EC3260 Industrial Economics 2: Strategy & Planning Summer Examinations 2020/21
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EC3260
Summer Examinations 2020/21
Industrial Economics 2: Strategy & Planning
Section A: Answer BOTH questions
If the buyer or seller switches to the new platform without the other then they pay the access price but cannot use the platform. The payoffs are given below:
Seller
|
|
Old Platform |
New Platform |
|
Old Platform |
10, 30 |
0, −pS |
|
New Platform |
−pB , 0 |
s |
Assume that the new platform suffers from ‘unfavourable beliefs’ in the following sense: each player believes the other will stay on the old platform unless it is a weakly dominant strategy for them to switch to the new platform.
(a) Solve for the optimal divide-and-conquer pricing strategy for the new platform. (7 marks)
(b) Suppose that investment in quality level x ≥ 0 costs the new platform cx2 . If the
platform can pick their investment level before their prices then what level x do they pick? (7 marks)
Now suppose that the new platform can show advertising to anyone who uses their platform. The platform must pick levels of advertising QB ≥ 0 and QS ≥ 0 to show each user. Advertising is annoying to the users of the platform so there is a ‘cost’ imposed on them of FQ for Q units of advertising.
The platform benefits from advertising by increasing their revenues. Advertising gives revenue aQ per user for Q units of advertising, but only if both parties actually use the platform to trade. Assume in what follows that a > 0 and F > 0.
(c) Fix the prices from part (a) and find the levels of advertising (QB and QS ) that are optimally set by the new platform. (5 marks)
(d) What is the level of quality (x ) provided? (5 marks)
2. A producer uses two stores to sell its unique product. The stores are located at each end of a street that is 1 mile long. Store 1 is located at the left end of the street and Store 2 at the right end. Buyers are uniformly distributed along the street and have a valuation of £8 for a unit of the product. Buyers incur a cost of £1 per mile for transportation. Neither the stores nor the producer have any costs and the stores choose prices simultaneously.
(a) Suppose that the producer needs to choose between the following two contracts that will be offered to the stores:
(i) The producer will receive 25 percent of the store’s revenue.
(ii) The store will pay the producer £0.50 for each unit it sells.
Assuming that neither of the stores will accept a contract that leaves it with a negative profit, which of the two contracts will the producer offer? (9 marks)
(b) How would your answer to part (a) above change if, in each of the two contracts above, the producer could also set a fixed lump sum to charge the stores? (7 marks)
(c) How would your answer to part (a) above change if in each of the two contracts above, the producer could also set a minimum price to consumers? (7 marks)
(d) How would your answer to part (a) above change if the two stores do not compete with each other but rather both belong to a profit-maximizing owner? (7 marks)
Section B: Answer ONE question
3. A new hotel opens in a town. Their quality is either sH = 3 or sL = 1 but neither buyers nor the hotel can observe the experienced quality before purchase.
There are N holiday makers who visit this town once per year and must stay at either the new hotel or an established hotel. If a holiday maker i stays at the new hotel they receive a payoff of ui = ei + s − p where ei ~U[0, 1] is the buyer’s type and s is the quality. Assume the public hold the view that E[s] ≥ 2 for the new hotel.
If the visitors stay in the established hotel their total utility after paying the price is 2.
(a) Find the expected demand for rooms at the new hotel as a function of the price per
room p, E[s] and the number of holiday makers N. (6 marks)
(b) Find the new hotel’s optimal price per room p* and their expected profit if all costs
are zero. (6 marks)
A reviewer writes a review of the new hotel before it opens for the season. They can give it either a good review (r = g) or a bad review (r = b). The reviewer always recognises a bad hotel and gives it a bad review but with probability e = 1/2 they give a bad review to a good hotel.
(c) Let the prior be Pr[s = sH] = 入 = 2/3. Find the expected quality after a good review and after a bad review. (8 marks)
(d) Allow the new hotel to alter their price after the review.
(i) Which prices would they pick in each case? (2 marks)
(ii) Would the hotel be better off if they made all the buyers book rooms before
the review is released? (8 marks)
(e) Would having multiple reviewers be beneficial to the hotels or buyers? Discuss with
reference to material throughout the module. (10 marks)
4. This question has two parts, please answer both parts.
Part A
Two firms produce vertically differentiated products. The demand that firm 1 faces is given by: q1 = 
and the demand that firm 2 faces is given by: q2 = 1 + 
, where pi is the price set by firm i (given in $s) and qi is the quantity demanded from firm i.
Please answer the following questions:
(a) Which product has the higher quality? (3 marks)
(b) Calculate the (Nash) equilibrium prices, quantities and profits. (6 marks)
Suppose now that firm 1 can change the quality of its product so that the demand for the products is given by: q1 = 
and q2 = 1 + 
.
Please answer the following questions:
(c) Does such a change represent an increase or a decrease in the quality of firm 1’s product? (3 marks)
(d) Should firm 1 make the change? (3 marks)
(e) Assume instead that it is firm 2 that can change the quality of its product so that the
demand for the products will look like those given in part b. above. Should firm 2 make the change? (3 marks)
(f) Assume now that the two demand functions are given by q1 = 
and q2 = 1 +
, where s2 is the quality of firm 2’s product. Assume that before the firms choose their prices, firm 2 can choose the quality of its product by making a lump
(s2)2
18
the level of quality that firm 2 will choose? What will be the profit of each firm in this case? (10 marks)
Part B
A firm operates in a market for infinitely many periods. The firm’s discount factor is δ, where 0 < δ < 1. In each period, the firm chooses the quality of its product, which can be either high (H) or low (L). The firm’s cost of providing a high-quality product is CH and providing a low-quality product is CL . In every period, consumers decide whether or not to purchase the product. A consumer’s willingness to pay for a high-quality product is VH and her willingness to pay for a low-quality product is 0. Assume that:
VH > CH > CL > 0.
Also assume that in each period, after the firm has chosen the quality of the product but before consumers decide whether or not to purchase it, there is a probability α, 0 < α < 1, that the quality of the product will become known at the beginning of the period. If, however, the quality does not become known at the beginning of the period, it becomes known at the end of the period with certainty to all future consumers.
Assume that consumers adopt a “boycott” strategy according to which once they learn that the firm’s product is low, they never buy the firm’s product in subsequent periods.
(a) Under what conditions will the firm choose to produce a high-quality product in
every period? (8 marks)
(b) Suppose that the firm can invest in a technology that will make it impossible for
consumers to observe the quality of the product before the end of the period. That is, by making the investment, α will be reduced to 0. Should the firm make the investment? (4 marks)
2023-06-02