Suppose a nonlinear price discriminating monopolist faces an inverse demand curve: P = 110-Q, and can set three prices depending on the quantity a consumer purchases. The firm's profit is: π = P₁ Q₁ + P₂ (Q₂ -Q₁) + P3 (Q3 Q₂) - mQ3, P2 - where p₁ is the high price charged on the first units Q₁ (first block) and p2 is a lower price charged on the next (Q₂-Q₁) units and p3 is the lowest price charged on the (Q3 - Q₂) remaining units. Q3 is the total number of units actually purchased, and m = 75 is the firm's constant marginal and average cost. Using calculus, determine the profit-maximizing values for P₁, P2, and p3, and the firm's profits. The profit-maximizing value for (round your answers to the nearest penny)

A firm is originally operating as a single-price monopolist that faces a market demand curve P(Q) = 198 –0 and total cost curve equal to TC (q) = 10, 500 + 32Q, with constant MC equal to MC(Q) = 32 for all units produced. Part (a): How much output does the firm produce and at what price is each unit sold for? Part (b): Calculate the firm's profit. The firm now realizes there are actually two distinct groups of consumers that purchase their product, with the following demand functions: P(q1) = 242 – qı P(q2) = 176 – 92 Their total and marginal cost curves have not changed. If the firm wanted to successfully practice third-degree price discrimination: Part (c): How many units of output would they sell to group 1 and how much will each consumer in group 1 pay? Part (d): How many units of output would they sell to group 2 and how much will each consumer in group 2 pay? Part (e): How much profit is earned by the firm when they practice third-degree price discrimination? Part (f): How much…

Consider a monopolist who sells its product in two distinct markets (and therefore can charge differentprices in these different markets). By the way, charging observably different group different prices is called3rd-degree price discrimination. The cost function is C(Q1 + Q2) = 0.25[Q1 + Q2]^2The inverse demand curves for these markets are p1(Q1) = 200 – Q1 for market 1 and p2(Q2) = 300 – Q2 formarket 2, where Q1 is the quantity sold in market 1 and Q2 is the quantity sold in market 2. At some pointbelow, you may wish to use the marginal cost function, which is MC(Q1 + Q2) = 0.5[Q1 + Q2].    a) State this 3rd-degree price discriminating monopolist’s maximization problem, using the particulars ofthis problem. Think carefully about what this monopolist is choosing and what it is trying to maximize. b) State two equations that an (interior) solution will satisfy. c) Solve for the optimal quantity to sell in each market. d) Solve for the price to charge in each market. e) Compute the…

Suppose a monopolist's total cost function is given by c = 0.004q +30q + 2000, and the revenue function is r = q(1200 - 6q), where c is measured in dollars and q is measured in tonnes per week. a. Determine marginal cost when g = 50. b. Express profit (n) as a function of q. Determine the profit-maximising level of output and the corresponding maximum profit. Justify your answers. C.