Elasticity and tax

# Elasticity and tax
## Week 4
### Krisna Gupta
### 1 March 2021 (updated: 2021-03-01)

---

## Recap on last week

- We use consumer and producer surplus to measure the efficiency of the economy. We want the combination of both to be generally bigger.

- The two face a constant political battle: consumer wants small prices, producers like high prices.

- When market is perfect, intervention often leads to various types of inefficiency

---

## Today

- We will learn about one more intervention: tax.

- before we go there, it is best to understand elasticity first.

---

## What's an elasticity?

- If you are a business owner, understanding elasticity is important aspect to get maximized profit.

- **Price elasticity of demand** of a good is a concept of how much the demand of that good change  its price changes.
  - we usually just say **elasticity** in short.
  
- Maximizing profit requires this knowledge:
  - sometimes it is better to sell cheap to gain huge market share, or sell high if niche.
  
---

## Calculating elasticity

- At `$P_1=10$`, the daily traffic is `$Q_1=140$`

- When `$P_2=11$`, daily traffic drops to `$Q_2=127.3$`
]

---

## Calculating elasticity

.s[
- To calculate elasticity of demand, we first calculate:
  1. percent change in the quantity demanded
  1. percent change in the price

- Formula for no.1:

$$
\tag{1}
\text{% change in }Q^D=\frac{Q_2^D-Q_1^D}{Q_1^D}\times 100
$$

- Formula for no.2:

$$
\tag{2}
\text{% change in P}=\frac{P_2-P_1}{P_1}\times 100
$$
]

---

## Calculating elasticity

- for our case, we have:

$$
`\begin{align*}
Q_1^D&=140 & Q_2^D&=127.3 \\ P_1&=10 & P_2&=11
\end{align*}`
$$

- Thus:

$$
`\begin{align}
\text{% change in }Q^D &= \frac{127.3-140}{127.3}\times 100 \\ &=-10 \%
\end{align}`
$$

$$
`\begin{align}
\text{% change in P} &= \frac{11-10}{10}\times 100 \\ &=10\%
\end{align}`
$$

---

## Calculating elasticity

- After we get the numbers from {1} and {2}, we use this formula:

.s[
$$
\tag{3}
\text{Price elasticity of demand}=\frac{\text{% change in }Q^D}{\text{% change in P}}
$$
]

- in our case, we have:
.s[
$$
`\begin{align}
\text{Price elasticity of demand}&=\frac{-10\%}{10\%} \\ &=-1
\end{align}`
$$
]

---

## Calculating elasticity

- Economists are also lazy in writing the minus sign.

- Usually we report demand elasticity in **absolute term**.
  - i.e., we drop the minus sign.
  
- However, since most demand curves are downward sloping, it must be negative
  - hence we automatically knows what it means even when we report in absolute term.

---

## About percent change

Using percent changes is more useful than absolute changes
- Things are usually move on proportion
  - A wealthy person will feel casual getting 1 million IDR because it's probably just a small % of her total wealth.
    
- Quantity and prices have many metrics
  - kgs, litres, units, pairs, units/day, etc
  - IDR, USD, btc, etc.

---

class:middle, center

# Note

In the exam, please use 3 digits decimals.

for example, `$\pi= 3.14159265359...$`

please report `$\pi=3.142$` on exam.

---

## interpreting elasticity

---

## Interpreting elasticity

- We have seen the elasticity of our toll road case is around 1, but what does this mean?

- Note that the elasticity formula has % change in Q at the top, and % change in P at the bottom.

- In a sense, the number shows how much quantity change given the price change.

- that means, the bigger the number of the price elasticity, **the more elastic it is**

---

---

## A market is elastic. So what?

Let's have a look at different 'kind' of elasticities and what they mean

We'll begin with two extreme cases of elasticity: zero (0) and infinity ( `$\infty$` )

---

## Two extreme cases of elasticity

- Suppose the toll road is the only way to go to work.
  - No matter how high the price, people will still need to use it.
  - Hence, change in the demand of toll road is zero for any change in price.
  
- Suppose shuttlecocks are priced 10.000 IDR
  - If people don't care about the shuttlecocks' color, everyone will buy the pink one if the price drop to 9.900 IDR
  - Everyone won't buy a single one if the price go up only to 10.100 IDR

---

## Two extreme cases of elasticity

.pull-left[
![](week4_files/figure-html/grafik2-1.png)
.s[an illustration of **perfectly inelastic demand**]
]

.pull-right[
![](week4_files/figure-html/grafik3-1.png)
an illustration of **perfectly elastic demand**]

---

## Types of elasticities

- Most goods are somewhere in between.

- We usually use elasticity=1 as another important division point.

- 1 is a useful barrier because when elasticity=1, that means a change in price by 1 % leads to a change in quantity demanded by 1 %

- elasticity < 1 means the quantity response less than a change in prices, while elasticity > 1 means the quantity is highly responsive, more than the change in price.

---

.pull-left[
![](week4_files/figure-html/grafik4-1.png)![](week4_files/figure-html/grafik4-2.png)
]

The flatter the curve, the closer its elasticity to `$\infty$`]

---

## Types of demand elasticities

| Elasticity | meaning |
| ---------- | ------- |
| 0 | **perfectly inelastic**. Price doesn't matter |
| < 1 | **inelastic**. Quantity is less responsive to price changes |
| 1 | **unit elastic**. Quantity change exactly the same as the price change in % terms|
| >1 | **elastic**. Quantity response heavily to price changes |
| `$\infty$` | **perfectly elastic**. A slight increase of price reduces demand to zero |

---

## Elasticities vary. So what?

- Suppose you wan't to increase the revenue from the toll road operation, what price will you set?

- It is intuitive to think that the higher the price, the better.
  - High price `$\Rightarrow$` more revenue

- Is there a problem with this logic?

- Remember, demand respond to price. High price `$\Rightarrow$` lower demand `$\Rightarrow$` less revenue

- The maximum price depends on the demand elasticity

---

![](week4_files/figure-html/grafik6-1.png)

---

![](week4_files/figure-html/grafik7-1.png)

---

## Impact of price increase

.pull-right[.s[
- Segment A is the **Quantity effect of price increase**
  - Negative effect since fewer units sold

- Segment C is the **Price effect of price increase**
  - positive effect since higher price for each unit sold
]]

---

## Impact of price increase

$$
B+C > B+A
$$

$$
C>A
$$
]

---

## Impact of price increase

.pull-right[
- In a market with high demand elasticity, the quantity effect outweighs the price effect.

- Increasing the price is not so clever if the market's demand is highly elastic.
]

---

---

## Last point on demand elasticity

- When elasticity = 1, then `$A=C$`
  - hence changing price has no impact on sales revenue.

- Profit oriented in the real life may not very realistic
  - Governments may want to serve as much people as possible
  - In the short run, growth and market cap may be more important than profit.

---

## Last point on demand elasticity

- We usually tied elasticity on a price point.
  - on our toll road case, our price point is 10.000 IDR
  
- Elasticity may differ in different price point.
  - Changing price from 10 to 11 may have different impact compared to changing price from 20 to 21.
      - the first one is an increase of 10%.
      - the second one is an increase of 5%.
      - in absolute term, both are a 1.000 IDR increase.

---

## Last point on demand elasticity

- Estimating elasticity is very hard

- There are many things also at play:
  - different condition in different time
  - different buyer with different characteristics behave differently
  - Income, taste, etc matters (remember what **shifts the demand curve?**)

---

## Factors determine demand elasticity

- A **necessity** good tend to have lower elasticity compared to a **luxury good**.

- The availability of **close substitutes**, like the case with pertamax and shell.

- **Share of income spent** on the good. Rich people may not care with toll road price.

- **Time**. Cigarettes may have low elasticity in the short run because it is so addictive, and adapt later in the long run.

---

## Other types of demand elasticity

- **Cross price elasticity of demand** is how the price of good `$B$` affects a demand of good `$A$`.

.s[
$$
\tag{4}
\text{Cross-Price elasticity}_{A,B}=\frac{\text{% change in }Q_A}{\text{% change in }P_B}
$$
]

- When good A and good B are subtitutes, then the effect is negative.
  - e.g., Samsung and Xiaomi

- When good A and good B are complements, the effect is positive.
  - e.g., Samsung and Telkomsel

---

## Other types of demand elasticity

- **Income elasticity of demand** is how the chanage on income affects your demand of good `$A$`

.s[
$$
\tag{5}
\text{Income elasticity of Demand}_A=\frac{\text{% change in }Q_A}{\text{% change in Income}}
$$
]

- It is usually positive if good `$A$` is a **normal good**.

- It is negative if good `$A$` is an **inferior good**.
  - you buy less instant noodle when you're richer.
  
---

## Other types of demand elasticity

- **Income elasticity of demand** is how the chanage on income affects your demand of good `$A$`

.s[
$$
\tag{5}
\text{Income elasticity of Demand}_A=\frac{\text{% change in }Q_A}{\text{% change in Income}}
$$
]

- A **necessity** good is usually **income inelastic** because you need to buy it no matter what.

- A **luxury** good can be **income elastic**. You only buy it if your main needs are covered so you can wait for a discount.

---

class:middle, center

# Price elasticity of Supply

---

## Price elasticity of Supply

- Supply also have elasticities. As a supplier, you can't afford to sell expensive if there are high competition.

- However, in many cases (such as toll road), entering the market is very hard.

- How easy it is to expand (or for new supplier to enter the market) matters to how responsive can supply react to the change in price.
.s[
$$
\tag{6}
\text{Price elasticity of supply} = \frac{\text{% change in }Q^s}{\text{% change in }P}
$$
]

---

## Two extreme cases of elasticity

.pull-left[
![](week4_files/figure-html/grafik11-1.png)
.s[an illustration of **perfectly inelastic supply**]
]

.pull-right[
![](week4_files/figure-html/grafik12-1.png)
.s[an illustration of **perfectly elastic supply**]]

---

## Two extreme cases of elasticity

- In a **perfectly inelastic supply** case, the market can't supply more even if the price increase. Toll road is like this: Building more toll road is expensive and takes time. Most times this is monopolized by the government.

- In a **perfectly elastic supply**, the market supply exactly zero when the price go up just by a little. A highly competitive market where all firms operate at the margin may behave this way.

- Again, most times, the supply curve is somewhere in between.

---

## What changes supply elasticity?

- A market tend to have a highly elastic price elasticity of supply when **inputs are abundant** and can be converted in and out of producion at a very low cost.

- Matters, as price elasticity of supply tend to be higher in the long run. Increasing production capacity may takes time since investing in a new land, building or machine requires **time**.
  - Some goods are even impossible to be increased, hence have zero elasticity. Radio spectrum is one example.
  
---

## European farm surplus

European Union **subsidised** their farmers heavily. They probably knew that subsidies create huge **surplus** (remember last week), but they thought the surplus would not be as big since farming land is **limited**.

However, EU farmers were able to expand production using things like fertilizers and pesticides, which are **readily available inputs**.

---

# The benefits and costs of taxation

---

## Excise Tax (_cukai_)

- The government often tax goods in the form of an excise tax.

- In Indonesia, some goods have an excise to its purchase:
  - Cigarettes & alcohol
  - Luxury goods (PPnBM)

- You can say that a value-added tax is another form of an excise tax.

---

## How tax works

- Tax acts like a price ceiling plus plus floor:
  - The government set a higher price for consumers to pay
  - At the same time, the producers are forced to produced at a lower price.
  
- A reminder: in a **price floor** scenario, surplus from consumer transferred to the producer, while in a **price ceiling**, surplus transferred from producers to consumers.

- in tax case, CS and PS are transferred to the government.

---

## The impact of tax

![](week4_files/figure-html/grafiks3-1.png)

---

## The impact of taxation

.pull-left[
![](week4_files/figure-html/grafiks6-1.png)
]
.pull-right[.s[
- The market price is `$P=P_E$`

- The price paid by consumers is `$P=P_C$`

- Producer receive payment at `$P=P_P$`

- The tax per purchased good paid to the government is `$t=P_C-P_P$`
]]

---

## The impact of taxation

- Producer lose `$C+D$`

- The government collects tax revenue `$TR=T \times Q_T$`

- This is equals to `$TR=A+C$`

- `$B+D=DWL$`
]]

---

## The impact of taxation

- As we learn, the tax revenue and the size of DWL depends highly in demand elasticity and supply elasticity of the good.

- The less elastic the demand and supply of a good, the higher revenue gained from taxing the good.
  - i.e., price effect > quantity effect.
  
- DWL also lower when the demand and/or supply of the good is highly inelastic.

---

.pull-left[
![](week4_files/figure-html/grafiks1-1.png)![](week4_files/figure-html/grafiks1-2.png)
]

.pull-right[
![](week4_files/figure-html/grafiks2-1.png)![](week4_files/figure-html/grafiks2-2.png)
]

---

## Implication

- If the government wants to collect revenue, its best to impose a tax on a good with low elasticities.

- If the government wants to change behaviour, tax a good with high elasticities.

- Taxing cigarettes to discourage smoking maybe ineffective
  - however, it can be used to gain revenue.
  
- Highly inelastic goods may suggest it's a necessity: people may be unhappy with the tax.

---

## Implication

- Same goes with the business people: be careful in increasing price if your product is highly elastically demanded.

- Next week, we will have a look a bit more detailed on the supply curve: 
  - what drives the elasticity of supply.
  - Different types of cost.
  
---

## Some recap before da quiz

- Elasticities is very important in determining surpluses: CS, PS, revenues.

- Elasticities can be estimated (albeit hard).

- Elasticities vary: `$0 \leq 1 \leq \infty$` .

- Many factors influence elasticities.

- You should be able to use elasticity formula and can draw how tax is calculated and drawn.

---

# Thank You