Tag Archives: Microeconomics

Snickerdoodle #Treats!

31 Oct

Making yummy #Snickerdoodles for the 8 #proctors of my #exam today ๐Ÿ˜Š  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

  1. Quantity (้‡) ~ How many productsย =ย Q (# ofย  ๐Ÿš—)
  2. Labor (ๅ‘˜ๅทฅ) ~ย The Number of Workers =ย L (๐Ÿ‘ฑ)
  3. Capital (่ต„้‡‘) ~ The Money ($$) we need =ย K (๐Ÿ’ฒ)
  4. Change (ๅ˜ๅŒ–) ~ย How much did the # change? =ย ฮ”(๐Ÿ”บ)
  5. Marginal (่พน้™…ๆˆๆœฌ) ~ย Result if you add ONE MORE (+1) Q
  6. Rate (ๆฏ”็Ž‡) ~ Ratio
  7. Substitution (ๅ–ไปฃ) ~ XK = 1L (Substitution asks “what is X?”)
  8. Input (่พ“ๅ…ฅ) ~ย All the resources you put into a product.ย 
    1. Ice Cream ๐Ÿฆhas many inputs:
      1. Milk๐Ÿฅ›
      2. Eggs๐Ÿณ
      3. Sugar
      4. Ice
      5. Salt
      6. Chocolate Sauce
  9. Output (ไบง้‡) ~ย The product you createย 
    1. Ice Cream ๐Ÿจ๐Ÿฆis the output!

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

Every product (ไบง้‡) can have lots of inputs (่พ“ๅ…ฅ), just like theย Ice Cream ๐Ÿฆย or a Car ๐Ÿš—. ย 

Input + Input + Input + Input = Output (๐Ÿš—)

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

๐Ÿ‘ฑ+๐Ÿ’ฒ=๐Ÿš—
Labor (๐Ÿ‘ฑ) + Money (๐Ÿ’ฒ) = Quantity (๐Ÿš—)
L (๐Ÿ‘ฑ)+ K (๐Ÿ’ฒ)= Q(๐Ÿš—)

Example:ย 
Justin sells 200 cars ๐Ÿš—every day. Not 201 cars. Not 199 cars. He sells EXACTLY 200 cars ๐Ÿš—every day.ย 

L (๐Ÿ‘ฑ) + K (๐Ÿ’ฒ) = 200 cars (๐Ÿš—)

Justin knows that inย ONE DAY๐Ÿ”†:

  • 1 worker ๐Ÿ‘ฑย can create 50% of a car ๐Ÿš—~ 2 workers ๐Ÿ‘ฑ๐Ÿ‘ฑcan create 100% of a car ๐Ÿš—(one car)
    • 1L = 0.5Qย ๐Ÿš—
    • 2L = 1Qย ๐Ÿš—
  • $5 ๐Ÿ’ฒย can pay for 20% of a car ๐Ÿš—~ $25 ๐Ÿ’ฒcan pay for 100% of a car ๐Ÿš—(one car)
    • 1K = 0.2Qย ๐Ÿš—
    • 5K = 1Qย ๐Ÿš—

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

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

Rule #3 ~ If Lย โฌ‡ย  and the # ofย ๐Ÿš—ย cars is still 200 (stay the same), K mustย โฌ†

Rule #4 ~ Ifย Kย โฌ‡ย  and the # ofย ๐Ÿš—ย cars is still 200 (stay the same), L mustย โฌ†

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

Today, Justin looks ๐Ÿค”at his Money ๐Ÿ’ฒand is NOT happy๐Ÿ˜ญ. He thinks he spends TOO MUCH money๐Ÿ˜ก! ย He wants to buy a new bicycle๐Ÿšฒ, so he decides to SAVE $100 ๐Ÿ’ฒ

This means today:

๐Ÿ‘ฑL + (๐Ÿ’ฒK – ๐Ÿ’ฒ100K) = ? Q๐Ÿš—

WHAT IS THE NEW Q (number of cars๐Ÿš—) that Justin Makes Today?

Day 1 (Yesterday): ๐Ÿ‘ฑL + ๐Ÿ’ฒK = ๐Ÿš—200Q

Day 2 (Today): ๐Ÿ‘ฑL + (๐Ÿ’ฒK – ๐Ÿ’ฒ100K) = ๐Ÿš—200Q – all the ๐Ÿš—cars $100K would pay for.ย 

Remember! ย ๐Ÿ’ฒ1K = ๐Ÿš—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!ย 

1K = 0.20 cars
๐Ÿ’ฒ-100K = -20 cars๐Ÿš—๐Ÿš—๐Ÿš—๐Ÿš—๐Ÿš—๐Ÿš—๐Ÿš—๐Ÿš—๐Ÿš—๐Ÿš—๐Ÿš—๐Ÿš—๐Ÿš—๐Ÿš—๐Ÿš—๐Ÿš—๐Ÿš—๐Ÿš—๐Ÿš—๐Ÿš—

ANSWER: Justin makes 180 cars today!

L + (K – 100K) = 200 cars – 20 carsย 
= 180 cars๐Ÿš—

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

OK?!?๐Ÿค”

NO!!! ย ๐Ÿ˜กRemember –> “Justin sells 200 cars ๐Ÿš—every 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 ๐Ÿ’ฒKย โฌ‡ย  and the # of ๐Ÿš—ย cars is 200 (the same), ๐Ÿ‘ฑL mustย โฌ†

 

QUESTION: HOW MUCH should ๐Ÿ‘ฑL ย go up (โฌ†)? ย 

  • Step 1 ~ How many extra cars ๐Ÿš—does 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 ๐Ÿš— – 180 ๐Ÿš—= 20๐Ÿš—
Justin needs to make
๐Ÿ‘ฑLย โฌ†ย enough to make 20 extra cars๐Ÿš— tomorrow.

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

?L + (K – 100K) = 200Q

Remember,

๐Ÿ‘ฑ1L = 0.5Qย ๐Ÿš— | ๐Ÿ‘ฑ๐Ÿ‘ฑ2L = 1Qย ๐Ÿš—
20Q ๐Ÿš—= 40L

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

๐Ÿ‘ซ๐Ÿ‘ซ๐Ÿ‘ซ๐Ÿ‘ซ๐Ÿ‘ซ๐Ÿ‘ซ๐Ÿ‘ซ๐Ÿ‘ซ๐Ÿ‘ซ๐Ÿ‘ซ๐Ÿ‘ซ๐Ÿ‘ซ๐Ÿ‘ซ๐Ÿ‘ซ๐Ÿ‘ซ๐Ÿ‘ซ๐Ÿ‘ซ๐Ÿ‘ซ๐Ÿ‘ซ๐Ÿ‘ซ

FINAL SOLUTION

*Substitution = Adding L to Decrease K

(๐Ÿ‘ฑL + ๐Ÿ‘ฑ40L) + (๐Ÿ’ฒK – ๐Ÿ’ฒ100K) = 200 Q (๐Ÿš—)

Part 3 ~ MRTS

MRTS = Marginal Rate of Technical Substitution

ย CodeCogsEqn.gif

Go Back to Part 2.

  • ๐Ÿ”บK๐Ÿ’ฒ
    • Yesterday, Justin had K๐Ÿ’ฒ
    • Tomorrow, Justin has -100K๐Ÿ’ฒ
    • ๐Ÿ”บK = -100K๐Ÿ’ฒ
  • ๐Ÿ”บL๐Ÿ‘ฑ
    • Yesterday, Justin had L๐Ÿ‘ฑ
    • Tomorrow, Justin has +40L๐Ÿ‘ฑ
    • ๐Ÿ”บL = +40L๐Ÿ‘ฑ

CodeCogsEqn.gif

CodeCogsEqn (2).gif

CodeCogsEqn (3).gif

MRTS = 5K : 2L |5๐Ÿ’ฒ : 2๐Ÿ‘ซ

This just tells us:

  1. For every 2 ๐Ÿ‘ซworkers Justin has, he spends $5๐Ÿ’ฒ๐Ÿ’ฒ๐Ÿ’ฒ๐Ÿ’ฒ๐Ÿ’ฒ.
  2. For every 1 ๐Ÿ‘ฑworker Just has, he spends $2.50๐Ÿ’ฒ๐Ÿ’ฒยฝ
  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 L๐Ÿ‘ฑ can be a substitute for K๐Ÿ’ฒ!

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