PLEASE USE WORD, OR AN APPROPRIATE WORD PROCESSING
PACKAGE WHICH CAN HANDLE MATHEMATICAL EXPRESSIONS.
FINAL SUBMISSIONS MUST BE MADE IN PDF FORMAT.
EQUATIONS MUST BE ENTERED CORRECTLY WITH PROPER
USE OF MATHEMATICAL NOTATION USING, FOR EXAMPLE,
EQUATION EDITOR IN WORD
QUESTION
Assume that two Örms, say Örm 1 and Örm 2, sell di§erentiated goods and
face the following demand functions:
q1 = 1
4
3
p1 +
2
3
p2 and q2 =
4
3
a +
2
3
p1
4
3
p2
where a > 1: In addition assume that Örms target own proÖt maximisation,
compete (simultaneously) in quantities and have marginal costs equal to c1 =
c2 = c. Assume that 1 > c 0. Describing the necessary mathematical steps
and providing the related economic intuition,
1. Önd and describe the inverse demands faced by the two Örms (HINT: solve
the two demands simultaneously with respect to prices)[15 marks]
2. derive and describe each Örmís best response function. Are quantities
strategic substitutes or complements? [25 marks]
3. derive and describe the equilibrium quantities [30 marks]
4. explain the economic intuition behind parameter a. What happens to
the equilibrium quantities and proÖts if a increases? Provide economic
intuition. [30 marks]
1NOTES:
Your discussion MUST include appropriate mathematical demonstrations
and arguments that justify your conclusions.
If there is no discussion of your answer (mathematical or otherwise), you
will get ZERO.
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