## Locating and Analyzing a Quarterly Electricity Bill

1. Locate a quarterly electricity bill and provide a copy of the first page in your assignment. Note: you may want to edit / hide any personal details. All that needs to appear are the dollar amounts and energy consumption. According to this bill, what is the: a. Price of electricity per kWh? b. Total consumption of electricity in kWh? c. Amount of any fixed charges? d. Total payable amount for the bill that you have presented?

2. Using the data in the bill, re-construct step-by-step with explanations how the total bill amount in Question #1d was calculated by the energy provider.

3. Using this bill as a representative bill, and using an annual discount rate of 8% (and ignoring inflation), what is the present value of 10 years of bills?

4. Consider a standard refrigerator: a. Quote its model and make. b. Quote its projected energy consumption in kWh, per quarter according to the manufacturer.

5. By how much would the electricity bill have been reduced if the refrigerator was not switched on for the entire quarter?

6. Presume that the entire energy consumption quoted in the bill resulted from the usage of only standard 60W light bulbs and no other electrical appliances. Obtain a standard 60W light bulb and quote its: a. Brand. b. Price. c. Expected lifespan in hours.

7. If the entire energy bill was due to the use of the 60W light bulbs in Question 6: a. How many light bulbs would have been used? b. How many hours of light were produced by these bulbs? c. What would have been the cost of buying these standard light bulbs for this billing period?

8. Obtain an energy-saving 15W light bulb quoting its: a. Brand. b. Price. c. Expected lifespan in hours.

9. Assuming that one 15W energy-saving bulb gives out the same light as one 60W standard bulb: a. How many energy-saving light bulbs could have been used instead of standard light bulbs above? b. What would have been the cost of buying these energy-saving light bulbs for this billing period?

10. Assume that a full set of solar-powered light bulbs exists today that costs $15,000. Assume that this set can provide all the needed hours of light calculated above for each quarter for 10 years and these bulbs consume zero energy from the energy grid. Should a family consider in investing in such a set of light bulbs? Remember, we are assuming that light bulbs are the only item that consumes electricity in the residence.

- A) The designated country for this assignment is El Salvador, Central America.
- B) As per the latest report on Human Develoment Index published by UNDP, HDI of the country , El Salvador is 0.662 in 2013.
- C)Here ,the supply curve is the MPC. This includes the cost to the producers for producing a given good or sevice and hence the name private cost.

**1.** Thus, MPC=

Total Private Cost (TPC) is given as = z Q^{3} +a Q ^{2 } +b Q

Where, z = HDI /10= 0.662/10= 0.0662

a= HDI /2.5 = 0.2648

b= 1

Substituting these values in the equation of TPC, we get **TPC= 0.0662 Q ^{3} + 0.2648 Q ^{2 } + Q**

Differentiating TPC with respect to Q, we get MPC which is the suppliers curve.

Thus **MPC= 0.1986 Q ^{2} + 0.5296 Q + 1**

## Reconstructing the Total Payable Amount Calculation

Hence , this is the suppliers curve.

In order to find competitive or market equilibrium, we equate marginal social benefit (MSB) to marginal private cost (MPC). MSB represents the demand side, whereas MPC represents the supply side (Smith 2011). The corresponding quantity is the equilibrium quantity Q* and the corresponding price is the equilibrium price P*. Here, we haven’t included the external costs.

Thus, MSB = MPC

Here, MSB is given as MSB = P = –dQ + 40

Where, d= HDI/7.5 =0.882

Substituting this value in MSB , we get **MSB= P = –0.882Q + 40**

Now in order to find a competitive equilibrium quantity, we equate MSB = MPC

–0.882Q + 40= 0.1986 Q^{2} + 0.5296 Q + 1

0.1986 Q^{2} + 1.4116 Q -39 =0

Q= 8.03

Hence, this is the competitive equilibrium quantity.

** 2.**

Substituting the value of Q found in question 1 in MSB which is equal to the price, we get

**MSB= P = –0.882Q + 40**= **–0.882 (8.03) + 40** **=-7.082 + 40 = 32.918**

This is the a competitive equilibrium price.

** 3.**

The market equilibrium found above in the question 1 and 2 is not the efficient equilibrium output and price because we have not considered the external cost . Here, we have not considered the negative externalities rising due to production, leading to the dead weight loss (Smith 2011). We have just considered the cost to the producers. We haven’t considered the cost to the society. Hence, we need to calculate the external cost that takes into account the negative externality into consideration. This external cost is shown as MEC, which is the marginal external cost. If we consider this, the output will be at an efficient level (Kolstad 2012).

Thus,

Marginal Social cost (MSC) = Marginal Private Cost (MPC) + Marginal External Cost (MEC)

**3.** MEC is found by differentiating TEC with respect to Q, and Total External Cost (TEC) is given as = *y Q ^{3}*

Thus,

MEC=

**MEC= = **** =2.648(3) ****= 7.944 **

Thus, MSC = **0.1986 Q ^{2} + 0.5296 Q + 1 +7.944 **

**=8.1426 ** **+ 0.5296 Q + 1**

At equilibrium at efficient output level where we have considered the external cost,

MSB = MSC

** –0.882Q + 40 =8.1426 **** + 0.5296 Q + 1**

** 8.1426 ** **+ 1.4116 Q - 39 =0**

** Q= 2.1**

This is the efficient equilibrium quantity at an efficient level where we have considered external costs(Smith 2011).

**4.**

The efficient equilibrium price found at the efficient level of output is **MSB= P = –0.882Q + 40**= **–0.882 (2.1) + 40** **=-1.852+ 40 = 38.15**

5.A.C Pigou (1877–1959) suggested a solution to the difficulty of externalities. The idea is to impose a per-unit tax on a good. The negative externalities generated is equal to the marginal externality at the social efficient quantity. This is known as a Pigouvian tax. Thus, at the efficient level of quantity, if the marginal external cost is $1, then a $1 per-unit tax would lead to the right decision on the part of the government to do away with thedead weight loss as well as negative externality.

Thus**,**** MEC= = **** =2**.648(3) = 7.944 = 35.03.

Hence, tax rate is 35.03%

Tax revenue equals tax rate * Efficient quantity level . Here tax revenue equals **35.03*2.1=73.56**

**7.**

In order to find the share of the tax borne by the consumers and the producers, we use the following formula (Kolstad 2012).

Tax borne by the consumers =

Tax borne by theproducers =

Thus, producers and consumers equally bear the tax.

Graph showing the share of tax borne by the consumers and producers

** 8.**

Price elasticity of demand=

= -1.137 * 4.098

= -4.65

** 9 .**

Price elasticity of supply =

= -1.33* 4.099

= -4.64

**10.**

The elasticity of the demand and supply curve determines on the incidence and burden of taxes that will be shared by the producers and consumers (Kolstad 2012).

Beginning with the elasticity of demand, this determines whether the burden of taxes will borne more by the consumers or the producers. If the demand curve of a good is elastic, so any increase in price of the product due to inclusion of tax would lead to the fall in the demand of that particular product. This would be a major loss to the producers and hence they would not shift the entire burden to the consumers. They bear at least half or more than half of the tax burden. If the demand is highly elastic, producers would bear more than half of the burden (Kolstad 2012). Whereas, if the demand for the product is the inelastic, this implies that increase in the price of the good will not have a significant impact on the quantity demanded of that product. Hence, in this case, the tax burden can be entirely shifted upon the consumers.Coming to elasticity of supply curve, if the supply curve is inelastic, he will produce the same quantity irrespective of the price.Thus, it will be impossible to shift the tax to the consumers.

References

Kolstad CD 2012, *Intermediate Environmental Economics, * Oxford University Press, New Delhi.

Smith S 2011, *Environmental Economics : a very short introduction, * Oxford University Press.

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