PPF question - opportuntiy costs.. in reverse (1 Viewer)

[WonkaHead22]

Question:

With the PPF and opportunity costs

say in a situation where we have 2 goods being produced , lets call them X and Y

A 0 X gooods , 100 Y Goods
B 10 X goods , 90 Y goods
C 20 X goods, 70 Y goods
D 30 X goods, 40 Y goods
e 40 X goods, 0 Y goods

now its obvious to see the opportuntiy cost of an additional 10 units of X goods .. as it goes first 10 of X means a sacrifice of 10 of y , The next 10 of X means a sacrifice of 20 of Y , and the Next 10 of X means a sacrifice of 30 of Y

But what i dont understand is The opportuntiy cost to get an extra UNIT OF Y???
how do i figure this out ?

 

[Ednaw]

hmm i cant remember that stuff really clearly but i thought production possibility opportunity cost stuff was meant to have a fixed ratio (ie cost for 10x is always equal to 10y) not variable.....lol

 

[WonkaHead22]

well it cant be fixed

because to produce more of one good , obviously a larger sacrficie of the other has to be made , as this is the opportunity cost...

 

[WonkaHead22]

Surely Someone Must Know The Answer!!!

 

[Will Hunting]

The Marginal Rate of Substitution (MRS) is a constant for a linear PPF and will vary for a curve (MRS is just the ratio X to Y, or the opportunity cost). If you like, the MRS is the gradient of the PPF (for a line), or the gradient function (for a curve).

To find the opportunity cost of a single unit of Y, you will want to find the derivative (gradient function) of the curve you have just described. However, no matter how the curve is drawn, or which axis it is drawn against, the equation of the curve is not easy to find, nevermind the derivative. By the information you've been given, the opportunity cost of a single unit of Y is:

1/4X for 0 < Y < 40
1/3X for 40 < Y < 70
1/2X for 70 < Y < 90
1X for 90 < Y < 100

This can be summarised in: An increase in the volume of Y means an increase in the sacrifice of X per unit of Y, though this occurs incrementally. If a differentiable curve could be drawn (although I don't think you'd be expected to do this),
x = f(y), it would have f'(y) < 0, f''(y) < 0. Don't worry too much about this though, man. Hope this helps

 

[gibbo67]

well it cant be fixed

because to produce more of one good , obviously a larger sacrficie of the other has to be made , as this is the opportunity cost...

on practical note, the opportunity cost is rarely ever going to be fixed (ie. the curve in a straight line), it generally increases because the resources are not all equally productive in all activities