## Abbreviations are CRAZY

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

12 Jun*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** ⬆

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

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🚗

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

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💲!

## Calculating the Value of a Company

25 Apr*As always, this lesson is not intended to be professional advice. This is simply my lesson material for ESL students in a Managerial Economics class. Posted here for their use or for helping other Economics students.*

**Finding the Value of the Firm**

We measure the success of a financial manager (how well they maximize profits) by finding the overall **Value of the Firm (公司的价值)**.

* Value of the Firm = Value of the Company = Present Value* (现值)= How much money ($$/￥/₩) the company would be worth if you tried to sell it today (多少钱该公司将是值得的，如果你想出售它). The Value of the Firm should include

- How much money the company is worth today
*and* - Expected profits in the future.

**Mathematical Equation for Calculating the Value of the Firm**

__Value of the Firm = Current Profit + Expected Future Profit__.

Each Year’s Profit is calculated with the following formula:

**X**= Current or Expected Accounting Profit (预期会计利润) = Revenue – Explicit Costs**R**= Risk-Adjusted Discount Rate (风险调整贴现率)*(although we hope we will make the expected accounting profit this year or in future years, there is always the possibility that we will not. No one will pay us the full expected value of the company because of this risk. So to give the buyer some protection, just in case, we*（我们从方程中删除的金额，因为我们现在可能不会真正使所有预期的利润，我们想要的）**remove**the Risk-Adjusted Discount Rate from the total.)**T**= Number of Years from Today

**EXAMPLE**

**Year 1, Company A makes $180,000. Year 2, Company A makes $150,000. Year 3, Company A makes $100,000. The Risk-Adjusted Discount Rate is 13%. **1年，公司180000美元。2年，公司150000美元。3年，公司100000美元。风险调整贴现率为13%

The Equation for 1 Year is:

The Equation for 3 Years is:

Filling in our known information, the equation for the Value of Our Firm is:

#### Value of the Firm = $346,069