Making yummy #Snickerdoodles for the 8 #proctors of my #exam today ๐ 320 students, 4 classrooms, one exam. Go #microeconomics students!!! Fighting!! Jiayou!

## Managerial #Economics ~ Understanding #MRTS the Fun Way!

12 Jun*As always, this lesson isย not intended to be professional advice. This is simply lesson materialย for ESL students in a Managerial Economics and Finance class. Posted here for their use or for helping other students.*

**PART 1 – Key Words**

- Quantity (้) ~
*How many products*ย =ย**Q (#**of**ย ๐)** - Labor (ๅๅทฅ) ~ย
*The Number of Workers =ย***L (๐ฑ)** - Capital (่ต้) ~
*The Money ($$) we need =ย***K (๐ฒ)** - Change (ๅๅ) ~ย
*How much did the # change? =ย***ฮ(๐บ)** - Marginal (่พน้
ๆๆฌ) ~ย
*Result if you add ONE MORE (+1) Q* - Rate (ๆฏ็) ~
*Ratio* - Substitution (ๅไปฃ) ~ XK = 1L (
*Substitution asks “what is X?”*) - Input (่พๅ
ฅ) ~ย
*All the resources you put into a product.ย*- Ice Cream ๐ฆhas many inputs:
- Milk๐ฅ
- Eggs๐ณ
- Sugar
- Ice
- Salt
- Chocolate Sauce

- Ice Cream ๐ฆhas many inputs:
- Output (ไบง้) ~ย
*The product you createย*- Ice Cream ๐จ๐ฆis the output!

**Part 2 – The Relationship Between L, K, and Q**

Every product (ไบง้) can have lots of inputs (่พๅ ฅ), just like theย Ice Cream ๐ฆย or a Car ๐. ย

Input + Input + Input + Input = Output (๐**)**

But in our class, we focus on TWO inputs: Laborย **(๐ฑ) **and Money **(๐ฒ)**

๐ฑ+๐ฒ=๐

Labor (๐ฑ) + Money (๐ฒ) = Quantity (๐)

L (๐ฑ)+ K (๐ฒ)= Q(๐)

Example:ย

Justin sells 200 cars ๐every day. Not 201 cars. Not 199 cars. He sells EXACTLY 200 cars ๐every day.ย

L (๐ฑ) + K (๐ฒ) = 200 cars (๐)

Justin knows that inย **ONE DAY๐:**

- 1 worker ๐ฑย can create 50% of a car ๐~ 2 workers ๐ฑ๐ฑcan create 100% of a car ๐(one car)
- 1L = 0.5Qย ๐
- 2L = 1Qย ๐

- $5 ๐ฒย can pay for 20% of a car ๐~ $25 ๐ฒcan pay for 100% of a car ๐(one car)
- 1K = 0.2Qย ๐
- 5K = 1Qย ๐

**Rule #1** ~ If L โฌ and Kย โฌ, then the # ofย ๐ย cars will alsoย โฌ

**Rule #2** ~ If L โฌ and Kย โฌ, then the # of ๐ย cars will alsoย โฌ

**Rule #3** ~ If Lย โฌย and the # ofย ๐ย cars is still 200 (*stay the same*), K **must**ย โฌ

**Rule #4** ~ Ifย Kย โฌย and the # ofย ๐ย cars is still 200 (*stay the same*), L **must**ย โฌ

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Today, Justin looks ๐คat his Money ๐ฒand is NOT happy๐ญ. He thinks he spends TOO MUCH money๐ก! ย He wants to buy a new bicycle๐ฒ, so he decides to SAVE $100 ๐ฒ

This means today:

๐ฑL + (๐ฒK – ๐ฒ100K) = ? Q๐

**WHAT IS THE NEW Q ( number of cars๐) that Justin Makes Today?**

Day 1 (Yesterday): ๐ฑL + ๐ฒK = ๐200Q

Day 2 (Today): ๐ฑL + (๐ฒK – ๐ฒ100K) = ๐200Q – all the ๐cars $100K would pay for.ย

Remember! ย ๐ฒ1K = ๐0.20Q (*one dollar pays for 0.20 cars in a day)*

If Justin does not spend $100 today, he will lose the money for 20 cars!ย

1K = 0.20 cars

๐ฒ-100K = -20 cars๐๐๐๐๐๐๐๐๐๐๐๐๐๐๐๐๐๐๐๐

**ANSWER:** Justin makes **180 cars** today!

L + (K – 100K) = 200 cars – 20 carsย

= 180 cars๐

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

OK?!?๐ค

NO!!! ย ๐กRemember –> “Justin sells 200 cars ๐every day. Not 201 cars. Not 199 cars. He sells EXACTLY **200 cars** every day. ” ย

**PROBLEM**: ย How can Justin still make and sell 200 cars tomorrow if he still saves the $100 (-100K) as today.

**Rule #4** ~ If ๐ฒKย โฌย and the # of ๐ย cars is 200 (*the same*), ๐ฑL **must**ย โฌ

**QUESTION: **HOW MUCH should ๐ฑL ย go up (โฌ)? ย

- Step 1 ~ How many extra cars ๐does Justin need to make? ~ย
*Justin can make 180 cars right now if he saves $100 (-100K) but L stays the same as yesterday. ย*

*200 ๐ – 180 ๐= 20๐
Justin needs to make* ๐ฑL

*ย โฌย enough to make 20 extra cars๐ tomorrow.*

- Step 2 ~ How much L does Justin have to add (+) to make 20 more cars tomorrow?

?L + (K – 100K) = 200Q

Remember,

๐ฑ1L = 0.5Qย ๐ | ๐ฑ๐ฑ2L = 1Qย ๐

20Q ๐= 40L

**ANSWER**: Justin will have to hire 40 workers (+40L) in order to make 20 more cars tomorrow.

๐ซ๐ซ๐ซ๐ซ๐ซ๐ซ๐ซ๐ซ๐ซ๐ซ๐ซ๐ซ๐ซ๐ซ๐ซ๐ซ๐ซ๐ซ๐ซ๐ซ

# FINAL SOLUTION

*Substitution = Adding L to Decrease K

(๐ฑL + ๐ฑ40L) + (๐ฒK – ๐ฒ100K) = 200 Q (๐)

**Part 3** ~** MRTS**

MRTS = Marginal Rate of Technical Substitution

ย

Go Back to Part 2.

**๐บK๐ฒ**- Yesterday, Justin had K๐ฒ
- Tomorrow, Justin has -100K๐ฒ
**๐บK = -100K๐ฒ**

**๐บL๐ฑ**- Yesterday, Justin had L๐ฑ
- Tomorrow, Justin has +40L๐ฑ
**๐บL = +40L๐ฑ**

MRTS = 5K : 2L |5๐ฒ : 2๐ซ

*This just tells us:*

- For every 2 ๐ซworkers Justin has, he spends $5๐ฒ๐ฒ๐ฒ๐ฒ๐ฒ.
- For every 1 ๐ฑworker Just has, he spends $2.50๐ฒ๐ฒยฝ
- If Justin wants to hire 1 worker (+1L) , he will save $2.50 (-2.50K)
- I Justin wants to save $40 (-40K), he must hire 16 workers (+16L)

MRTS shows how much L๐ฑ can be a substitute for K๐ฒ!