*As always, this lesson is not intended to be professional advice. This is simply lesson material 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 (量) ~
*How many products*=**Q (#**of**🚗)** - Labor (员工) ~
*The Number of Workers =***L (👱)** - Capital (资金) ~
*The Money ($$) we need =***K (💲)** - Change (变化) ~
*How much did the # change? =***Δ(🔺)** - Marginal (边际成本) ~
*Result if you add ONE MORE (+1) Q* - Rate (比率) ~
*Ratio* - Substitution (取代) ~ XK = 1L (
*Substitution asks “what is X?”*) - Input (输入) ~
*All the resources you put into a product.*- Ice Cream 🍦has many inputs:
- Milk🥛
- Eggs🍳
- Sugar
- Ice
- Salt
- Chocolate Sauce

- Ice Cream 🍦has many inputs:
- Output (产量) ~
*The product you create*- Ice Cream 🍨🍦is the output!

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

Every product (产量) can have lots of inputs (输入), just like the Ice Cream 🍦 or a Car 🚗.

Input + Input + Input + Input = Output (🚗**)**

But in our class, we focus on TWO inputs: Labor **(👱) **and Money **(💲)**

👱+💲=🚗

Labor (👱) + Money (💲) = Quantity (🚗)

L (👱)+ K (💲)= Q(🚗)

Example:

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

L (👱) + K (💲) = 200 cars (🚗)

Justin knows that in **ONE DAY🔆:**

- 1 worker 👱 can create 50% of a car 🚗~ 2 workers 👱👱can create 100% of a car 🚗(one car)
- 1L = 0.5Q 🚗
- 2L = 1Q 🚗

- $5 💲 can pay for 20% of a car 🚗~ $25 💲can pay for 100% of a car 🚗(one car)
- 1K = 0.2Q 🚗
- 5K = 1Q 🚗

**Rule #1** ~ If L ⬆ and K ⬆, then the # of 🚗 cars will also ⬆

**Rule #2** ~ If L ⬇ and K ⬇, then the # of 🚗 cars will also ⬇

**Rule #3** ~ If L ⬇ and the # of 🚗 cars is still 200 (*stay the same*), K **must** ⬆

**Rule #4** ~ If K ⬇ and the # of 🚗 cars is still 200 (*stay the same*), L **must** ⬆

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Today, Justin looks 🤔at his Money 💲and is NOT happy😭. He thinks he spends TOO MUCH money😡! He wants to buy a new bicycle🚲, so he decides to SAVE $100 💲

This means today:

👱L + (💲K – 💲100K) = ? Q🚗

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

Day 1 (Yesterday): 👱L + 💲K = 🚗200Q

Day 2 (Today): 👱L + (💲K – 💲100K) = 🚗200Q – all the 🚗cars $100K would pay for.

Remember! 💲1K = 🚗0.20Q (*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!

1K = 0.20 cars

💲-100K = -20 cars🚗🚗🚗🚗🚗🚗🚗🚗🚗🚗🚗🚗🚗🚗🚗🚗🚗🚗🚗🚗

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

L + (K – 100K) = 200 cars – 20 cars

= 180 cars🚗

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OK?!?🤔

NO!!! 😡Remember –> “Justin sells 200 cars 🚗every day. Not 201 cars. Not 199 cars. He sells EXACTLY **200 cars** every day. ”

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

**Rule #4** ~ If 💲K ⬇ and the # of 🚗 cars is 200 (*the same*), 👱L **must** ⬆

**QUESTION: **HOW MUCH should 👱L go up (⬆)?

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

*200 🚗 – 180 🚗= 20🚗
Justin needs to make* 👱L

*⬆ enough to make 20 extra cars🚗 tomorrow.*

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

?L + (K – 100K) = 200Q

Remember,

👱1L = 0.5Q 🚗 | 👱👱2L = 1Q 🚗

20Q 🚗= 40L

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

👫👫👫👫👫👫👫👫👫👫👫👫👫👫👫👫👫👫👫👫

# FINAL SOLUTION

*Substitution = Adding L to Decrease K

(👱L + 👱40L) + (💲K – 💲100K) = 200 Q (🚗)

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

MRTS = Marginal Rate of Technical Substitution

Go Back to Part 2.

**🔺K💲**- Yesterday, Justin had K💲
- Tomorrow, Justin has -100K💲
**🔺K = -100K💲**

**🔺L👱**- Yesterday, Justin had L👱
- Tomorrow, Justin has +40L👱
**🔺L = +40L👱**

MRTS = 5K : 2L |5💲 : 2👫

*This just tells us:*

- For every 2 👫workers Justin has, he spends $5💲💲💲💲💲.
- For every 1 👱worker Just has, he spends $2.50💲💲½
- 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 L👱 can be a substitute for K💲!

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