td style="text-align:center;"> 96 </td>
   <td style="text-align:center;"> 109.50 </td>
  </tr>
  <tr>
   <td style="text-align:center;"> 9 </td>
   <td style="text-align:center;"> 1080 </td>
   <td style="text-align:center;"> 12.00 </td>
   <td style="text-align:center;"> 108 </td>
   <td style="text-align:center;"> 120.00 </td>
  </tr>
  <tr>
   <td style="text-align:center;"> 10 </td>
   <td style="text-align:center;"> 1308 </td>
   <td style="text-align:center;"> 10.80 </td>
   <td style="text-align:center;"> 120 </td>
   <td style="text-align:center;"> 130.80 </td>
  </tr>
</tbody>
</table>
]

- AFC drives ATC down: Fixed cost doesn't change no matter how much fancy footwear is produced (**spreading effect**).

- AVC increases as Q increases due to **diminishing returns effect**.

- at what Q does ATC at its lowest point?
]]

---

### Liv's fancy footwear Average Total Cost Curve

![](week5_files/figure-html/liv4-1.png)

---

## MC and ATC

- It is probably best to produce at the lowest ATC. Q=3 is the **minimum-cost output**.

- Note that:
  - at `$Q=3$`, `$ATC=MC$`;
  - at `$Q<3$`, `$ATC<MC$`;
  - at `$Q>3$`, `$ATC>MC$`.
  
- Works like your GPA: At GPA=3.0, an additional A will increase your GPA, a C will decrease your GPA, while a B doesn't change your GPA.

---

### Cost Curves

![](week5_files/figure-html/liv5-1.png)
---

## Cost curves

- Note that in our graph, ATC is not exactly equals to MC.

- This is because MC is an incremental cost from Q:
  - for example, a marginal cost from Q=1 to Q=2 should be plotted somewhere between Q=1 and Q=2, not exactly at Q=2.

- It easier to understand the logic when we use function.

- The logic remains: a Q where cost is lowest is when MC=ATC

---

## Short run and long run

- In the long run, Liv can upgrade (or downgrade) her capacity by changing her fixed cost.

- Higher fixed cost leads to higher overall cost, but typically can reduces variable cost at a higher Q.

- If Liv's client is just 3 people, buying a automated sewing machine might be an overkill.

- If Liv's business is forecasted to grow in the future, she can prepare for an upgrade.

---

## High capacity vs low capacity

![](week5_files/figure-html/liv6-1.png)

---

## High capacity vs low capacity

- Upgrading is only worth it if Liv sell at least 5 pairs of shoes.

- If upgraded, the minimum-cost output is `$Q=6$`

- In the long run, fixed cost can be changed (hence become variable to some extent)

- The most important is to know:
  - How the different capacity ATC looks like;
  - How easy each input can be changed;
  - whether changes in the market is long lasting or not.

---

## High capacity vs low capacity

---

## Long run cost curves

- **Long run average cost** (LRAC) is an average total cost which treat the fixed cost as a variable cost.

- Calculating LRAC requires many curves corresponding with different level of fixed cost.

- In fact, with so many other costs, using graph may no longer be practical.

- We won't cover it in this course, but it is useful to know that LRAC exists and can be useful for you in the future.

---

## Returns to scale

- Upgrading makes sense if the industry is having an **increasing returns to scale**.

- Increasing returns to scale happens when scaing up leads to lower LRAC.
  - in liv's case, she scaling up leads to lower cost overall, which may lower the price.
  - this is also the case for many industries, where big firms are able to offer their products at a lower price.
  
- When increasing scale leads to higher cost, we say **decreasing returns to scale**. Happens when a firm is too big, coordination gets costly.

---

# Calculating profit

---

## Perfect competition

- We learned in the perfect competition, producer takes price as given.

- This is called **price-taking producers** (and **price-taking consumers**)

- essentially means nobody can affect prices.

- How much should Liv produce? Depends on the **revenue**.

- For now, let's assume that the fancy footwear a highly competitive industry, where P=$100

---

### Liv's cost, revenue and profit (Total)

---

### Liv's cost, revenue and profit (total)

![](week5_files/figure-html/pc2-1.png)

---

### Liv's cost, revenue and profit (per unit)

---

## Profit under perfect market

- The necessary condition for profit maximisation is as close as possible with:

$$ MR = MC $$

- MR is short for **Marginal Revenue**, how much additional revenue you get from selling one more good.

$$
MR = \frac{\Delta TR}{\Delta Q}
$$
- It is like **marginal cost**, but revenue.

- This is why **marginal cost** is important.

---

## Marginal Revenue & Marginal Cost

<table class="table table-striped" style="font-size: 20px; margin-left: auto; margin-right: auto;">
 <thead>
<tr>
<th style="border-bottom:hidden;padding-bottom:0; padding-left:3px;padding-right:3px;text-align: center; " colspan="1"><div style="border-bottom: 1px solid #ddd; padding-bottom: 5px; ">Quantity <br> sold</div></th>
<th style="border-bottom:hidden;padding-bottom:0; padding-left:3px;padding-right:3px;text-align: center; " colspan="1"><div style="border-bottom: 1px solid #ddd; padding-bottom: 5px; ">Total <br> cost</div></th>
<th style="border-bottom:hidden;padding-bottom:0; padding-left:3px;padding-right:3px;text-align: center; " colspan="1"><div style="border-bottom: 1px solid #ddd; padding-bottom: 5px; ">Total <br> revenue</div></th>
<th style="border-bottom:hidden;padding-bottom:0; padding-left:3px;padding-right:3px;text-align: center; " colspan="1"><div style="border-bottom: 1px solid #ddd; padding-bottom: 5px; ">Total <br> Profit</div></th>
<th style="border-bottom:hidden;padding-bottom:0; padding-left:3px;padding-right:3px;text-align: center; " colspan="1"><div style="border-bottom: 1px solid #ddd; padding-bottom: 5px; ">Marginal <br> revenue</div></th>
<th style="border-bottom:hidden;padding-bottom:0; padding-left:3px;padding-right:3px;text-align: center; " colspan="1"><div style="border-bottom: 1px solid #ddd; padding-bottom: 5px; ">Marginal <br> cost</div></th>
<th style="border-bottom:hidden;padding-bottom:0; padding-left:3px;padding-right:3px;text-align: center; " colspan="1"><div style="border-bottom: 1px solid #ddd; padding-bottom: 5px; ">condition</div></th>
</tr>
  <tr>
   <th style="text-align:center;"> Q </th>
   <th style="text-align:center;"> TC </th>
   <th style="text-align:center;"> TR </th>
   <th style="text-align:center;"> TR-TC </th>
   <th style="text-align:center;"> MR </th>
   <th style="text-align:center;"> MC </th>
   <th style="text-align:center;"> MR-MC </th>
  </tr>
 </thead>
<tbody>
  <tr>
   <td style="text-align:center;"> 1 </td>
   <td style="text-align:center;"> 120 </td>
   <td style="text-align:center;"> 100 </td>
   <td style="text-align:center;"> -20 </td>
   <td style="text-align:center;"> 100 </td>
   <td style="text-align:center;"> 12 </td>
   <td style="text-align:center;"> 88 </td>
  </tr>
  <tr>
   <td style="text-align:center;"> 2 </td>
   <td style="text-align:center;"> 156 </td>
   <td style="text-align:center;"> 200 </td>
   <td style="text-align:center;"> 44 </td>
   <td style="text-align:center;"> 100 </td>
   <td style="text-align:center;"> 36 </td>
   <td style="text-align:center;"> 64 </td>
  </tr>
  <tr>
   <td style="text-align:center;"> 3 </td>
   <td style="text-align:center;"> 216 </td>
   <td style="text-align:center;"> 300 </td>
   <td style="text-align:center;"> 84 </td>
   <td style="text-align:center;"> 100 </td>
   <td style="text-align:center;"> 60 </td>
   <td style="text-align:center;"> 40 </td>
  </tr>
  <tr>
   <td style="text-align:center;background-color: blue !important;"> 4 </td>
   <td style="text-align:center;background-color: blue !important;"> 300 </td>
   <td style="text-align:center;background-color: blue !important;"> 400 </td>
   <td style="text-align:center;background-color: blue !important;"> 100 </td>
   <td style="text-align:center;background-color: blue !important;"> 100 </td>
   <td style="text-align:center;background-color: blue !important;"> 84 </td>
   <td style="text-align:center;background-color: blue !important;"> 16 </td>
  </tr>
  <tr>
   <td style="text-align:center;"> 5 </td>
   <td style="text-align:center;"> 408 </td>
   <td style="text-align:center;"> 500 </td>
   <td style="text-align:center;"> 92 </td>
   <td style="text-align:center;"> 100 </td>
   <td style="text-align:center;"> 108 </td>
   <td style="text-align:center;"> -8 </td>
  </tr>
  <tr>
   <td style="text-align:center;"> 6 </td>
   <td style="text-align:center;"> 540 </td>
   <td style="text-align:center;"> 600 </td>
   <td style="text-align:center;"> 60 </td>
   <td style="text-align:center;"> 100 </td>
   <td style="text-align:center;"> 132 </td>
   <td style="text-align:center;"> -32 </td>
  </tr>
  <tr>
   <td style="text-align:center;"> 7 </td>
   <td style="text-align:center;"> 696 </td>
   <td style="text-align:center;"> 700 </td>
   <td style="text-align:center;"> 4 </td>
   <td style="text-align:center;"> 100 </td>
   <td style="text-align:center;"> 156 </td>
   <td style="text-align:center;"> -56 </td>
  </tr>
  <tr>
   <td style="text-align:center;"> 8 </td>
   <td style="text-align:center;"> 876 </td>
   <td style="text-align:center;"> 800 </td>
   <td style="text-align:center;"> -76 </td>
   <td style="text-align:center;"> 100 </td>
   <td style="text-align:center;"> 180 </td>
   <td style="text-align:center;"> -80 </td>
  </tr>
  <tr>
   <td style="text-align:center;"> 9 </td>
   <td style="text-align:center;"> 1080 </td>
   <td style="text-align:center;"> 900 </td>
   <td style="text-align:center;"> -180 </td>
   <td style="text-align:center;"> 100 </td>
   <td style="text-align:center;"> 204 </td>
   <td style="text-align:center;"> -104 </td>
  </tr>
  <tr>
   <td style="text-align:center;"> 10 </td>
   <td style="text-align:center;"> 1308 </td>
   <td style="text-align:center;"> 1000 </td>
   <td style="text-align:center;"> -308 </td>
   <td style="text-align:center;"> 100 </td>
   <td style="text-align:center;"> 228 </td>
   <td style="text-align:center;"> -128 </td>
  </tr>
</tbody>
</table>

---

## MR, MC and AC in action

![](week5_files/figure-html/pc5-1.png)

---

![](week5_files/figure-html/pc6-1.png)

---

![](week5_files/figure-html/pc7-1.png)

---

## MR & MC

- Profit is equals to margin times quantity sold

$$ \pi=(P-ATC) \times Q$$

- hence the red area on the previous 2 graphs.

- When `$MR < MC$`, the additional Q that we produce reduces profit.

- When `$MR > MC$`, the additional Q that we produce increases profit.

- That is why at `$MR = MC$`, we have **profit-maximizing output**.

---

## MR & MC

- In Liv's case, she doesn't have any point where `$MR=MC$`

- In this case, she produce as close as possible with `$MR=MC$`, but still `$MR>MC$`

- profit is starting to go down when `$MR<MC$`
  
- In a bigger firm with more Q and more continuous data point, `$MR=MC$` is very useful and approachable.

---

## Perfect market

- In the perfect market, producers are price-taking (_pasrah_).

- That is why `$MR=P$`
  - no matter how much (or less) a producer produce, the price will always be the same
  
- We will see next week how the market will look like when producer's action can change prices.