Micro doubt

[lucy]

Assuming a downward sloping linear demand curve and a constant Marginal cost of
production, the dead weight loss due to monopoly pricing ( as against the marginal cost
pricing rule) is
A. equal to the profits ofthe monopolist
B. is roughly equal to 1/3 rd ofthe monopoly profits
C. is equal to one half of the monopoly profits
D. is equal to one fourth of monopoly profits

[Rajat]

it should be C. one half of monopoly profit

[Rajat]

it should be C. one half of monopoly profit

[lucy]

Pls explain your answer. Thanks

[Rajat]

Under monopoly, MR= MC.
MR curve is twice as steep as demand curve.
If you draw the two curves, DW loss will be given by the triangle with base Y2-Y1 and height P2-P1.
(P2,Y2) is a point on the demand curve. (P2,Y1) is a point on the MR curve. (P1,Y1) is a point on the demand curve right above (P2,Y1) on the MR curve.
These three points form the vertices of the DW loss triangle. also, P1 = 2P2 and Y2=2Y1.

Please note that MC would be a horizontal line that cuts the the MR curve at (P2,Y1) and the demand curve at (P2,Y2).
Monopolist profit  = P1Y1 - P2Y1 = P2Y1.
Area of the DW loss triangle is 1/2*(P1-P2)(Y2-Y1) = 1/2*P2Y1.

Hence C it is.

[Rajat]

the horizontal line passing through B and A is the MC curve.
Let
A be (Y2,P2)
B be (Y1,P2)
C be (Y1,P1)

the two slanting lines are the demand curve and MR curve. MR curve is twice as steep as the demand.
DW loss will be given by area of the  triangle ABC.
P1 = 2P2
Y2 = 2Y1

Using this relation, we can compute the area. Hope this helps

[radhika00]

The inverse demand function is given as P = 35 - 2x-x2 where x is the amount of
commodity demanded. Calculate consumer's surplus amount at x = 3 units. (Hint: Apply
integration method)
A. 60
8.9
c. 35
D. 27