3. An earlier edition of your text had the following theorem and proof about partial equilibria. Theorem: If q':]R+ > R, is continuous, q":]R+ * R has a continuous inverse qd '1, and at least one of q'(p) or q\"(p) is bounded from above, then there exists some [3* such that qdlp'\") = qslp\"). Proof: Let E z 0 be the smaller of the two bounds on q'(p) and qd(p) if both are bounded, or the upper bound on thegne that is bounded if only one upper bound exists. Define A = {q | 0 s q s q}. Note that A is nonempty, convex, and compact. Define the composite function qsoq\" = q'(q' '1(q)). Note that q'oqd '1: A * A. Note that qsoqd '1 is continuous because q' and q\" are. Thus Brouwer's Fixed Point theorem assures us that there is a fixed point q* E: A. The equilibrium price is p* = qd '1(q*). It's the equilibrium because supply equals demand: qd(p*) = q* and q'(p*) = q*. I The proof contains a logical error and the theorem is not correct. What is its logical error? Explain. (Comment: The functions q5 and qd are supply and demand functions Bounded from above means that there is a quantity that the functions do not exceed regardless of price. You will find the Brouwer Fixed Point Theorem on page 523 of your text.)