Consider local water utility company that faces an inverse demand function for monthly water consumption of has a marginal and average cost of $5. Calculate producer surplus, consumer surplus, total...

Monopolist:
Inverse demand Qd = 100-P
P = 100-Q
MC = 5
AVC = 5
AVC = TC / Q
TC = AVC*Q
TC = 5Q
Under perfect competition P=MC
100-Q = 5
Q =95
P =5
TR =P*Q
TR = 100Q – Q^2
MR = ∂TR / ∂Q
MR = 100 – 2Q
a.
Under single pricing
MR = MC
100 – 2Q = 5
95 = 2Q
Q = 47.5
Q = 48 (appx)
P = 100 – 48
P = 52
TR = 52*48
TR = 2496
TC = 5*48
TC = 240
Total Economic profit = TR-TC
Total Economic profit = 2496-240
Total Economic profit = 2254
Consumer surplus = ½*(48)*(100-52)
Consumer surplus = (24)*(48)
Consumer surplus = 1152
Producer surplus = ½*(48)*( 52-5)
Producer surplus = 24* 47
Producer surplus = 1128
Dead weight loss =1/2* (52-5)*(95-48)
Dead weight loss =1/2* (47)*(47)
Dead weight loss =1105(appx)
b.
Under perfect price discrimination producer will charge two different price for different consumer groups
Q = 100-P
P = P1+P2
MC1=MC2=5
TR1 = (100-P1-P2)*P1
MR1 = 100-2P1-P2
MR1 =MC1
100 – 2P1-P2 = 5
2P1+P2 = 95
P1 = (95-P2)/2
MR2=MC2
TR2 = (100-P1-P2)*P2
MR2 =...