QUESTION 25

1. Consider aCournotoligopoly with two firms, where the demand curves are given by

P1 = 100 -Q - 2Q2

P2 = 100 - 2Q1 - Q2

and that costs are given byTC (Q1) = Q²₁ MC₁ = 2Q₁, TC

(Q₂) = Q²₂ and MC₂ = 2Q₂

Also, marginal revenues can be written asMR₁ = 100 - 2Q₁ - 2Q₂, MR₂ = 100 - 2Q₁ - 2Q₂.

Now, suppose that a marketing company approaches firm 1 and tells them that they can help them differentiate their product, so that instead of firm 2 affecting their demand curve in the manner described by the equation inP₁above, they guarantee that firm 1's demand equation after marketing will be of the form

P1 = 100 - Q1 - beta Q₂

where betais estimated to lie somewhere between 0 and 1. In this case, firm 1's marginal revenue function would be

MR₁ = 100 - 2Q₁ - betaQ₂

Without any further information, and knowing only that betawill fall somewhere between 0 and 1, what is themaximum amount firm 1 should be prepared to pay for these marketing services? (There is an exact answer to this question, which I hope for you to arrive at. But in order to avoid decimal/rounding error, please choose the range within which the correct answer falls).

a. Between $650-700.

b. Between $350-400.

c. Between $250-300.

d. Between $1000-1500.

Without any further information, and knowing only that betawill fall somewhere between 0 and 1, what is theminimum amount firm 1 should be prepared to pay for these marketing services? (There is an exact answer to this question, which I hope for you to arrive at. But in order to avoid decimal/rounding error, please choose the range within which the correct answer falls).

a. Between $650-700.

b. Between $350-400.

c. Between $250-300.

d. Between $1000-1500.