Industrial Economics

Industrial Economics (01OJAPH)

September 17, 2015

ISTRUCTIONS

Available time: 2 hours.

If the text is not clear enough, explicitly illustrate the assumptions that you are introducing.

Neatly present the analytical results; the qualitative discussion needs to be brief, clear and to the point.

Solve the exercises 1/2 and the exercises 3/4 on separate sheets. Please, put your name on every sheet.

Exercise 1

Solve the equilibrium in an oligopoly à la Cournot with N firms and inverse demand p = 1 – Q with Q = Σ i=1…N qi . The total production costs are symmetric and equal to C(q) = c q2.

Discuss the trend of the consumer surplus as a function of N.

Solution outline

The profit of the j-th firm is πj = qj (1 – Q) – c qj2.

The FOC is ∂πj/∂qj = 1 – Σ i=1…N, i≠j qi – 2 qj – 2 c qj = 0.

Invoking symmetry, the quantity at the equilibrium will be q* = 1/(1+N+2c), and consequently p* = (1+2c)/(1+N+2c) and π* = (1+c)/(1+N+2c)2.

Since the price is reduced when N increases, the consumer surplus must correspondingly increase. This result could be obtained with no calculation considering that the consumer surplus increases with N in the case of linear costs, and this must be true for a still stronger reason in case of decreasing scale returns, as in the case of our exercise.

The consumer surplus is anyway (1–p*) Q*/2 = Q*2/2 = N2/[2(1+N+2c)2], actually increasing with N.

Exercise 2

Consider a ‘traditional’ Hotelling pricing game: two firms (A and B) are located at the extremes of a linear city of unit length; the consumer mass is normalized to 1; consumers are uniformly distributed and their reserve utility is equal to 1. Production costs are assumed to be null and the firms fix their prices (pA and pB) simultaneously. Transport costs c (x) (i.e., the cost for travelling a distance x), however, are equal to t1 if x < ½ and to t2 if x ≥ ½ (where t2 < 1 and t2 – t1 = Δt > 0.

1. Individuate the position of the indifferent consumer as a function of pA and pB and verify the market coverage (i.e., verify who is ready to consume given a given couple of prices).
2. Verify whether pA = pB = 1 – t1 is a Nash equilibrium.

Solution outline

1. If pA = pB ≤ 1 – t2 the indifferent consumer is located in x = ½ and the market is covered.

If 1 – t1 ≥ pA = pB > 1 – t2, the consumers located in x < ½ purchase from A, the consumers located in x > ½ purchase from B, the consumer located in x = ½ is not willing to consume.

If pA = pB > 1 – t1 no one will consume.

If pA < pB and pB – pA ≤ Δt the consumers located in x < ½ purchase from A, the consumers located in x > ½ purchase from B as long as pA, pB ≤ 1 – t1. The consumer located in x = ½ purchases (from A) only if pA ≤ 1 – t2. Otherwise he will not consume.

If pA < pB and pB – pA > Δt every consumer prefers A with respect to B; those positioned in x < ½ will actually consume if pA ≤ 1 – t1; those positioned in x ≥ ½ will actually consume if pA ≤ 1 – t2, otherwise they will not consume.

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