Compute the following microeconomic equations. If any clarifications are needed please leave a comment.

Consider a city where there are one million identical households. Each household has the following inverse demand curve for electricity: p = 200 - 2Q where Q is the quantity demanded per household per year and p is the price per unit. (i) Suppose that electricity is supplied by perfectly competitive firms, at a constant marginal cost of $50 per unit. There are no fixed costs. Find the equilibrium price and the equilibrium quantity demanded per household per year. Denote this quantity by Qe, where the subscript c in Q, indicates that this is the outcome under perfect competition. (ii) Now suppose that the perfectly competitive firms merge into a single firm (a monopoly). The marginal cost remains unchanged. Assume that the monopoly is required by a regulatory agency to charge a single price. What is the single price that maximizes the monopoly's profit? Denote this price by p. and the associated quantity demanded (per household per year) by Qm. Find the monopoly's profit, and denote it by Im. Find the ratio Qm/Qe- Compute the dead-weight loss under single-price monopoly. (iii) Now suppose that the regulatory agency changes its mind and allows the monopoly to use a two-block pricing scheme. The monopoly can announce a first quantity-block Q1 (per household per year) such that the price per unit for all units in this first block is equal to p(Q1), and a second quantity-block (Q2 -Q1) such the price per unit for all units in this second block is equal to p(Q2). If any household wants to buy more than Q, units per year, it must pay for each of these additional units the price p(Q2) per unit. Write the monopoly's profit as a function of Q, and Q2. Denote by Q; and Q; the solutions for Q, and Q, that maximize the monopoly's profit. Find Q;, @; and the associated prices pi = p(Q1) and p; = p(Q;). Compute the monopolist's profit under this two-block pricing scheme. (iv) Compute the deadweight loss under the two-block pricing scheme, and compare it to the dead weight loss under single-price monopoly. Should the regulatory agency allow the monopoly to increase the number of blocks? Please give the reasons for your answer (maximum length: 50 words). (v) Using your answers to (i) and (iii), compute the following ratios: Qi n = Q; - Q1 1 and 1 = 25 -Q; Qe What are the meaning of these ratios? Is it true that r, = 1 and ry = =? If it is true, can you tell whether this result is accidental or whether there is some plausible explanation behind it? Please give the reasons for your answer (maximum length: 50 words)