# What is Production Possibility Frontier (PPF) diagram drawn on consumption-leisure?

When explaining basic macroeconomics model involving consumption-leisure tradeoff, often diagram showing production possbility frontier (PPF) is drawn with leisure on x-axis and consumption on y-axis. But what exactly is the meaning of this production possibility frontier?

Production Possibility Froniter diagram is often drawn on two-goods basis (for example, like butter on x-axis and milk on y-axis) but I am confused on what PPF might be on consumption-leisure basis.

## 1 Answer

Edited because wrnog answer, did not took the time to read the page.

Without maths

So your PPF would just be the link between leisure and consumption set by technology : the amount of leisure you choose give the time you can spend working, so the wage you earn and therefore the consumption you have (since there is no saving, all you earn is what you consume).

With a bit of math

You have a fixed amount of time, which we normalize to $1$. You can spend it either in leisure F (fun) or in work L (labour) so that $$1=L+F$$ Then you get a wage $w$, that is related to $L$ in some way : $w=\psi(L)$, and you consume $C=w=\psi(L)$, so that $L=\psi^{-1}(C)$

Then your PPF is $$F+\psi^{-1}(C)=1$$ It is a relation between leisure $F$ and consumption $C$ set by technology (the way wages are fixed).

Then the program is to maximize the agent utility $U(C,F)$ subject to this contraint. You can visualize it by the common tangent between iso-utility curves and your PPD.

• But in the reference link, iso-utility curve seems to be represented by curve I... – Newark Jan 16 '15 at 12:01
• I changed my answer, which was incorrect – Anthony Martin Jan 16 '15 at 13:37