All problems are with regards to the following set up. A monopolist uses two part tarrifs to extract surplus in two different markets. The monopolist has no costs (so most importantly, mc = 0.) There are n₁ = n identical consumers in market 1, and non (with > 0) identical consumers in market 2. Each consumer in market 1 has P₁(91) a1-91 for her indiviual (inverse) demand. Each consumer in market 2 has P2(92) = 02-92 for his indiviual (inverse) demand. We assume a2a1. For problems (1), (2), and (3), we assume that the monopolist set can charge different access fees (A1 and A2) and per unit charges (p1 and p2) in the two markets. (Note: because marginal costs are constant and we allow different prices in the two markets, you can think of the monopoly as solving for profits in each market seperately.) (1) (12.5 points) For each market, let A; (pi) denote the optimal access fee as a function of the per unit charge in that market. Find A₁ (p1) and A2(p2). Either show your work or explain (briefly) where your answer comes from. (2) (12.5 points) Using part (a), we can now think of the firm's profit maximization problem as an unconstrained maximization problem. Write down the firm's profit maximization problem. (3) (12.5 points) What are the profit maximizing choices for p₁ and p2? Either show your work or explain your answer verbally. For the remaining problems, assume that the firm must choose one access fee, A = A₁ = A2, and one per unit charge, p = p₁ = p2, for both markets. For problems (4), (5), (6), and (7), assume that at the optimal p, we have Q₁(p) = a₁p > 0 and Q2(p) a2 p>0. (That is, the firm ends up making sales to consumers in both markets.) (4) (12.5 points) The firm will set A = A₁ (p). Explain why this must be the profit maximizing choice? (5) (12.5 points) Using your answers to (a) and (d), write down the firm's profit maximization problem. (Hint: since prices must be the same in the two markets, it is easier to have the firm choose p rather than having the firm choose q₁ and 92 with the constraint of a common per unit charge.) I (6) (12.5 points) Solve for the profit maximizing per unit charge p*. Show your work. (7) (12.5 points) What condition on a₂ yeilds p* = mc = 0? What condition on yields p* = mc = 0? Give an intution as to why p* = mc when one of these two condition hold, but p* mc when neither condition holds. For problem (8), set a2 = 10, a₁ = 6, and x = 1. (8) (12.5 points) Calculate p*, A₁ (p*) and the firm's profits when operating in both markets. Will the firm choose to operate in both markets or only one? Show your work.