If demand for a monopoly\'s product is given by P = 180 - 4q, and total cost is

Question

If demand for a monopoly's product is given by P = 180 - 4q, and total cost is given by TC = 0.5q_2, then what is (a) the monopoly output and (b) the monopoly price?. If demand for a monopoly's product is given by P = 330 - 5q, and total cost is given by TC 0.5q_2, then what is (a) the monopoly output and (b) the monopoly price?. If demand for a monopoly's product is given by P = 240,000/Q_3, and total cost is given by TC = 0.5q_2. then what is (a) the monopoly output and (b) the monopoly price?

Explanation / Answer

7. P = 180 - 4q

TR = P*q = (180 - 4q)q

MR = dTR/dq = 180 - 8q

TC = 0.5q2

MC = dTC/dq = q

Mooonopoly will produce till MR = MC

= 180 - 8q = q

q = 20

P = 180 - 4*20 = 100

8.

  

. P = 330 - 5q

TR = P*q = (330 - 5q)q

MR = dTR/dq = 330 - 10q

TC = 0.5q2

MC = dTC/dq = q

Mooonopoly will produce till MR = MC

330 - 10q = q

q = 30

P = 180 - 4*30 = 60

9

. P = 2,40,000/q^3

TR = P*q = (240,000/q^3)q

MR = dTR/dq = -1/2*240,000q^-3 = -120,000q^-3

TC = 0.5q2

MC = dTC/dq = q

Mooonopoly will produce till MR = MC

120,000q^-3 = q

q^4 = 120,000

q = 18.61

P = 180 - 4*18.61 = 105.5

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