A firm operates in an industry whose market structure is that of free competition with barriers to entry. The industry's demand is XI=4200001-10000Px and the industry supply is XI=1+20000Px The cost function of the firm is C(Xf )= .5Xf2+4. Where XI is the industry quantity and Xf is the firm's quantity. 1. Find the industry (equilibrium) output and price. 2. What is the firm's demand function in this freely competitive market?. Explain why the firm's price, and its MR are identical? 3. Find the firm's supply function, assuming for simplicity that the firm's supply function is given by its MC above its Average cost. Using this supply function, find out what is the optimal quantity that the firm should produce and what is the firm's profit?