Explain briefly, the meaning of this theorem about producer theory. THEOREM 3.7 Properties of the Prot Function If f satises Assumption 3'], then for p 2 0 and w 3 0, the prot function 11(p, w), where well-dened, is continuous and I . Increasing in p, 2. Decreasing in w, 3. Homogeneous of degree one in (p, w), 4. Convex in (p, w), 5. Dierentiable in (p, w) >> 0. Moreover; under the additional assumption that f is strictly concave (Hotelling 's lemma), 3n(p,w) =y(p,w), and 37r(p,w) =x~ ,w, i=1,2,...,n. 3p 3w,- :09 )