Find and describe the inverse demand functions

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Business Economics Questions

ANSWER BOTH QUESTIONS.

QUESTION 1 - Assume that two firms, say firm 1 and firm 2, sell differentiated 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 firms target own profit 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. Find and describe the inverse demand functions faced by the two firms (HINT: solve the two demands simultaneously with respect to prices)

2. Derive and describe each firm's best response function.

3. Derive and describe the equilibrium quantities. What happens to the equilibrium quantities if a increases? Provide economic intuition.

QUESTION 2 - Consider a market where consumers are uniformly distributed on a line of length equal to 1. The market is served by two firms, say firm 1 and firm 2, that sell a good differentiated in terms of quality and location. Firms are located at the extremes of the segment; specifically, firm 1 is located at point x₁ = 0 and firm 2 is located at point x₂ = 1. To purchase the good consumers incur linear transportation costs. In particular, a consumer located at point x on the segment who wants to reach a firm located at x_i, i = 1; 2; will bear transportation cost t|x - x_i|, where t > 0 is a parameter representing the transportation cost per unit of distance. The utilitility of the generic consumer located at point x and buying from firm i is:

U_i (x) = v + q_i - p_i - t|x - x_i|

where v > 0 is the products intrinsic utility and q_i is the quality of good i. Firms select simultaneously prices pi to maximise own profits. Describing the necessary mathematical steps and providing the related economic intuition,

1. Find and describe the location of the marginal consumer who is indifferent to buying from either firm.

2. Assume now that q₁ = 0 and q₂ = q. Find and describe the prices in equilibrium.

3. Assume that q₁ = q₂ = q. Find and describe the prices in equilibrium.

Reference no: EM131715586

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len1715586

11/10/2017 2:53:51 AM

NOTES: 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. SUSPECTED PLAGIARISM WILL BE INVESTIGATED AND, IF PROVEN, WILL RESULT IN DISCIPLINARY ACTION (Do not submit someone else’s work as your own; do not copy someone else’s work without attribution; do not "cut and paste" from lecture slides and/or any other source.) If NOT submitted in PDF format, your will NOT be marked.

11/10/2017 2:53:43 AM

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.

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