Consider a market with demand given by Q = 400/p^2. To enter the market a firm m

Question

Consider a market with demand given by Q = 400/p^2. To enter the market a firm must first pay an entry cost of k, thereafter it ean produce at a constant marginal cost of 2 with no other fixed costs. (a) If a government grants a firm an exclusive monopoly in this market, how low must kappa be for the declared monopolist to enter the market? (b) If instead there are a two potential entrants who will engage in symmetric Court not competition if they both enter, how low must kappa be for them both to enter the market?

Explanation / Answer

Q = 400/P^2

P = 20/Q^1/2

Total Revenue = TR = P*Q = 20/Q^1/2*Q = 20*Q^1/2

MR = dTR/dQ = 10/Q^1/2

MC = 2

Entry cost = K

Total cost = K + 2Q

For Monopoly, Profir will be maximized at

MR = MC

  10/Q^1/2 = 2

Q = 25

P = 20/5 = 4

monopoly profit = PQ - TC

= 4*25 - k - 2*25

= 50 - k

So for profit to be positve for monopoly

50 - k > =0

K = < 50

So minimum k = 50

For Oligopoly , Q = q1 +q2

Profit for first oligopoly firm = TR - TC = P*q1 - TC =   (20/(q1 +q2)^1/2)*q1 - k - 2q1

dProfit/dq1 = -1/2(20*(q1 +q2)^-3/2) + 20/(q1 +q2)^1/2 - 2

dProfit/dq1 = 0

-10 = q1 + q2 +

Sorry could n't solve this equation as i don't have pen and paper right now and it''s getting difficult here . But like in first part , you have find profit equation and put it equal to 0.

Please don't review the same . If don't understand comment , I'll revert back on the same .:)

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