Production Possibility Frontiers

Holmes

Econ 10

What is a PPF?

Production Possibility Frontier (PPF) is a representation of all possible combinations of two goods that our given resources can produce. We only graph the “biggest” combinations, so we look at the frontier of the combinations.

Example (classical school)

Butter

Guns (50,100)

(100,75)

(150,20)

If we choose to produce 50 pounds of Butter, then we can make 100 Guns.

Why is it bowed out?Some resources are more suitable in the production of one of the goods (how can we use cows in our production of guns?)

Suppose we are making as many guns as we can. We wish to make one pound of butter. We take one cow, one worker, and one butter churn. How much does our production of guns fall? Not much. Thus, the opportunity cost of the first pound of butter is rather low.

Butter

Guns

0 B, 120 G 1 B,

119.8 G

Why is it bowed out?…but as we get further out and are trying to make the last pound of butter, then we take all the gunpowder and steel and somehow use this to produce more butter. These resources add little to our production of butter but decrease our production of guns dramatically. Thus, the opportunity cost of the last pound of butter is rather high.

Butter

Guns

200 B, 0 G

199 B, 5 G

What does this imply?

Our first pound of butter cost .2 gunsOur last pounds of butter cost 5 guns.

What happens to our cost of one unit?Does this agree with anything else we have done this semester?

Note we say nothing about the relative attractiveness of combinations; we are just saying what we could achieve.

A more tangible exampleSuppose we have two types of people in our economy.

We have 10 Carlas: these people are really good at dancing-they produce 15 Quality Dance Routines per hour.

We also have 10 Joshs: these people can kick field goals: 20 per hour.

Unfortunately, Carla can only make 1 FG/hour and Josh can make 2 QDR’s per hour.

What kinds of combinations can they produce?

Graph of ALL combinationsF

ield

Goa

ls

10 Joshs and 10 CarlasQuality Dance Routines

0 170

0

210

All make FG

All J make FGAll C make DR

All C make FGAll J make DR All make QDR

Fie

ld G

oa

ls

10 Joshs and 10 CarlasQuality Dance Routines

0 170

0

210

But we only care about the frontierF

ield

Go

als

10 Joshs and 10 CarlasQuality Dance Routines

0 170

0

210

Suppose we add another type of person

Let’s suppose there are now 5 Marks. Marks can make 5 FG/hr and 5 QDR/hr.

JoshDR MarkDR CarlaDR

With 5 MarksQuality Dance Routines

0 195

0

235 0 0 0 0 0 1 0 0 2 0 0 3 0 0 4 0 0 5 0 0 6 0 0 7 0 0 8 0 0 9 0 0 100 1 10

0 2 100 3 10

0 4 100 5 10

1 5 10

2 5 10

3 5 10

4 5 10

5 5 10

6 5 10

7 5 10

8 5 10

9 5 10

10 5 10

Carlas do DR

Joshs do DR

Marks do DR

Two economies

Economy A: 3 FG/DR Economy B: 1 FG/4DRIf each splits their workforce:

A makes 30 FG, 10DR B makes 10 FG, 40 DR= 40 FG, 50 DR

If each makes what they are best at:A makes 60 FG B makes 80 DR

=60 FG, 80 DR

Can trade at 1 FG = 1 DR

Suppose instead...Economy A

FG

: Eco

n A

DR: Econ A0 20 40

0

80

60

Economy B

FG

: Eco

n B

DR: Econ B0 20 40

0

80

60

Economy A: 3 FG/ 1DR per person Economy B: 4 FG / 2DR per person

B is better at both. Now what?Split: A: 18 FG 14 DR

B: 40 FG 20 DR 58 FG 34 DR

Suppose instead...Economy A

FG

: Eco

n A

DR: Econ A0 20 40

0

80

60

Economy B

FG

: Eco

n B

DR: Econ B0 20 40

0

80

60

Economy A: 3 FG/ 1DR per person Economy B: 4 FG / 2DR per person

Specialize: A gives up 3 FG/DR, B gives up 2 FG/DR, so B should make DR

A: 60 FG. B: 40 DR.We say that A has a comparative advantage in FG, B has a CA in DR.

TradeTrade: A buys DR at 1 DR = 2.5 FGA likes: 1 DR costs 3 FGB likes: 1 DR costs 2 FG

FG DRA 60B 40

FG DRA 60-2.5*16 +16B +2.5*16 40-16

FG DRA 20 16B 40 24

Better off than was originally!

Moral

Even “superior” economies can benefit from trade. In our last example, B could do both better. Yet trading with A was still better than trying to do it by themselves.

Practice Problem:Suppose that some high-powered lawyer can write 5 lawsuits per hour and type 3 letters per hour. Her paralegal can write 1 lawsuit per hour and type 2 letters per hour. Why doesn’t the lawyer type her own letters?