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Department of Economics Trent University ECON3400H - Managerial Economics Winter Semester, 2017 Peterborough Campus Assignment #2 Due at Final Exam...


15 marks) Consider an oligopolistic market with ???? identical firms. Inverse market demand is given by ???? = ???? − ???????? where ???? and ???? are market price and output, respectively. Total cost for each firm is given by ???????? = ???????? where ???? is firm-level output.

Verify that marginal revenue is given by ???????? = ???? − ????(2???????? + ∑????????≠????), where ???????? is output of firm ???? and ∑ ????????≠???? is the sum of all other firms’ output ????????≠????.

Recognizing the symmetric nature of the equilibrium, derive the expression for the Cournot equilibrium output ???????????? for firm ???? as a function of the model’s parameters ????,

????, ???? and ????.

Verify that the Cournot equilibrium market output ???????? approaches the competitive

level ????∗ as the number of firms grows without bound. 

Department of Economics Trent University ECON3400H – Managerial Economics Winter Semester, 2017 Peterborough Campus Assignment #2 Due at Final Exam on April 18, 2017 Instructions : This assignment has 6 questions worth a total of 100 marks, and is worth 15% of the course grade. The marks for each question are as indicated, and are evenly divided among the components of a question. Answers to the assignment must be legible, concise and submitted in hard copy at the beginning of the exam. While students may work together on the assignment, they must develop, write up and submit answers independently. Questions: 1. (15 marks) Consider pricing with market power: a. Briefly define price discrimination and state the four conditions for it to be viable. b. A monopolist is considering a choice between two alternative pricing strategies: (i) perfect price discrimination and (ii) two-part pricing. Assume both strategies are feasible and the demand side of the market comprises identical consumers. Determine which of the two strategies will earn the monopolist the greater amount of profit. For each strategy, determine the share of consumer surplus the monopoly is able to extract as profit. c. A cable utility is considering various pricing strategies over the provision of internet and TV services. The table below summarizes the reservations prices ($/month) for these services by type of customer: Customer Type Internet TV Bundle Millennial $80 $0 $80 Standard $80 $70 $150 Traditional $50 $70 $120 The utility cannot observe customer type and the marginal cost of serving an additional consumer with either service is zero. From the utility’s perspective, rank the following pricing strategies by determining the associated revenue-maximizing prices: (i) separate pricing, (ii) pure bundling and (iii) mixed bundling.
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2. (15 marks) Consider an oligopolistic market with ° identical firms. Inverse market demand is given by ? = ± − ?² where ? and ² are market price and output, respectively. Total cost for each firm is given by ³´ = ?µ where µ is firm-level output. a. Verify that marginal revenue is given by ¶· = ± − ?(2µ ¸ + ∑µ ¹≠¸ ) , where µ ¸ is output of firm º and ∑ µ ¹≠¸ is the sum of all other firms’ output µ ¹≠¸ . b. Recognizing the symmetric nature of the equilibrium, derive the expression for the Cournot equilibrium output µ ¸ » for firm º as a function of the model’s parameters ± , ? , ? and ° . c. Verify that the Cournot equilibrium market output ² » approaches the competitive level ² as the number of firms grows without bound. 3. (20 marks) Consider a town of ° homes for which annual fire loss is independently and identically distributed according to a probability distribution where the expected value is ¼ percent of the home’s value. Each homeowner is risk-averse and has a risk premium of ½ percent of his or her home’s value in respect of the risk of fire. Recognizing this, the homeowners decide to pool their risk by forming a non-profit mutual insurance cooperative to which each homeowner contributes an annual insurance premium ? (measured in dollars) in exchange for full fire insurance, according to the value of his or her home. For simplicity, assume the cooperative has no explicit costs other than insurance claims. a. Briefly define the term “risk premium”. b. Since the cooperative comprises risk-averse members, it too is risk-averse. For each home, the cooperative has a risk premium of ½ ¾ percent of the home’s value, which is an implicit cost. Based on the Law of Large Numbers, briefly argue that ½ ¾ < ½ and that ½ ¾ → 0 as ° → ∞ . That is, argue that the cooperative faces less risk than an individual member, and that this risk approaches zero as the number of members grows without bound. c. For a homeowner with a home valued at ¿ (measured in dollars), express the annual insurance premium ? as function of ¼ , ½ ¾ , and ¿ . Is this an actuarially fair premium? d. Supposing ¼ = 0.20% and ½ ¾ = 0.05 %, determine the value of ? paid by a homeowner with a home worth ¿ = $600,000 . 4. (15 marks) Consider the problems arising from asymmetric information: a. Define the following terms: (i) adverse selection, (ii) moral hazard, (iii) screening, (iv) signaling, (v) principal-agent problem and (vi) efficient contract. b. Consider government-provided health insurance, such as OHIP in Ontario, and government-mandated insurance, such as Obamacare in the United States. Are such programs intended to combat adverse selection or moral hazard? Briefly characterize the tradeoff between adverse selection and moral hazard in respect of health insurance public policy.
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