Question

Municipal Electric is an electric utility that faces demand curve D1 during night hours (2300–0700) and demand D2 during daytime hours (0700–2300). Municipal Electric is required to provide service to satisfy demand, but can vary prices in an effort to curtail demand and ensure that the supply grid is not overtaxed. Municipal Electric is the monopoly provider of electricity. The demand and marginal revenue functions are: D1 : P1 = 4 − 0.001Q1 MR1 = 4 − 0.002Q1 D2 : P2 = 16 − 0.001Q2 MR2 = 16 − 0.002Q2 where Q = MW delivered per hour. The marginal cost of generating and delivering electricity depends on the amount delivered: MC = 1 + 0.004Q (a) In order to ensure grid reliability, the utility’s management uses peak-load pricing. This scheme raises prices during high-demand periods to ensure that demand does not exceed grid capacity. Calculate the appropriate prices to charge (P1 and P2) and determine the amount of electricity delivered, Q1 and Q2. (b) Explain how switching from a uniform pricing scheme to a peak load pricing scheme affects the market. Be as precise as you can about the differences between uniform and peak-load pricing. Use no less than one and no more than three complete sentences.

Answer 1

Given

D1 : P1 = 4 − 0.001Q1

MR1 = 4 − 0.002Q1

D2 : P2 = 16 − 0.001Q2

MR2 = 16 − 0.002Q2

MC = 1 + 0.004Q

Where,

Q = MW delivered per hour= Q1+Q2

D1 : night hours (2300–0700)

D2 : daytime hours (0700–2300)

From above we can deduct following equations

MC1= 1 + 0.004Q1

MC2= 1 + 0.004Q2

Firm will charge two different prices at two different time frames

Equilibrium takes place where MR=MC

Case-I: D1

4 − 0.002Q1= 1 + 0.004Q1

3=0.006Q1

Q1= 3/0.006= 500

We know

P1 = 4 − 0.001Q1

P1= 4-0.001*500 = 4-0.5 = 3.5

Price charged: 3.5

Quantity supplied: 500

Case II- D2

16 − 0.002Q2 = 1 + 0.004Q2

15 = 0.006Q2

Q2= 15/0.006 =2500

We know

P2 = 16 − 0.001Q2

P2 = 16- 0.001*2500= 16-2.5= 13.5

Price charged: 13.5

Quantity supplied: 2500

Total Quantity supplied = Q1+Q2= 500+2500=3000

b) if firm charges uniform price in both the cases then,

Given

D1 : P1 = 4 − 0.001Q1

D2 : P2 = 16 − 0.001Q2

Q1= (4-P1)/0.001

Q2= (16-P2)/0.001

Q = (20-2P)/0.001     [Q=Q1+Q2,   P1=P2=P]

0.001Q= 20-2P

P= (20-0.001Q)/2

TR= (20Q-0.001Q^2)/2

MR= (20-0.002Q)/2 = 10-0.001Q

MC = 1 + 0.004Q

Equilibrium takes place at MR =MC

10-0.001Q= 1+0.004Q

9 = 0.005Q

Q= 1800

We know

Q = (20-2P)/0.001

1800*0.001= 20-2P

2P =20-1.8=18.2

P= 9.1

Price charged in both the cases : 9.1

Total quantity supplied (Q1+Q2): 1800

Total quantity supplied in uniform pricing is lesser than total quantity supplied in Peak load pricing.