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2017-2018_MBA50-EX1.pdf - MASTER’S DEGREE PROGRAMME IN...

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MASTER’S DEGREE PROGRAMME IN BUSINESS ADMINISTRATION1Final Exam for ΜΒΑ50 (Economics for Managers)Sunday, May 27, 2018Instructions: Please answer all 4 questions. The weight of each question is indicated as a percentage of the entire exam. Themaximum grade in the entire exam is 10. All sub-sections have equal weight, unless it is denoted otherwise. You are welcometo use any examples and graphs you consider useful. Cooperation among students and copying is prohibited and is penalizedwith exemption from the exams. The use of calculators with memory and mobile phones is banned. You are not allowed toborrow any device, e.g., calculator, mobile phone, etc. The duration of the exam is two and a half (2.5) hours.STUDENT LAST NAME………………………………………………………………………STUDENT FIRST NAME………………………………………………………………………STUDENT E-MAIL………………………………………………………………………GROUPMBA50…….………………………………………………………..TUTOR FULL NAME………………………………………………………………………QUESTION 1 (25%)In a small country, Power Telephony is the only telecommunications provider and observes thatthere are two distinct groups of customers: i) businesses and ii) families. The businesses’demand function is given by𝑞= 100 − 𝑝, where𝑞denotes the hours of telephone servicesthat businesses purchase per week and𝑝is the price per hour charged to businesses. On theother hand, the families’ demand function is given by𝑞ி= 150 − 0.5𝑝ி, where𝑞ிand𝑝ிrepresent hours of telephone services and price, respectively. The company has a cost functionequal to𝐶(𝑞) = 𝑞, where𝑞 = 𝑞+ 𝑞ி.a)Assume that Power Telephony can price discriminate between the two groups.Calculatethe price it charges and the hours of telephone services it sells to each group as well as thecompany’s total profit. [Mark:0.75]b)Calculate the consumer and the producer surplus under price discrimination. [Mark: 0.75]c)Suppose the government forbids price discrimination. Solve again the monopolist’s profitmaximization problem and calculate the consumers and producer surplus. Is the societybetter off under uniform pricing relative to price discrimination? [Mark: 1.0][Hint: Price discrimination in (a) requires perfect separation of the two markets. That means,resale of services from one group to the other is not possible].Indicative Answera)Given𝑇𝑅= 𝑝∙ 𝑞= (100 − 𝑞)𝑞, 𝑀𝑅= 100 − 2𝑞, and given𝑇𝑅ி= 𝑝ி∙ 𝑞ி=(300 − 2𝑞ி)𝑞ி, 𝑀𝑅ி= 300 − 4𝑞ி.Given𝑇𝐶(𝑞, 𝑞ி) = 𝑞+ 𝑞ி, 𝑀𝐶= 𝑀𝐶ி= 𝑀𝐶 = 1. The monopolist will producewhere𝑀𝑅= 𝑀𝐶and𝑀𝑅ி= 𝑀𝐶ி(FOC):𝑀𝑅= 𝑀𝐶 ⟺ 100 − 2𝑞= 1 ⟺ 𝑞= 49.50
MASTER’S DEGREE PROGRAMME IN BUSINESS ADMINISTRATION2𝑀𝑅ி= 𝑀𝐶 ⟺ 300 − 4𝑞ி= 1 ⟺ 𝑞ி= 74.75Therefore,𝑝= 100 − 49.50 = 50.50and𝑝ி= 300 − 2(74.75) = 150.50. Total profitsare𝜋 = 𝑇𝑅+ 𝑇𝑅ி− 𝑇𝐶(𝑞, 𝑞ி) = 50.50(49.50) ++150.50(74.75) − (49.50 + 74.75) = 13,625.38.b)The businesses’ surplus is the area of the triangle below the demand curve𝑞and above thehorizontal line at𝑝= 50.50. The families’ surplus is the area of the triangle below thedemand curve𝑞ிand above the horizontal line at𝑝ி= 150.50. The sum of the two surplusesis the consumer surplus (CS):𝐶𝑆 = [(1 2⁄ ) ∙ (49.50) ∙ (100 − 50.50)] + [(1 2⁄ ) ∙ (74.75) ∙ (300 − 150.50)] == 1,225.12 + 5,587.56 = 6,812.68.

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