Question 1. Suppose that a monopoly firm supplies to two different markets with the demand functions: Market 1: q1 = 100 – 2p1 + P2 (1.1) Market 2: q2 = 150 + P1 – 3p2 (1.2) (a) Derive the inverse demand functions for both markets, and explain the relationship between the demand for the two goods. Assume that the firm's cost function is (q, + q2)² .
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- Assume that we are in a monopoly and demand curve is given by following expression:p(q) = 45 - q2And further it is known that marginal cost (MC) is given by:MC(q) = 6 + (q2/4)Under assumption that utility is maximized, answer:(a) Calculate marginal revenue (MR) and equilibrium point of monopoly. Graphb) Calculate consumer surplus (CS). Show it on the graphNOTE: remember that functions ARE NOT LINEAR. Consumer surplus is calculated as (see attached image)Consider a monopoly with a constant marginal cost of 10 that faces the following inverse demand function from senior citizens: PS = 50 − 2QS The monopoly also faces the following inverse demand function for all other customers: PO = 35 −Q0 a) List and explain the three conditions that must be satisfied for a firm to be able to price discriminate. b) Solve for the monopoly’s profit maximizing price and output levels assuming that they can price discriminate. c) In this example, who benefits and who loses from price discrimination? Be sure to explain/justify your answer.If a monopoly faces an inverse demand curve of p=450-Q, has a constant marginal and average cost of $30, and can perfectly price discriminate, what is its profit? What are the consumer surplus, welfare, and deadweight loss? How would these results change if the firm were a single-price monopoly? Profit from perfect price discrimination () is $88200. (Enter your response as a whole number.) Corresponding consumer surplus is (enter your response as whole numbers): welfare is and deadweight loss is Profit from single-price profit-maximization is = $44100. (Enter your response as a whole number.) Corresponding consumer surplus is (enter your response as whole numbers): welfare is and deadweight loss is CS = $0 W = $ 88200 DWL = $0. CS = $ 22050 W = $ 66150 DWL = $ 22050
- A monopoly faces a demand curve with two types of consumers: Group A with demand PA = 900 - 1/2 Q₁ and Group B with demand PB = 800- 1/8 QB. The firm cost function is given by C(Q) =100Q and MC=100. Suppose the firm cannot price discriminate, and must set a single price for both markets. What inverse demand curve does the monopoly face when both groups are active in the market? ( i.e, the aggregate demand for the case when P<800) esents when allIf a monopoly faces an inverse demand curve of p=330-Q, has a constant marginal and average cost of $90, and can perfectly price discriminate, what is its profit? What are the consumer surplus, welfare, and deadweight loss? How would these results change if the firm were a single-price monopoly? Profit from perfect price discrimination () is $ 28800. (Enter your response as a whole number.) Corresponding consumer surplus is (enter your response as whole numbers): welfare is and deadweight loss is CS=$ W = $ DWL = $ AQuestion 8 C(Q) = 120. Determine graphically, and clearly label all of the following: The equilibrium price and quantity for both the competitive market, and for monopoly; the area that correspond to the total benefit to society (the sum of net-benefit to consumers and firms) when replacing the monopoly by a competitive market. Demand is given in the grid below. Suppose firms have cost functions P, Costs 40 38 36 34 32 30 28 26 24 22 20 18 16 14 12 10 8 6 4 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40
- Suppose that a monopoly firm supplies to two different markets with the demand functions: Market 1: q, = 100 – 2p1 +P2 (1.1) Market 2: q2 = 150 + p1 – 3p2 (1.2) ( Assume that the firm's cost function is (q1 + 92)². a. Suppose there is a restriction of q2 < 20 in the market for good 2. What is the profit maximising price and output? Now suppose the firm has a resource constraint such that it can produce a maximum of 40 units of both goods in total, i.e., q, + q2 5 40. b. What is the impact on the firm's output in both markets, as well as on the maximum profit?Suppose a certain city has a monopoly cable-television company. This company has total costs TC = 0.25Q2 + 30Q + 70. (Hint: using calculus, this means MC = 0.5Q+ 30since MC is the derivative of TC with respect to output.) The demand in the community is approximated by the equationQd = 60- P/2(alternatively, you can write the demand equation as Qd = 60–0.5P). Graphically depict the demand curve as well as the marginal cost (MC) curve. If the cable company is free to choose its own pricePm and quantityQm, graphically depictthe monopoly equilibrium price and quantity. Add any other curve(s) to your diagram that may be required to obtain this outcome. Compute and state the exact monopolist equilibrium pricePm and quantityQm that you depicted graphically.Suppose a monopoly market faces a demand curve given by Q = (20 – P)(1 + 0.1A – 0.01A²) %3D - - and the cost function is given by C = 10Q + 15 + A %3D What output level will be chosen if the firm chooses its optimal level of advertising expenditures (A)? (a) Qm = 3 (b) Qm = 6.05 (c) Qm = 90.75 %3D %3D
- A firm has three factories for which costs are given by: C (Q1) = 10Q, C2 (Q2) = 40Q, C (Qs) = 80Q; The firm faces the following demand curve: P= 2,000 - 20 where Q is total output, i.e. Q - Q + Q, + Q3 What would be the Lerner index of monopoly power for this monopolist?[Please choose the closest-answer O 0.175 O 0.245 O 0.137 0.108 0.142 0.121 O 0.215 NestA monopoly sells its good in the U.S. and Japanese markets. The American inverse demand function is Pa = 90 - Qa' and the Japanese inverse demand function is P₁ = 80 - 2Qj, where both prices, På and p₁, are measured in dollars. The firm's marginal cost of production is m = $25 in both countries. If the firm can prevent resales, what price will it charge in both markets? (Hint: The monopoly determines its optimal (monopoly) price in each country separately because customers cannot resell the good.) The equilibrium price in Japan is $ (round your answer to the nearest penny) The equilibrium price in the U.S. is $. (round your answer to the nearest penny)A monopoly sells its good in the U.S. and Japanese markets. The American inverse demand function is Pa = 90-Qa' and the Japanese inverse demand function is P₁ = 80 - 2Q;, where both prices, på and p₁, are measured in dollars. The firm's marginal cost of production is m = $25 in both countries. If the firm can prevent resales, what price will it charge in both markets? (Hint: The monopoly determines its optimal (monopoly) price in each country separately because customers cannot resell the good.) The equilibrium price in Japan is $ 52.50. (round your answer to the nearest penny) The equilibrium price in the U.S. is $. (round your answer to the nearest penny)