Question

Consider a monopolist with the (inverse) demand function: Pb = 120 - 5 Qb. Given an increasing marginal cost: mc = 11 + 3 Q, how much DWL is created ? (Assume fixed costs = 10 .)

Answer 1

the firm produces at MR=MC

MR=120-10Q ....... An MR curve is double sloped than a inverse linear demand curve
MC=11+3Q
equating both
120-10Q=11+3Q
13Q=109
Q=8.38461538
P=120-5*8.38461538
P=78.0769231
MC=11+3*8.38461538
MC=36.1538461
=======
A efficient output is at MC=P
equating both equations
11+3Q=120-5Q
8Q=109
Q=109/8
Q=13.625
=======
DWL=0.5* change in output *(P-MC)
DWL=0.5*(13.625-8.38461538)*(78.0769231-36.1538461)
DWL=109.846524
the DWL is $109.85

(note the answer is acurate with 14 decimals)