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.
1. Ice Cream 🍦has many inputs:
  1. Milk🥛
  2. Eggs🍳
  3. Sugar
  4. Ice
  5. Salt
  6. Chocolate Sauce
Output (产量) ~ The product you create
1. 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👱