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EC3260

Summer Examinations 2019/20

Industrial Economics 2: Strategy & Planning

Section A: Answer BOTH questions

1. A monopolist smartphone manufacturer faces ܰ potential buyers with utility function

ݑ ௜ ݌ − ݏ ௜ ߠ =

Where ݏ is the observable quality, ݌ is the price and ߠ௜∈ {ߠ ௅ , ߠ ு } is the buyer’s type. Assume that ߠு> 2ߠ ௅ > 2 and that buyers are equally likely to be ߠு or ߠ௅.

The company are considering a premium and a budget version of their new smartphone. The premium version has cost per unit of ܿு= 1 and quality ݏு> 0. The budget version has cost per unit of ܿ௅= 0 and quality ݏ௅, where 0 ≤ ݏ ௅ ≤ ݏ ு .

(a) If the monopolist only releases the premium version then what is their optimal price and profit? (5 marks)

(b) Suppose the monopolist wants the high type buyers to purchase the premium version and the low type buyers to purchase the budget version. What prices would they optimally pick for each version? (5 marks)EC3260

Suppose now that the value of ݏு and ݏ௅ can be chosen by the manufacturer. This incurs a cost per unit of ݏு ଶ for the premium version and ݏ௅ଶ for the budget version (in addition to the previous marginal cost of production).

(c) Fix prices as in part (b) and answer the following questions:

i. What are the values of ݏு and ݏ௅ chosen by manufacturer? (7 marks)

ii. Is the socially optimal level of ݏு and ݏ௅ chosen? Why/why not? (8 marks)

iii. How do your answers to (i) and (ii) change if ߠ௅< ߠ ு < 2ߠ ௅ ? (5 marks)

2. Two differentiated goods, apples and bananas, are sold at the extremes of a linear product space of length 1. Consumers are uniformly distributed along this interval [0,1]. Firm ܻ is an apple monopoly (located at ݔ= 0) but no one is producing bananas (located at ݔ= 1).

The utility of a consumer located at ݔ∈ [0,1] is ݏ̅ − ݐ ݔ ଶ − ݌ ஺ if they consume an apple, ( ݔ − 1) ݐ −̅ ݏ and ଶ− ݌ ஻ if they consume a banana. Only one good can be consumed and a buyer’s payoff is 0 if they don’t consume.

The price of an apple is ݌஺ and the price of a banana is ݌஻. The marginal cost of each good is ܿ. There is no fixed cost.

(a) Suppose firms ܻ and ܼ both enter the banana market. Assume ݐ> 0 and find:

i. The demands for each firm (3 marks)

ii. The best responses for each firm. (3 marks)

iii. The symmetric equilibrium prices. (2 marks)

(b) Assume that Firm ܼ will only enter the banana market if they expect to eventually earn a strictly positive profit. Would Firm ܻ choose to deter entry by Firm ܼ to the banana market by also selling at ݔ= 1? (7 marks)

(c) Suppose Firm ܻ incurred large exit costs from leaving the banana market. Would this affect either Firm ܼ’s decision to enter or Firm ܻ’s decision to deter entry in the first place? (5 marks)

(d) Now assume that Firm ܼ’s marginal cost of producing bananas is ݇> ܿ . Also assume that ܿ= 0, ݇= 2 and ݐ= 4.

Could Firm ܻ deter entry by Firm ܼ and would they optimally choose to do so? (Hint: What would be the new demands, prices and profits?) (10 marks)

Section B: Answer ONE question

Please use a separate booklet

3. Recall the model of herding from Lecture 2. A sequence of buyers arrives at a seller and must decide whether to purchase or not. The price is ݌= 1 and utility from buying is equal to ݑ= ݏ − ݌ where ݏ∈ {0,2} is the unknown quality of the seller. Sellers are equally likely to be ݏ= 0 or ݏ= 2 ex-ante. If buyers do not purchase then their reservation utility is 0.

A new buyer arrives at each period ݐ∈ {1,2,3, … } and observes a private signal (ߪ ௧ ) of the seller’s quality. If ݏ= 2 then ߪ௧= 2 with probability ߙ> 1/2 and ߪ௧= 0 with probability (1 − ߙ ). If ݏ= 0 then ߪ௧= 0 with probability ߙ> 1/2 and ߪ௧= 2 with probability (1 − ߙ ).

In addition to the private signal, buyers also observe a public signal which is the purchasing decisions of all previous buyers.

(a) Derive the posterior beliefs of a buyer at period ݐ= 1 if they receive either a ߪଵ= 2 signal or a ߪଵ= 0 signal. (7 marks)

(b) What is ‘herding’ and how can it occur in this model at ݐ= 3? (7 marks)

(c) Is herding always detrimental for a buyer at period ݐ= 3? Explain why/why not. (10 marks)

(d) Comment on how the following changes might alter the outcome of the herding model.

i. An increase in the accuracy (ߙ ) of the private signal. (4 marks)

ii. Public aggregation of all private signals (e.g. all buyers publicly discussing private opinions about a movie before it is released). (4 marks)

iii. If sellers could alter their price in response to changes in the public signal. (4 marks)

iv. If there are some ‘stubborn’ buyers who only look at their private signal and ignore the public signal when purchasing. (4 marks)

4. Answer the following:

(a) Time inconsistent preferences may lead consumers to sub-optimal choices. Discuss. (10 marks)

(b) Describe how sophistication and naiveté affect firms’ profit-maximising contract design. (20 marks)

(c) Based on your answer in (b), what will be the welfare implications of the designed contracts for sophisticated and naive users? (10 marks)