Please show step by step work: Suppose that a particular customer has the follow
ID: 1104245 • Letter: P
Question
Please show step by step work:
Suppose that a particular customer has the following demand curve relating the quantity demanded (measured in Kilowatt hours, KWH) to the price of electricity (measured in cents per KWH):
KWH = 1600 - 100*P
Note that an alternative way to represent the same relationship is in terms of the maximum price that the customer would be willing to pay for each KWH of electricity, or
P = 16 - .01*KWH
This customer's demand for electricity would, if plotted, look like Figure 1:
Now we will consider a number of rate schedules used by utilities, and we will examine their effects on electricity consumption and expenditure.
Question 1: Philadelphia Electric prices electricity using a simple flat rate of $.08 per KWH. How much electricity would be demanded by a customer with the demand curve given above and who lives in Philadelphia? What would be her monthly bill?
Question 2: If the rate were lowered to $.07, how much electricity would she buy? What would be her monthly bill in this case?
Question 3: How much electricity would a customer with the demand schedule depicted in
Figure 1 would buy if she lived in Chicago? What would be her monthly bill?
Question 4: What if she lived in Arizona? How much electricity would the consumer demand? What would be her monthly bill?
Utilities sometimes use an additional pricing tactic, "multi-part pricing," that involves charging the same consumer different rates for additional units purchased. Northern Indiana Power, for example, has a rate schedule approximately like this:
Question 5: How much electricity would a customer with the demand schedule depicted in Figure 1 would buy if she lived in Northern Indiana? What would be her monthly bill?
Question 6: Compute the average rate per KWH for this consumer in Philadelphia and in Indiana, and verify that they are the same (8c/WKH). Given that the consumer pays the same on average, why does she buy more electricity in Indiana? Is she better off in Indiana? Why or why not?
Detroit gets electricity from Detroit Edison, which is one of a small number of utilities that uses a multi-part schedule that is inclining rather than declining. This schedule is the result of pressure from environmental groups that call declining rates "promotional pricing" and favor an inclining rate to promote conservation, and additional pressure from advocates for the poor, who believe that this type of rate is more "fair."
A residential customer in Detroit faces the following rate schedule:
Question 7: What would our customer's consumption, electric bill, and average rate in Detroit be? Is she better off or worse off than in Philadelphia or Indiana?
Question 8: If all customers had identical demand curves, utility companies could increase revenues by increasing the fixed monthly charge and decreasing the charge per KWH. What is the maximum fixed charge a customer with demand represented by Figure 1 would be willing to pay? How much electricity would she use? What would her average rate per KWH be? Would she be better or worse off than she would have been under Philadelphia's pricing system of $.08 per KWH?
Question 9: A “Pareto improvement” is defined as a change which makes someone better off without making anyone else worse off. Show that, if all consumers had identical demand curves equal to that from Figure 1, the “Chicago” price scheme represents a Pareto improvement compared to the “Philadelphia” scheme.
Question 10: Fill in the table (Electric Power Purchasing Worksheet) at the end of this handout and answer the following questions:
Which is the consumer’s preferred price schedule?
And which is her least preferred?
Which is the Utility’s preferred price schedule?
And which is its least preferred?
Which price schedule yields the lowest average price?
The highest?
Which price schedule yields the largest gains from trade?
The smallest?
Question 11: According to a report recently released by the U.S. Energy Information Administration, the average price paid by industrial consumers of electricity is 5.09 cents per KWH in Michigan compared to 4.30 cents per KWH in Ohio. An industrial consumer of electricity (with a downward sloping demand for electricity) choosing where to locate a plant solely on the basis of electricity rate schedules should:
Definitely locate its plant in Ohio because its average cost of electricity will be lower
Definitely locate its plant in Ohio if its average cost of electricity is lower in Ohio than in Michigan given the quantity of electricity it will actually use
Definitely locate its plant in Ohio if its total expenditures on electricity would be lower in Ohio than in Michigan
None of the above
Explain your answer.
Question 12: Consider a slight variation of the Northern Indiana rate schedule. What if the price of the first 100KWH had been 18cents/KWH (instead of 14c/KWH)?
How much electricity would the customer buy? What would be her monthly bill? Her consumer surplus?
Question 13: Looking at the completed Electric Power Purchasing Worksheet, you will notice a positive relationship between quantity consumed and total welfare (i.e., total welfare [consumer surplus + utility revenue] is higher when the quantity consumed is higher). Why is this the case? [Hint: We are assuming that the marginal cost of producing and distributing electricity is zero].
Explanation / Answer
Question 1
Demand curve is as follows -
KWH = 1,600 - 100P
P = $0.80 per KWH
KWH = 1,600 - (100*0.08)
KWH = 1,600 - 8
KWH = 1,592
The customer would demand 1,592 KWH of electricity.
Calculate the monthly bill -
Monthly bill = Price * Quantity
Monthly bill = $0.08 * 1,592
Monthly bill = $127.36
Her monthly bill would be $127.36
Question 2
Demand curve is as follows -
KWH = 1,600 - 100P
P = $0.70 per KWH
KWH = 1,600 - (100*0.07)
KWH = 1,600 - 7
KWH = 1,593
The customer would demand 1,593 KWH of electricity.
Calculate the monthly bill -
Monthly bill = Price * Quantity
Monthly bill = $0.07 * 1,593
Monthly bill = $111.51
Her monthly bill would be $111.51