(20 marks) Suppose 1n 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 Q9, = 1900 50P, solve the long-run equilibrium price (P"), equilibrium output per firm (Q;), equilibrium output of the market (Qy,), 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 mputs increase as the industry output increases, 1s the market long-run supply curve honizontal, upward slopping or downward slopping