Question

1. An energy company has recently enhanced its capabilities for generating electricity, resulting in a 10% reduction in the cost/kwh. The company, which is regulated by the state, is required to pass the savings on to consumers via a 10% reduction in rates/kwh. Assume that the company has 100,000 residential customers who paid an average of $60/month consuming each 500 kwh/month in the year prior to implementing the new system; the same 100,000 customers paid $58/month following the shift to the new system with its lower prices. The total revenue therefore dropped from $6 million per month to $5.8 million per month. Based upon these facts,

1. • What was the increase in volume of electricity that was generated? What was the percentage increase?

Hint: Evaluate first what would have been the average bill if the volume had stayed the same after the fare reduction

1. • Was there a change in the demand function? If so, what is the new demand function? If not, why did the power company have to produce more electricity?

1. • What was the price elasticity in the demand for electricity?  

1. • What was the increase in consumer surplus as a result of the reduction in prices?

Answer 1

A. Demand function will not change, a decrease in cost instead increase the supply function. The company may be a public company or regulated company forced to sell at cost price. So the has to reduce the price by 10%.

B. Total revenue (TR)per consumer =P×Q $60 =P×500 so, P =$0.12 Initial price =0.12 initial quantity demand =500

new price =0.12—10%of0.12 =0.12—0.012=0.108 TR at new price per consumer =new price ×new quantity 58 =0.102× new quantity Thus new quantity =58/0.102 =537 (approx)

Now ep=(delta Q/deltaP) × P/Q =(37/0.012)×0.12/500 ep=4.44/6 =0.74

Thus the demand is price inelastic (e<1).

C. Change in the consumer surplus perconsumer =( change in price × initial quantity demand ) +1/2 ×change price ×change in quantity demand.

or, change in CS =(0.012 ×500)+(1/2 ×0.012×37 =6.22

This is individual CS, Total CS = 6.22×100000 =622000 (approx).

diagram is just for understanding.