MGEA02 LEC1

opportunity cost

is what you give up when you choose something else.

Imagine you have enough money to buy one toy: a teddy bear or a toy car. If you pick the teddy bear, you can’t get the toy car. The opportunity cost is the toy car — because that’s what you gave up to get the teddy bear.

So:

Opportunity cost = the next best thing you didn’t choose.

trade-off

is when you have to give up one thing to get something else.

Let’s say you have 1 hour after school. You can either:

• Play outside, or

• Watch your favorite cartoon

But you can’t do both at the same time. You have to choose one. That’s a trade-off — when you decide to do one thing, you give up something else.

So:

Trade-off = choosing one thing means giving up another.

It’s like when you only get one dessert — you can’t have both ice cream and cake, so you have to pick! 🍦🎂

production possibility frontier

Imagine you run a lemonade and cookie stand.
You have just enough time and ingredients to make only lemonade, only cookies, or a mix of both in one day.

The Production Possibility Frontier (PPF) is like a line that shows all the different ways you can split your time to make lemonade and cookies.

• If you only make lemonade, you make a lot of lemonade but no cookies.

• If you only make cookies, you make a lot of cookies but no lemonade.

• If you make some of both, you get fewer of each.

So, the PPF helps us see our choices and the trade-offs we make when using our time or stuff in the best way!

PPF = A picture of all the different ways you can use your stuff (like time or ingredients) to make different things.

diminishing marginal product

Imagine you and your friends are making cookies.

• At first, it’s just you in the kitchen. You make some cookies.

• Then, one friend joins — now you make cookies faster!

• Another friend comes — even more cookies!

• But after too many friends show up, the kitchen gets crowded. People bump into each other, and it’s harder to work.

So, each new friend helps less and less than the one before.

That’s diminishing marginal product:

The more of something you add (like workers), the less extra help each new one gives.

It’s like: the first few helpers are super useful, but after a while, too many cooks spoil the cookies! 🍪

value function

Imagine you’re playing a video game 🎮. You collect coins, and the more coins you have, the happier you feel.

The value function is like a magic chart that shows how happy you are based on how many coins you get.

• When you go from 0 to 1 coin, you're super excited!

• From 1 to 2 coins, you're still happy, but a bit less.

• From 2 to 3, even less happy.

So the value (your happiness) goes up, but more slowly each time. That’s what the value function shows — how much satisfaction you get from each extra coin.

Value function = a way to show how much something is worth to you (like fun or happiness) when you get more of it.

• Combining the PPF with a Value (or Utility) Function to find the most efficient production point that maximizes value.

OCx and OCy

opportunity cost of x, opportunity cost of y

Opportunity cost of X (OCx):

OCx = -dY/ dX

• This is the slope of the PPF (multiplied by -1 to make it positive).

• It tells you how much of Good Y you give up to make one more unit of Good X.

• Example: If you have to give up 3 units of Y to make 1 more unit of X, OCX = 3.

Opportunity cost of Y (OCy)

OCy = -dX/dY   = -(1/ dY/dX ) = 1/OCx

• This is the inverse of OCX.

• It tells you how much of Good X you give up to make one more unit of Good Y.

• Example: If OCX = 3, then OCY = 1/3.

  • literally half of OCx

slope of PPF (linear and increasing)

Linear slope of PPF = dY/dX

increasing slope of PPF = d(OCx)/dX = d²Y/dX² > 0

• The curve is bowed outward (concave) — not a straight line.

• The slope becomes steeper as you move along the curve to the right (producing more X).

• This visualizes that opportunity cost of X is increasing.

• This means that the opportunity cost of X is rising as you make more of it.

• The second derivative being positive shows the curve bends outward.