Question

The following table shows the demand curve facing a monopolist who produces at a constant marginal cost of $8.00: Price 18 16 14 12 10 8 6 4 2 0 Quantity 0 4 8 12 16 20 24 28 32 36 Calculate the firm's marginal revenue curve. The firm's marginal revenue (MR) curve is A. MR = 18 - 1.000. B. MR = 10-0.50Q. C. MR = 18 -0.13Q. D. MR = 18 -0.50Q.

Answer 1

from the table at puce P=16, Q1=4 at puce P2 = 14, Q2=8 Now basic demand care Q = atbp Where b= slope of demand cure a= entical in Incept of demad care. Now Slope b = (Q2-Q1) (8-4) (P2-P1) (14-16) 4 thes demand equation Q = a - 2P Now to get as we substitute first ordered pain (PjQ1) = (16,4) (16,4) in the demand equation. = -2 2 Huce, 4 - a- 2(16) a 32 45 =) 0:36 =) the demand equation Q= 36-2p =) 36-Q=2 P =) p = 18- 0.5Q When Q20 => p=18, p=0 =) 18-0.5Q -0. 5) Q = 36 .Now; Total reveues TR=PQ = 180 - 0.5Q 2 Marginal revemes MRE ACTR) QQ 18- 1.00Q 2 Whin = 19-0.5(2) => MR ther the auswn will be A. MRS 18-1.00Q CS Scanned with CamScanner

When Q=0 =) MR = 18 when MR-0 =) 18- 1.000 =0 a) 18=Q Now, Monopolist's profit marining condition.- MR = MC the MC= 88.00 =) 18- 1.000 = 8 3 10= Q output =) Huces The firm's profit marimizing 10 funts =) he The corresponding puce will be, p= 18-0.5Q P2.18-(0.5 x10) = $ 13 fim's profit will be T= Total revine (PQ)- Total cost MC= 8 tuce, total cost e=8Q Hamrej 77- (13/10) - 8(10) ( 130-80) = $150 Now, profit Condition in pubect competition, p= MC 18-0.5Q=8 10 = 0.5 -) Q = 20 price will be P= MC = $8 c) TT- mariniring 8 =) c) CS Scanned with CamScanner

Consum would gain an anont equal to = Area of Drve The compettive pure would be $18.00 wits. 20.50 The competitive quantly would be ap M 19 T 13 MC 8 v Q * 20 0 10 36 18 The social gain would be equal to = Area of AABC = £x base Xheight - Î x( 20-10)*(13-8) 25.00 " Now, it monopoly is forced to produce at competitive levels their monopoly would lose = Area of TABU base x height = (10-0) x (13-8) $150.00 £xbase x height = { x (20-0) XC 18-8) = $1.100.00 CS Scanned with CamScanner