Ans in full steps including diagram

Q2. In a perfectly competitive market, market demand and supply functions are respectively : Demand : Q. = 500 - 0.5P. Supply : Q, = -800 + 2P Where P is price while Q and Q. are quantity demanded and supplied for the whole market respectively. (a). Solve the equilibrium price (P) and the market quantity (Q). (b). Suppose the supply side is composed of 1000 firms with identical cost functions. Assume that average variable cost (AVC) curve is below marginal cost (MC) for all q, where q is the output of a single firm. Find a typical firm's MC function. [Hint : If there are only two firms, whose MC functions are respectively MC, = a + bq, and MC, - a + bq>, then since firms produce at where P - MC, the quantity supplied by the two firms are respectively q, - (P - a)/b and q2 = (P - a)/b. The market supply is q, + q2 - 2(P - a)/b or Q, =-2a/b + 2P/b. Using this logic, you can do the reverse : finding MC from market supply.] (c). Solve the typical firm's profit-maximization output (q). You should provide a numerical value. (d). The typical firm's average total cost (ATC) is U-shaped. ATC is the lowest when q - 0.2. Draw a diagram to indicate a typical firm's MC, ATC, the point where q - 0.2, and the profit- maximization output