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

  1. Quantity (量) ~ How many products = Q (# of  🚗)
  2. Labor (员工) ~ The Number of Workers = L (👱)
  3. Capital (资金) ~ The Money ($$) we need = K (💲)
  4. Change (变化) ~ How much did the # change? = Δ(🔺)
  5. Marginal (边际成本) ~ Result if you add ONE MORE (+1) Q
  6. Rate (比率) ~ Ratio
  7. Substitution (取代) ~ XK = 1L (Substitution asks “what is X?”)
  8. 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
  9. 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 Land K ⬆, then the # of 🚗 cars will also ⬆

Rule #2 ~ If Land 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

 CodeCogsEqn.gif

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👱

CodeCogsEqn.gif

CodeCogsEqn (2).gif

CodeCogsEqn (3).gif

MRTS = 5K : 2L |5💲 : 2👫

This just tells us:

  1. For every 2 👫workers Justin has, he spends $5💲💲💲💲💲.
  2. For every 1 👱worker Just has, he spends $2.50💲💲½
  3. If Justin wants to hire 1 worker (+1L) , he will save $2.50 (-2.50K)
  4. 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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