As always, this lesson isΒ not intended to be professional advice. This is simply lesson materialΒ 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 (ι) ~ How many productsΒ =Β Q (# ofΒ π)
- Labor (εε·₯) ~Β The Number of Workers =Β L (π±)
- Capital (θ΅ι) ~ The Money ($$) we need =Β K (π²)
- Change (εε) ~Β How much did the # change? =Β Ξ(πΊ)
- Marginal (θΎΉι
ζζ¬) ~Β Result if you add ONE MORE (+1) Q
- Rate (ζ―η) ~ Ratio
- Substitution (ε代) ~ XK = 1L (Substitution asks “what is X?”)
- Input (θΎε
₯) ~Β All the resources you put into a product.Β
- Ice Cream π¦has many inputs:
- Milkπ₯
- Eggsπ³
- Sugar
- Ice
- Salt
- Chocolate Sauce
- Output (δΊ§ι) ~Β The product you createΒ
- Ice Cream π¨π¦is the output!
Part 2 – The Relationship Between L, K, and Q
Every product (δΊ§ι) can have lots of inputs (θΎε
₯), just like theΒ Ice Cream π¦Β or a Car π. Β
Input + Input + Input + Input = Output (π)
But in our class, we focus on TWO inputs: LaborΒ (π±) and Money (π²)
π±+π²=π
Labor (π±) + Money (π²) = Quantity (π)
L (π±)+ K (π²)= Q(π)
Example:Β
Justin sells 200 cars πevery day. Not 201 cars. Not 199 cars. He sells EXACTLY 200 cars πevery day.Β
L (π±) + K (π²) = 200 cars (π)
Justin knows that inΒ ONE DAYπ:
- 1 worker π±Β can create 50% of a car π~ 2 workers π±π±can create 100% of a car π(one car)
- 1L = 0.5QΒ π
- 2L = 1QΒ π
- $5 π²Β can pay for 20% of a car π~ $25 π²can pay for 100% of a car π(one car)
- 1K = 0.2QΒ π
- 5K = 1QΒ π
Rule #1 ~ If L β¬ and KΒ β¬, then the # ofΒ πΒ cars will alsoΒ β¬
Rule #2 ~ If L β¬ and KΒ β¬, then the # of πΒ cars will alsoΒ β¬
Rule #3 ~ If LΒ β¬Β and the # ofΒ πΒ cars is still 200 (stay the same), K mustΒ β¬
Rule #4 ~ IfΒ KΒ β¬Β and the # ofΒ πΒ cars is still 200 (stay the same), L mustΒ β¬
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Today, Justin looks π€at his Money π²and is NOT happyπ. He thinks he spends TOO MUCH moneyπ‘! Β He wants to buy a new bicycleπ², so he decides to SAVE $100 π²
This means today:
π±L + (π²K – π²100K) = ? Qπ
WHAT IS THE NEW Q (number of carsπ) that Justin Makes Today?
Day 1 (Yesterday): π±L + π²K = π200Q
Day 2 (Today): π±L + (π²K – π²100K) = π200Q – all the πcars $100K would pay for.Β
Remember! Β π²1K = π0.20Q (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!Β
1K = 0.20 cars
π²-100K = -20 carsππππππππππππππππππππ
ANSWER: Justin makes 180 cars today!
L + (K – 100K) = 200 cars – 20 carsΒ
= 180 carsπ
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
OK?!?π€
NO!!! Β π‘Remember –> “Justin sells 200 cars πevery day. Not 201 cars. Not 199 cars. He sells EXACTLY 200 cars every day. ” Β
PROBLEM: Β How can Justin still make and sell 200 cars tomorrow if he still saves the $100 (-100K) as today.
Rule #4 ~ If π²KΒ β¬Β and the # of πΒ cars is 200 (the same), π±L mustΒ β¬
QUESTION: HOW MUCH should π±L Β go up (β¬)? Β
- Step 1 ~ How many extra cars πdoes Justin need to make? ~Β Justin can make 180 cars right now if he saves $100 (-100K) but L stays the same as yesterday. Β
200 π – 180 π= 20π
Justin needs to make π±LΒ β¬Β enough to make 20 extra carsπ tomorrow.
- Step 2 ~ How much L does Justin have to add (+) to make 20 more cars tomorrow?
?L + (K – 100K) = 200Q
Remember,
π±1L = 0.5QΒ π | π±π±2L = 1QΒ π
20Q π= 40L
ANSWER: Justin will have to hire 40 workers (+40L) in order to make 20 more cars tomorrow.
π«π«π«π«π«π«π«π«π«π«π«π«π«π«π«π«π«π«π«π«
FINAL SOLUTION
*Substitution = Adding L to Decrease K
(π±L + π±40L) + (π²K – π²100K) = 200 Q (π)
Part 3 ~ MRTS
MRTS = Marginal Rate of Technical Substitution
Β 
Go Back to Part 2.
- πΊKπ²
- Yesterday, Justin had Kπ²
- Tomorrow, Justin has -100Kπ²
- πΊK = -100Kπ²
- πΊLπ±
- Yesterday, Justin had Lπ±
- Tomorrow, Justin has +40Lπ±
- πΊL = +40Lπ±
MRTS = 5K : 2L |5π² : 2π«
This just tells us:
- For every 2 π«workers Justin has, he spends $5π²π²π²π²π².
- For every 1 π±worker Just has, he spends $2.50π²π²Β½
- 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 Lπ± can be a substitute for Kπ²!
Tags: business, Econ, Economics, emoji, EmojiBiz, Equation, ESL, Finance, formula, Managerial Economics, Microeconomics, MRTS, Understanding
Deceptively Blonde 