2.10 Another function we will encounter often in this book is the "power function"

y = x where 0 ^ 5 ^ 1 (at times we will also examine this function for cases where 5 can be negative too, in which case we will use the form y — x s /8 to ensure that the derivatives have the proper sign).

a. Show that this function is concave (and therefore also, by the result of problem 2.8, quasi-concave). Notice that the 8 = 1 is a special case and that the function is "strictly"
concave only for 8 < 1.

b. Show that the multivariate form of the power function is also concave (and quasi-concave). Explain why, in this case, the fact that/12 = fi>i — 0 makes the determination of concavity especially simple.
One way to incorporate "scale" effects into the function described in part b is to use the monotonic transformation giXl,x2) =yi= [(x,)
s + (x2)
s ]y where y is a positive constant. Does this transformation preserve the concavity of the function? Is g quasi-concave?