2/20/12

Constructing a PPF and calculating opportunity costs



This post goes over the economics of PPF construction and opportunity cost calculations, for more info on the theories behind this check out this post of PPFs and opportunity costs.

Summary:  A PPF has increasing opportunity costs if the opportunity cost of a good gets larger as more of it is produced (this punishes specialization) and the PPF will be bowed out (a circle shape).  A PPF has constant opportunity cost if the opportunity cost of a good stays the same no matter how much of it is being produced so the PPF will be a straight line (a triangle shape).  Finally, a PPF has decreasing opportunity costs if the opportunity cost of a good gets smaller as more of it (this promotes specialization) and the PPF will be bowed in (like a crescent moon).


Given the following table, we need to find the opportunity cost of moving from each point to another point, and construct the PPF.
Point
Computers (Y)
Leather Jacket (X)
Opportunity Cost of Computer
Opportunity Cost of Leather Jacket
A
12
0
.5 Leather J.

B
10
1
.5 Leather J.
2 Computers
C
8
2
.5 Leather J.
2 Computers
D
6
3
.5 Leather J.
2 Computers
E
4
4
.5 Leather J.
2 Computers
F
2
5
.5 Leather J.
2 Computers
G
0
6

2 Computers

Calculating the opportunity cost requires you to figure out how much you are getting of a good, and dividing that number by how much you are giving up of the other good. 

What we give up/what we get. 

For example, moving from point A to point B, we are getting 1 leather jacket, and giving up 2 computers, this means that the opportunity cost of 1 leather jacket is 2 computers (2/1).  Likewise, if we move from point B to point A, we are giving up 1 leather jacket, and getting 2 more computers, so the opportunity cost of 2 computers is .5 leather jackets (1/2).  Note that the two opportunity costs are inverses of each other.

You can see from the graph that the opportunity costs are constant as we move along the various points of the PPF.  If the opportunity costs were increasing, then we would see the opportunity cost rise as we produced more and more of that specific good.  For example, the opportunity cost of a leather jacket at point G would be higher than point B.

Finally, to graph this PPF, we just take the points as given and plot them on a graph, then connect the lines to get a PPF.  In this case, it is a linear PPF.



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