# (5 points) This question studies the representative consumer’s trade off between current and future leisure (or current and future labour supplied)….

2. (5 points) This question studies the representative consumer’s trade off between current and future leisure (or current and future labour supplied). To simplify we abstract from consumption choices by assuming that current consumption (C) and future consumption (C) are set to some pre-determined values denoted C and C’. In other words, we assume C = C and C’ = C’.

Suppose that the representative consumer’s lifetime budget constraint1 can now be written as

w (h-l)+ (w(h-l’)/1+r) + 25 = 0.

The consumer takes w,w’, and r as given.

(a) Suppose that you wanted to represent the constraint above in a diagram where

l’ is measured on the vertical axis and l is measured on the horizontal axis. Use calculus to find the slope of the constraint that would appear in your diagram (you do not actually have to draw the diagram)PS: I think the answer is to rearrange the equation into y=mx+b (y=l’) (x=l), the answer should look something like this, -w(1+r)/w’