Final Exam, Econ 6006 Market Structure & Strategic Behaviour

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Final Exam, Econ 6006 Market Structure & Strategic Behaviour

2011 Semester 2

Question 1. [40 Points] Price Discrimination

A nightclub manager realizes that demand for drinks is more elastic among students, and is trying to determine the optimal pricing schedule. Specifically, he estimates the following average demands:

•  Under 25 (students):              qs = 18 − 5p

•  Over 25 (non-students):        qn = 10 − 2p

The two age groups visit the nightclub in equal numbers on average. Assume that drinks cost the nightclub $2 each.

(a) [ 10 Points] If the market cannot be segmented, what is the uniform monopoly price?

(b) [ 10 Points] If the nightclub can charge according to whether or not the customer is a student but is limited to linear pricing, what price (per drink) should be set for each group?

(c) [ 10 Points] If the nightclub can set a separate cover charge and price per drink for each group, what two-part pricing schemes should it choose?

(d)  [ 10 Points] Now suppose that it is impossible to distinguish between types. If the nightclub lowered drink prices to $2 and still wanted to attract both types of consumer, what cover charge would it set?

Question 2. [30 Points] Product Differentiation and Merger

Aike (Brand A) and Beebok (Brand B) are the leading brand names of sports shoes. The direct demand functions facing each producer are given by

qA(pA; pB) = 180 - 2pA + pB and qB(pA; pB) = 120 - 2pB + pA :

Note: The demand functions are not symmetric. To make it simple, assume zero production cost (cA = cB = 0) and solve the following problems.

(a)  [ 15  Points]  Solve  for  the  Nash-Bertrand  equilibrium  prices,  (pAb ;  pBb).  Then,  compute  the equilibrium output levels (qAb ; qBb), the equilibrium profits (πAb ; πBb), and aggregate industry profit πAb + πBb .

(b) [ 15 Points] Suppose now that the two firms merge while the demands remain the same as before. However, they decide to keep selling the two brands separately and charge, possibly, different prices. Compute the prices (pAm ; pBm) which maximize joint profit πm . Then, compute aggregate profit and compare it to the aggregate industry profit made under Bertrand competition which you have already computed under separate ownership.

Question 3. [30 Points] How Sweet it will be?

Food Inc is a soda manufacturer. The customers who buy Food soda have different tastes y for sugar content, with y ranging from 0 to 1. For each y, there is an equal density of customers with taste y (so we normalize the population of consumers to 1). If y is the customer’s most preferred sugar content, and the drink has sugar content x, then customer y is willing to pay 1 − 0.4 |y − x| for the can of soda. The marginal cost of producing one can of soda of any sugar content is equal to c = 0. 1. Assume that the manufacturer always serves all the market.

(a) [ 15 Points] Suppose you are the CEO of Food Inc, and decide to manufacture just one type of soda, the Thirstbuster. What sugar content x will you select? What price per can will you  set? Assume that the fixed cost of introducing this product has been already paid in full. What is the profit?

(b) [ 15 Points] Suppose that your product manager proposes a complete product line overhaul. In particular, his plan is to eliminate the Thirstbuster altogether and to offer two new types of soda instead: Thirstbuster-lite and Thirstbuster-sweet. Each product type will cost F = 0.04 to introduce. What must be the sugar contents of the new products and their prices in order to maximize profit? Is this project going to raise the profits and, if so, by how much (compared to the profit you get from (a))?


2023-06-15