Question

Using calculus and our five-step method or the Excel spread sheet I sent you, solve for the following:

1. Single price monopolist. P, Q, TR, TC, Profit and elasticity at profit max.

2. Using two markets and price segmentation approach, solve for P, Q, TR, TC, profit and elasticity in each market.

Regardless of which approach you take, show how you calculated monopoly demand.

Assume the following:

TC = 500 + 20Q

Q1 = 60 - .25P1   Q2 = 100 - .5P2

Answer 1

1)Q1=60-0.25p1

Q2=100-0.5p2

Aggregate demand,:Q=Q1+Q2=160-0.75p

Inverse aggregate demand:P=640/3 - 4Q/3

MR=640/3 -8Q/3

MC=20

MR= MC , profit maximizing condition

640/3 -8Q/3=20

Q=580/8=72.5

P=640/3 -4*72.5/3=350/3

TR=350/3 *72.5=25,375/3

TC=500+20*72.5=1950

Profit=25,375/3. -1950=19,525/3

Elasticity=(-0.75)*[(350/3)/72.5]=-1.2

2)Q1=60-0.25p1

P1=240-4q1

MR1=240-8q1

20=240-8q1

Q1=220/8=27.5

P1=240-4*27.5=130

Profit=(130-20)*28.5=3025

Elasticity=(-0.25)*(130/27.5)=-1.18

Market 2,

Q2=100-0.5p2

P2=200-2q2

MR2=200-4q2

20=200-4q2

Q2=180/4=45

P2=200-2*45=110

Profit=(110-20)*45=90*45=4050

Elasticity=(-0.5)*(110/45)=-1.22

Total profit=3025+4050-500=6575