(20 marks) Suppose in a perfectly competitive market, all firms and potential entrants are identical, their long-run total cost function is TC(Q) = 20Q 0.5Q* + 0.01Q? and the marginal cost function is MC(Q) = 20 Q + 0.03Q%. (1) Given the market demand curve as Q4, = 1900 50P, solve the long-run equilibrium price (P*), equilibrium output per firm (Qy), equilibrium output of the market (Qj,), and the total number of the firms in the market (n*). (2) Suppose the market demand increases to Q% = 2400 50P, what will happen to the long- run equilibrium price (P\"), equilibrium output per firm (Q;). equilibrium output of the market (Qm), and the total number of the firms in the market (n*)? (3) If the production in this specific industry uses scarce inputs, meaning that the prices of the inputs increase as the industry output increases, is the market long-run supply curve horizontal, upward slopping or downward slopping