Question

(QUESTION 1)

Assume two firms that produce complementary components, X and Y.

The components are always consumed in a fixed proportion, i.e. for every

unit of X, two units of Y are required. The respective prices are Px and Py.

Consequently, the package price is Pp = Px + 2Py. Assume that the demand

function for the package is, Q = a – Pp, with a > 0 and where Q = X = Y/2.

(i) Suppose that the X and Y firms are independent. Find the Nash-Bertrand equilibrium in prices,

the quantity produced of each component and their profits.

(ii) Assume now that the firms merge. Calculate the monopoly equilibrium prices, quantities and the monopoly profit.

(iii) Compare finally the package prices and profits of the firms before and after the merger and argue if the merger

improved the welfare of society or not.

(QUESTION 2)

Assume a “Hotelling” line of a distance

l = 1

. There are two companies

A and B, both of them being located at a longer distance. Company A is placed

closer to the end of the line, while company B is placed further away. The

distance from the beginning of the line to company A is a (

a > l

) and to B is b (

b

> a > l

). Assume also that an indifferent consumer is located close to the

beginning and the distances to A and B are, x and y respectively, where y = x +

b – a. Assume quadratic transportation costs, i.e. cx2

and cy2, and prices PA and PB Find the equilibrium prices and the condition under which both firms will

have positive sales. (Hint: Assume that the quantity demanded of firm A is qA = a – x). (difficult!)

Answer 1

The answer to Question 1 is given below:

i) part

ii)part

iii)part

For any queries, please comment.

thanks