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Consider the horizontal differentiation model of "Linear City" the consumers are uniformly distributed on the segment [0.1]. . 1/2 Consumers have a transport cost td where d is the distance traveled. 1/2 All consumers have a valuation s. 1/2 The marginal cost of producing the good is c. 1/2 The fixed cost to open a store is f for every location.a) How high would have to be s for a monopolist located at 1/2 decided to put a price at which all consumers are served? 1/2 (All decide to eat). 1/2

b) If F =t/2 and the monopolist must decide between one or two locations, how many locations would it choose? 1/2 What will be its profit? 1/2

c) How many locations would choose a social planner if F =t/2? 1/2(Suppose the social planner sets p = c) 1/2

d) Given the same fixed cost of F =t/2, if the government decides to auction a license to exploit the monopoly market how much would be willing to pay a maximum of a company by that license? 1/2

Consider a model of vertical differentiation where two firms offer goods with qualities v1 = 1 and v2 = 2, both produced at zero cost. There is a continuum of consumers that value a good of quality v as: s + xiv where xi (the marginal valuation of quality) is uniformly distributed along[1, 2].

a) What are the equilibrium prices for v1 = 1 and v2 = 2?

b) If firms choose their quality levels simultaneously (v1,v2) {1, 2}, before competition in prices take place, what would be the levels of (v1,v2)? Why?

Consider the following system of inverse demand functions: pA = 120 4qA 2qB and pB = 120 4qB 2qA. Assume that firms A and B do not bear any production costs (that is, cA = cB = 0). Solve the following problems:

a) Suppose the firms compete in quantities, where firm A sets qA and firm B sets qB, simultaneously. Formulate the profit function of each firm as a function of the quantity supplied by both firms. Formally, write down and spell out the exact equations of each firm's maximization problem.

b) Solve for the firms' quantity best-response functions qA = RA(qB) and qB = RB(qA). Plot both best-response functions where you denote the vertical axis by qA and the horizontal axis by qB. Indicate whether these best-response functions are upward or downward sloping.

c) Solve for the Nash equilibrium quantity levels, qA and qB, the corresponding prices, pA and pB,as well as the equilibrium profit levels, A and B

2. Solve for the two direct demand functions from the system given in exercise 1 of two inverse demand functions. Formally, compute the parameters a, b, and c of the direct demand functions qA = a bpA + cpB and qB = a bpB + cpA, which are consistent with the above-given inverse demand functions.

a) Suppose now that the firms compete in prices, where firm A sets pA and firm B sets pB,simultaneously. Formulate the profit function of each firm as a function of both prices. Formally, write down and spell out the exact equations of each firm's maximization problem.

b) Solve for the firms' price best-response functions pA = RA(pB) and pB = RB(pA) . Plot both best-response functions where you denote the vertical axis by pA and the horizontal axis by pB. Indicate whether these best-response functions are upward or downward sloping. c) Solve for the Nash equilibrium prices, pA and pB, the corresponding quantities, qA and qB, as well as the equilibrium profit levels, A and B .

Compare with Nash equilibrium of the quantity game to the Nash equilibrium of theprice game with respect to the quantity produced, prices, and profit levels. Explain these differences.

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