Economics 4440/5440 Homework #3 Dr. Michael Nieswiadomy

Economics of Natural Resources and the Environment Due: Oct. 20, 2015, 11:59 p.m.

All answers should be typed. Assemble everything into one combined pdf or MS Word

document.

1) (20 points) Assume that Alessi Balsamic Vinegar sells for $3.50 for a 4 year old

bottle and that a 20 year old bottle sells for $10.50. Calculate the annual rate of

return that the company is expecting to earn. Show your work. Do not use a

calculator with a built-in function for calculating rate of return. You can use a

calculator for natural logarithms and Euler’s constant. Hint: use natural

logarithms.

Solution:-

Here,

Price of 4 year old Vinegar bottle (P4) = $3.50

Price of 20 year old vinegar bottle (P20) =$10.50

We know,

F = P (1+r) n

Where, F = future value

P = present value

r = rate of annual return

n = number of years

So,

$3.50 = P (1+r) 4 ...............................................eqn(1)

$10.50 = P (1+r) 20……………………………. eqn(2)

Dividing eqn(2) by eqn(1) we get

4

20

)1(

)1(

5.3

5.10

rP

rP

Or, 3 = (1+r) 16

Taking log on both sides

Log3 = 16 log (1+r)

Or, 0.4771 = 16 log (1+r)

Or, )1log(16

4771.0r

Or, 0.02982 = log (1+r)

Now,

)1log(02982.0 ree

Or, 1.0294 = 1+r

Or, r = 0.0294

Therefore, required annual return is 2.94%

2) (20 points) Calculate the levelized payment for a $1 annuity lasting 50 years

growing at 3% and discounted at 5%. Show your work, using the technique that I

showed you in class.

Solution:-

Here, A = $1

n = 50

Rate of Discount ( r ) = 5% =0.05

Annual growth Rate ( g) = 3% = 0.03

Net discounted rate (r*) = 1

1

1

g

r

= 103.1

05.1

= 0.0194

Formula to calculate present value of annuity =

nrr

A

**1

11

We can calculate the levelized Payment for 50 years

PVannuity =

500194.01

11

0194.0

1

=

500194.1

11546.51

=

6135.2

11546.51

=

6135.2

6135.1546.51

= 6135.2

1722.83 =$31.82

Therefore, Levelized payment for a $1 annuity lasting for 50 years at 3% growth rate and

5% discount rate is $31.82.

3) (20 points) Go to www.cityofdenton.com. You should find a pdf document that

has this header

Consumer Information Denton Municipal Utilities

The effective date at the bottom of the page is Oct. 1, 2015. Find the residential

monthly water rates for the Summer (May through October) for the 4 blocks: 1st

block: up to 15,000 gallons; 2nd block: 15,001 to 30,000 gallons; 3rd block: 30,001

to 50,000 gallons; and 4th block: 50,000 + gallons.

a) Print out these results and attach them to your homework. Highlight them

with a “yellow highlighter” in MS Word of Adobe Acrobat.

Answer

Consumer Information

Denton Municipal Utilities

ELECTRIC RATES

Residential Facility Charge $8.25/bill (single phase) $16.50/bill (three phase) Energy Charge Winter (November-April) 6.18¢/KWH first 600 KWH 4.11¢/KWH all additional KWH Summer (May-October) 6.18¢/KWH all KWH Energy Cost Adjustment* Adjusted Periodically Transmission Cost Recovery Factor** Adjusted Periodically

Residential Renewable Energy

Facility Charge $8.25/bill (single phase) $16.50/bill (three phase) Energy Charge Winter (November-April) 6.18¢/KWH first 600 KWH 4.11¢/KWH all additional KWH Summer (May-October) 6.18¢/KWH all KWH Renewable Cost Adjustment* Adjusted Periodically Transmission Cost Recovery Factor** Adjusted Periodically

General Service Small Facility Charge $15.80/bill (single phase) $21.10/bill (three phase) Energy Charge First 2,500 KWH 7.67¢/KWH All additional KWH 4.02¢/KWH Energy Cost Adjustment* Adjusted Periodically Transmission Cost Recovery Factor** Adjusted Periodically

Commercial Renewable Energy

1,000 KWH Blocks RCA* Rate/KWH 100% of Actual Energy Consumption RCA* Rate/KWH *The Energy Cost Adjustment (ECA) and Renewable Cost Adjustment (RCA) rates are adjusted periodically as the energy market fluctuates. Call for current rates. **The Transmission Cost Recovery Factor (TCRF) rate is adjusted periodically as ERCOT transmission tariffs fluctuate. Call for current rates.

SOLID WASTE RATES

Residential Refuse and Recycling

Trash Cart Size One Cart Two Carts Large Trash Cart $32.00/bill $58.50/bill Standard Trash Cart $26.75/bill N/A (Each rate includes one standard-size recycling cart. A second recycling cart is available at no extra cost.)

Commercial Front and Side Load

WATER RATES Residential

Facility Charge 3/4” Meter $13.85/bill 1” Meter $18.40/bill

1 1/2” Meter $23.85/bill 2” Meter $30.35/bill

Volume Charge Winter (November-April) $3.80/1,000 gallons (all consumption) Summer (May-October) $3.80/1,000 gallons (up to 15,000 gallons/bill) $5.50/1,000 gallons (15,001-30,000 gallons/bill) $7.40/1,000 gallons (30,001-50,000 gallons/bill) $9.75/1,000 gallons (50,000+ gallons/bill)

Irrigation Customers See rate ordinance for applicable rates.

Commercial/Industrial Facility Charge 3/4” Meter $22.60/bill 1” Meter $27.05/bill 1 1/2” Meter $32.05/bill 2” Meter $42.60/bill

Volume Charge $4.15/1,000 gallons Irrigation Customers

Winter (November-April) $4.15/1,000 gallons Summer (May-October) $5.50/1,000 gallons

WASTEWATER RATES Residential

Facility Charge $10.35/bill Volume Charge $3.95/1,000 gallons effluent

(Billing based on 100 percent of average monthly water billed from December-February.) (18,000 gallon wastewater volume cap.)

Commercial/Industrial Facility Charge $25.70/bill

Volume Charge $5.00/1,000 gallons effluent (Billing based on 90 percent of monthly water consumption.)

Equipment Services and Eating Establishments

Facility Charge $25.70/bill Volume Charge $6.80/1,000 gallons effluent

(Billing based on 90 percent of monthly water consumption.)

DRAINAGE RATES

Residential Square Feet in Block Monthly Charge per Bill

Container Size Billing per Cubic Yard Commercial Side Load $32.50 Front Load (<4 cubic yards) $25.00 Front Load (>4 cubic yards) $22.50 (All solid waste commercial rates are based upon one collection per week.)

Commercial Open Top (Roll-Off) Monthly Rental $160.00 Collection Charge* $270.00 *Plus landfill fees based on weight.

0-600 $.50 601-1,000 $1.00 1,001-2,000 $3.35 2,001-3,000 $5.45 3,001-4,000 $7.60 4,001-5,000 $9.75 5,001-6,000 $12.00

b) Calculate the cost of consuming 60,000 gallons of water in a summer month.

Assume the house has a ¾” meter. You do not need to calculate the

wastewater costs. Show your work.

Solution:-

Bill to be paid for consumption of 60000 gallons in the summer month can be calculated

as

60000 gallons = 15000 gallons +15000 gallons +20000 gallons + 10000 gallons

= 153.8+155.5+207.4+109.75

= $382

Total cost = $382+$13.85

= $395.85

c) Draw the price schedule similar to one of those in Figure 9.4 in your text.

Make sure to show the each block point e.g., 15,000 gallons, 30,000 gallons &

50,000 gallons. You can draw this in Word using its drawing feature (Insert,

Shapes, Drawing Canvas).

Solution:-

Per

Unit

Cost

$

Usage

Gallons

3.8

5.5

30000

7.4

9.7

5

15000

Inverted block rate structure

50000 50000+

4) (20 points) Go to www.cityofdenton.com. Use the same information sheet

described above. Find the residential solid waste (i.e., garbage) rates in dollars.

a. (6 pts.) What is the charge for a large cart, medium cart, and a small cart

per month? Mark them with a “yellow highlighter” in MS Word or Adobe

Acrobat.

Solution:-

Consumer Information

Denton Municipal Utilities

ELECTRIC RATES

Residential Facility Charge $8.25/bill (single phase) $16.50/bill (three phase) Energy Charge Winter (November-April) 6.18¢/KWH first 600 KWH 4.11¢/KWH all additional KWH Summer (May-October) 6.18¢/KWH all KWH Energy Cost Adjustment* Adjusted Periodically Transmission Cost Recovery Factor** Adjusted Periodically

Residential Renewable Energy

Facility Charge $8.25/bill (single phase) $16.50/bill (three phase) Energy Charge Winter (November-April) 6.18¢/KWH first 600 KWH 4.11¢/KWH all additional KWH Summer (May-October) 6.18¢/KWH all KWH Renewable Cost Adjustment* Adjusted Periodically Transmission Cost Recovery Factor** Adjusted Periodically

General Service Small Facility Charge $15.80/bill (single phase) $21.10/bill (three phase) Energy Charge First 2,500 KWH 7.67¢/KWH All additional KWH 4.02¢/KWH Energy Cost Adjustment* Adjusted Periodically Transmission Cost Recovery Factor** Adjusted Periodically

Commercial Renewable Energy

1,000 KWH Blocks RCA* Rate/KWH 100% of Actual Energy Consumption RCA* Rate/KWH *The Energy Cost Adjustment (ECA) and Renewable Cost Adjustment (RCA) rates are adjusted periodically as the energy market fluctuates. Call for current rates. **The Transmission Cost Recovery Factor (TCRF) rate is

WATER RATES Residential

Facility Charge 3/4” Meter $13.85/bill 1” Meter $18.40/bill

1 1/2” Meter $23.85/bill 2” Meter $30.35/bill

Volume Charge Winter (November-April) $3.80/1,000 gallons (all consumption) Summer (May-October) $3.80/1,000 gallons (up to 15,000 gallons/bill) $5.50/1,000 gallons (15,001-30,000 gallons/bill) $7.40/1,000 gallons (30,001-50,000 gallons/bill) $9.75/1,000 gallons (50,000+ gallons/bill)

Irrigation Customers See rate ordinance for applicable rates.

Commercial/Industrial Facility Charge 3/4” Meter $22.60/bill 1” Meter $27.05/bill 1 1/2” Meter $32.05/bill 2” Meter $42.60/bill

Volume Charge $4.15/1,000 gallons Irrigation Customers

Winter (November-April) $4.15/1,000 gallons Summer (May-October) $5.50/1,000 gallons

WASTEWATER RATES Residential

Facility Charge $10.35/bill Volume Charge $3.95/1,000 gallons effluent

(Billing based on 100 percent of average monthly water billed from December-February.) (18,000 gallon wastewater volume cap.)

Commercial/Industrial Facility Charge $25.70/bill

Volume Charge $5.00/1,000 gallons effluent

adjusted periodically as ERCOT transmission tariffs fluctuate. Call for current rates.

SOLID WASTE RATES

Residential Refuse and Recycling

Trash Cart Size One Cart Two Carts Large Trash Cart $32.00/bill $58.50/bill Standard Trash Cart $26.75/bill N/A (Each rate includes one standard-size recycling cart. A second recycling cart is available at no extra cost.)

Commercial Front and Side Load

Container Size Billing per Cubic Yard Commercial Side Load $32.50 Front Load (<4 cubic yards) $25.00 Front Load (>4 cubic yards) $22.50 (All solid waste commercial rates are based upon one collection per week.)

Commercial Open Top (Roll-Off) Monthly Rental $160.00 Collection Charge* $270.00 *Plus landfill fees based on weight.

(Billing based on 90 percent of monthly water consumption.)

Equipment Services and Eating Establishments

Facility Charge $25.70/bill Volume Charge $6.80/1,000 gallons effluent

(Billing based on 90 percent of monthly water consumption.)

DRAINAGE RATES

Residential Square Feet in Block Monthly Charge per Bill 0-600 $.50 601-1,000 $1.00 1,001-2,000 $3.35 2,001-3,000 $5.45 3,001-4,000 $7.60 4,001-5,000 $9.75 5,001-6,000 $12.00

b. (6 pts.) What is the size of each cart? It is not on the rate page. Search on

the city of Denton website. This may take some searching. Attach the

printed web page.

Solution:- TRASH CARTS

Three sizes of green trash carts are available: small (45-gallon), medium (65-gallon), and

large (95-gallon).

Bag your trash!

Bagging trash helps to prevent litter during collection and transport,

protects your container, and reduces litter on the streets and at the ECO-

W.E.R.C.S. Landfill.

Examples of Trash: This is not a comprehensive list of items considered trash.

c. (6 pts.) Calculate the average cost per gallon for a medium cart. Show

your work.

Solution:- Size of medium cart = 65 -gallon

Price per medium (standard trash) cart = $26.75

Average cost per gallon = 75.26

65

= $2.43

d. (6 points) Calculate the average cost per gallon for a large cart. Show your

work.

Solution:- Size of large trash cart = 95 -gallon

Price per large trash cart = $26.75

Average cost per gallon = 32

95

= $2.97

e. (6 points) Calculate the marginal cost per gallon when a person increases

their garbage usage from a medium cart to a large cart. Show your work.

Solution:- We have,

Average cost per gallon for medium cart =$2.43

Average cost per gallon for large cart =$2.97

Marginal cost per gallon (from medium to large cart)

=$2.97-$2.43

= $.54

= 54 cents

5) (20 points) Use Figure 1 below to determine the profit maximizing price that will

be set by OPEC as the price leader/dominant firm. Show the output produced by

OPEC and the fringe firms. Draw your lines using MS Word Shapes, under the

Insert tab.

Answer : -

From the given figure after drawing the required lines, we can clearly see that

Profit maximizing price set by OPEC = $50

Output produced by OPEC = 30

Output produced by fringe firms = 30

Total output produced = 60

0

5

10

15

20

25

30

35

40

45

50

55

60

65

70

75

80

85

90

95

100

105

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80

$

Figure 1: OPEC Price Leadership Model

Quantity supplied

World Oil

Demand

MC OPEC

Supply of

Non-

OPEC/Fringe

Firms

MROPEC