All the questions are in the filePotential Mid-Term exam questions Format : Required question in...

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All the questions are in the filePotential Mid-Term exam questions    Format : Required question in Part A. Do 1 out of 3 questions in Part B. Questions that don’t  appear on the mid-term will be potential exam questions for the final exam. Questions will  appear exactly as below except that some of the parameter values might change. Question 1: Third Degree Price Discrimination   A monopolist sells in 2 markets. There are Ni buyers in each market. Each buyer in market  i has demand given by qi = ai – pi where a1 > a2. Total Costs are given by ? = ?? + ? 2 ?2  where Q = Q1 + Q2 and where Qi = Niqi is the total output produced in market i, i = 1,2.  a) (10 marks). Monopolist cannot price discriminate.    Derive the profit function as a function of Q   Derive the FOC. Verify the SOC. Find the profit maximizing Q   Find price and output in each market    Determine if both markets are served.     Calculate profits and welfare  b) (10 marks). Monopolist can price discriminate.   Derive the profit function as a function of Q1 and Q2.   Derive the FOC. Verify the SOC.  Find the profit maximizing Q1 and Q2    Find the price in each market.   Calculate profits and welfare   Is price discrimination profitable? Does it raise welfare? Parameter values: N1 = 12, N2 = 12, a1 = 30, a2 = 24, c = 12 and ? = 1 6  Fall 2021  EC620 Potential Mid-term Exam Questions Page | 2    Question 2: Linear and Non-linear pricing.  A monopolist sells to 2 buyer types labelled 1 and 2. Buyer 2 is the high demand buyer.  There are Ni buyers of type i. Buyer type i has demand given by qi = ai – bip. Costs are  given by C = cQ where Q = N1q1 + N2q2 The monopolist cannot price discriminate and  either uses linear pricing or is able to use tie-ins to offer nonlinear pricing. In each case  the parameters of the model are such that the monopolist serves both buyer types.  a) (5 marks). Linear pricing (p).   i.  Derive the profit function as a function of p  ii.  Derive the FOC (i.e.  ?? ?? = 0) and solve for p. Find q1 and q2. Verify the SOC.    b) (5 marks) Single two part tariff (p,F).   i. Derive the profit function as a function of p.   ii. Derive the FOC (i.e.  ?? ?? = 0) and solve for p. Find q1 and q2. Verify the SOC.  iii.  Compare the FOC in a) and b) to explain why p in b) is higher or lower than in a).  c) (5 marks) Two part tariff menu Contract 1: (p1, F1) and Contract 2: (p2, F2).   i. Find p2 and q2. Derive the profit function as a function of p1.   ii. Derive the FOC (i.e.  ?? ??1 = 0) and solve for p1. Find q1. Verify the SOC.  iii.  Compare the FOC in b) and c) to explain why p1 in c) is higher or lower than p in b).  d) (5 marks) Block pricing menu: Contract 1 (q1, F1) and Contract 2 (q2, F2).   i. Find q2. Derive the profit function as a function of q1.   ii. Derive the FOC (i.e.  ?? ??1 = 0) and solve for q1. Verify the SOC.  iii.  Compare the FOC in c) and d) to explain why q1 in d) is higher or lower than q1 in c).  Parameter values: a1 = a2 = 60, c = 16, b1 = 1.5, b2 = 1, N1 = N2 = N Fall 2021  EC620 Potential Mid-term Exam Questions Page | 3    Question 3: Cournot and innovation  There are n firms who produce identical products at constant marginal cost and engage  in Cournot competition. Firms who innovate pay a fixed amount F to reduce marginal  cost from c to c – x > 0. Non-innovator marginal cost equals c. Inverted market demand is  given by P = a – Q where a > c. There are m innovators and n − m non-innovators.   a) (5 marks) Cournot equilibrium   Solve for the Cournot equilibrium outputs and profits as functions of a, c, x, n, m   Now let parameter values be a = 120, c = 60    b) (10 marks) Innovation and market structure   If n = 3 and m = 1 is the initial market structure then derive an expression for a  firm’s incentive to innovate as a function of x.    If n = 4 and m = 1 then repeat the above   Determine the values of ? for which an increase in n from 3 to 4 causes the  incentive to innovate to increase.  c) (5 marks). Innovation and Welfare.    If n = 3, m = 1 is the initial market structure and x = 24 then determine the values  of F for which innovation (i) is profitable (ii) raises welfare.   Does profitable innovation raises welfare? Fall 2021  EC620 Potential Mid-term Exam Questions Page | 4    Question 4: Capacity constrained Bertrand  Consider a capacity constrained Bertrand model consisting of n = 3 firms. Each firm has  marginal cost of c = 60 and faces inverted demand given by P = 120 – Q. For each set of  capacities and prices determine whether each firm’s price is a best response. a) (10 marks). k1 = 30, k2 = 10 and k3 = 10.  i.  p1 = 80  p2 = 70  p3 = 70  ii. p1 = 70  p2 = 80  p3 = 80  b) (10 marks). k1 = 15, k2 = 15 and k3 = 15.  i.  p1 = 75  p2 = 75  p3 = 75  ii. p1 = 80  p2 = 80  p3 = 85  [Note: In the exam any of the numbers indicated above could change]    Fall 2021  EC620 Potential Mid-term Exam Questions Page | 5    Question 5: Stackelberg and Limit Pricing  Consider the Limit pricing and Stackelberg models in which the incumbent chooses  capacity first and then the entrant chooses whether or not to enter. The portion of  incumbent’s marginal cost that is sunk after the incumbent’s capacity choice is given by s.  Inverted demand is given by P = a – Q, where ‘a’ is the market size parameter. Marginal  cost is constant and equal to c and fixed costs are F for both entrant and incumbent. a) (10 marks). Limit pricing.  (i) Solve for the incumbent’s entry deterring level of output,  limit price and profits as a function of ‘a’. (ii) Find the levels of ‘a’ for which entry is  blockaded. (iii) Find the levels of ‘a’ for which limit pricing is ‘credible’. b) (10 marks) Stackelberg. (i) Solve for the incumbent’s Stackelberg level of output and  profits as a function of ‘a’. (ii) Find the values of ‘a’ for which Stackelberg is credible. (iii)  Pick a value of ‘a’ for which entry is not blockaded and limit pricing and Stackelberg are  both credible and determine whether Stackelberg or limit pricing is more profitable.   Parameter values s = .9, c = 300, F = 400 Fall 2021  EC620 Potential Mid-term Exam Questions Page | 6    Question 6: Oligopoly, welfare and entry   A conjectural variation oligopoly market consists of n identical firms. Firm I’s total cost  function is given by ?? = ??? + ??? 2 + ?. Inverted market demand is given by ? = ? − ? ?   where S = market size.  Each firm’s conjectural variation is denoted ? = ??−? ???  where the  range of v is given by −1 ≤ v ≤ n − 1 a) (5 marks). Solve for the conjectural variation equilibrium output per firm. b) (10 marks). Determine the comparative static effects of entry (n) on (i) output per firm  (ii) industry output (iii) profits per firm (iv) industry profits (v) consumer surplus. c) (5 marks). Determine if profitable entry raises welfare (i.e. Does  > 0 imply  ?? ?? > 0? ). Fall 2021  EC620 Potential Mid-term Exam Questions Page | 7    Question 7: Exclusive dealing contracts with uncertain entry    Market structure    1 incumbent, 1 entrant   Demand     1 buyer, Buyer buys one unit   Willingness to pay, v  Competition with no contract  Bertrand (price matching favours entrant)  Incumbent cost    c  Entrant cost    cL = c – x with probability p   cH = c + x with probability 1 – p where 0

Soma · Accepted Answer

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b) Price discriminating monopolist: 
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Question: 3

Potential Mid-Term exam questions Format : Required question in Part A. Do 1 out of 3 questions in Part B. Questions that don’t appear on the mid-term will be potential exam questions for the final...

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