Consider an economy with the following aggregate production function: Y = a [xK + (1 x)MP] (1/p) +bP where K is capital, M is mental labor and P is physical labor. Assume that (i) a, b>0, (ii) x = (0, 1) and (iii) p (, 1). (a) Take the cross-derivatives interpret. aY and ay Determine their sign and (b) Define y = Yt/Pt and analogously k = K/Pt and m = Mt/Pt. Rewrite the production function in lower-case letters. Then assume factors are paid their marginal products and derive the wages for physical (WP) and mental labor (wm).