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
- Quantity (้) ~ How many productsย =ย Q (# ofย ๐)
- Labor (ๅๅทฅ) ~ย The Number of Workers =ย L (๐ฑ)
- Capital (่ต้) ~ The Money ($$) we need =ย K (๐ฒ)
- Change (ๅๅ) ~ย How much did the # change? =ย ฮ(๐บ)
- Marginal (่พน้
ๆๆฌ) ~ย Result if you add ONE MORE (+1) Q
- Rate (ๆฏ็) ~ Ratio
- Substitution (ๅไปฃ) ~ XK = 1L (Substitution asks “what is X?”)
- Input (่พๅ
ฅ) ~ย All the resources you put into a product.ย
- Ice Cream ๐ฆhas many inputs:
- Milk๐ฅ
- Eggs๐ณ
- Sugar
- Ice
- Salt
- Chocolate Sauce
- Output (ไบง้) ~ย The product you createย
- Ice Cream ๐จ๐ฆis the output!
Part 2 – The Relationship Between L, K, and Q
Every product (ไบง้) can have lots of inputs (่พๅ
ฅ), just like theย Ice Cream ๐ฆย or a Car ๐. ย
Input + Input + Input + Input = Output (๐)
But in our class, we focus on TWO inputs: Laborย (๐ฑ) and Money (๐ฒ)
๐ฑ+๐ฒ=๐
Labor (๐ฑ) + Money (๐ฒ) = Quantity (๐)
L (๐ฑ)+ K (๐ฒ)= Q(๐)
Example:ย
Justin sells 200 cars ๐every day. Not 201 cars. Not 199 cars. He sells EXACTLY 200 cars ๐every day.ย
L (๐ฑ) + K (๐ฒ) = 200 cars (๐)
Justin knows that inย ONE DAY๐:
- 1 worker ๐ฑย can create 50% of a car ๐~ 2 workers ๐ฑ๐ฑcan create 100% of a car ๐(one car)
- 1L = 0.5Qย ๐
- 2L = 1Qย ๐
- $5 ๐ฒย can pay for 20% of a car ๐~ $25 ๐ฒcan pay for 100% of a car ๐(one car)
- 1K = 0.2Qย ๐
- 5K = 1Qย ๐
Rule #1 ~ If L โฌ and Kย โฌ, then the # ofย ๐ย cars will alsoย โฌ
Rule #2 ~ If L โฌ and Kย โฌ, then the # of ๐ย cars will alsoย โฌ
Rule #3 ~ If Lย โฌย and the # ofย ๐ย cars is still 200 (stay the same), K mustย โฌ
Rule #4 ~ Ifย Kย โฌย and the # ofย ๐ย cars is still 200 (stay the same), L mustย โฌ
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Today, Justin looks ๐คat his Money ๐ฒand is NOT happy๐ญ. He thinks he spends TOO MUCH money๐ก! ย He wants to buy a new bicycle๐ฒ, so he decides to SAVE $100 ๐ฒ
This means today:
๐ฑL + (๐ฒK – ๐ฒ100K) = ? Q๐
WHAT IS THE NEW Q (number of cars๐) that Justin Makes Today?
Day 1 (Yesterday): ๐ฑL + ๐ฒK = ๐200Q
Day 2 (Today): ๐ฑL + (๐ฒK – ๐ฒ100K) = ๐200Q – all the ๐cars $100K would pay for.ย
Remember! ย ๐ฒ1K = ๐0.20Q (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
๐ฒ-100K = -20 cars๐๐๐๐๐๐๐๐๐๐๐๐๐๐๐๐๐๐๐๐
ANSWER: Justin makes 180 cars today!
L + (K – 100K) = 200 cars – 20 carsย
= 180 cars๐
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OK?!?๐ค
NO!!! ย ๐กRemember –> “Justin sells 200 cars ๐every 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 ๐ฒKย โฌย and the # of ๐ย cars is 200 (the same), ๐ฑL mustย โฌ
QUESTION: HOW MUCH should ๐ฑL ย go up (โฌ)? ย
- Step 1 ~ How many extra cars ๐does 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 ๐ – 180 ๐= 20๐
Justin needs to make ๐ฑLย โฌย enough to make 20 extra cars๐ tomorrow.
- Step 2 ~ How much L does Justin have to add (+) to make 20 more cars tomorrow?
?L + (K – 100K) = 200Q
Remember,
๐ฑ1L = 0.5Qย ๐ | ๐ฑ๐ฑ2L = 1Qย ๐
20Q ๐= 40L
ANSWER: Justin will have to hire 40 workers (+40L) in order to make 20 more cars tomorrow.
๐ซ๐ซ๐ซ๐ซ๐ซ๐ซ๐ซ๐ซ๐ซ๐ซ๐ซ๐ซ๐ซ๐ซ๐ซ๐ซ๐ซ๐ซ๐ซ๐ซ
FINAL SOLUTION
*Substitution = Adding L to Decrease K
(๐ฑL + ๐ฑ40L) + (๐ฒK – ๐ฒ100K) = 200 Q (๐)
Part 3 ~ MRTS
MRTS = Marginal Rate of Technical Substitution
ย 
Go Back to Part 2.
- ๐บK๐ฒ
- Yesterday, Justin had K๐ฒ
- Tomorrow, Justin has -100K๐ฒ
- ๐บK = -100K๐ฒ
- ๐บL๐ฑ
- Yesterday, Justin had L๐ฑ
- Tomorrow, Justin has +40L๐ฑ
- ๐บL = +40L๐ฑ



MRTS = 5K : 2L |5๐ฒ : 2๐ซ
This just tells us:
- For every 2 ๐ซworkers Justin has, he spends $5๐ฒ๐ฒ๐ฒ๐ฒ๐ฒ.
- For every 1 ๐ฑworker Just has, he spends $2.50๐ฒ๐ฒยฝ
- 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 L๐ฑ can be a substitute for K๐ฒ!
Tags: business, Econ, Economics, emoji, EmojiBiz, Equation, ESL, Finance, formula, Managerial Economics, Microeconomics, MRTS, Understanding