ECON131 Quantitative Methods assignment 代写

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ECON131

Quantitative Methods in

Economics, Business and Finance

Session 1, 2017

Assignment

Due: June 16th, 2017, 11 am

PLEASE READ THIS DOCUMENT CAREFULLY

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ECON131 Quantitative Methods assignment 代写

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Marks: The maximum mark for this assignment is 75.

The assignment consists of three sections, A, B and C. Each of the sections is

worth a total of 25 marks.

Due date: On or before 11 am June 16th, 2017. Submissions made after this time will receive

a mark of zero. Extensions of time over this due date will be granted ONLY in cases

of serious illness or other exceptional circumstances. In such cases, a formal

disruption to studies application must be submitted within 5 workings days of the

due date. Please see BESS for advice on this procedure.

Plagiarism: Each assignment must represent the student's own work. In particular, this means

that the written answers submitted by the student should be composed by that

student. The copying of another student's answer, textbooks or any website, is

clearly regarded as plagiarism. All assignments will be scanned by software that

detects plagiarism. Cases of plagiarism will be dealt with severely. For further

information on plagiarism and how to avoid it, please refer to the unit outline.

Section A: Population Growth

The populations of the world’s two largest countries, China and India, are both growing rapidly.

Consider the official populations estimates for China and India in 2011 and 2015, below:

2011 2015

China 1 344 1 371

India 1 247 1 311

Population, millions. Source: World Bank

The population growth rate, r, is a single number that describes this rate of growth. Below, we will

derive a formula for this number, and then analyse the growth rates of both countries.

We usually think about population growth as following an exponential path:

? ? = ? 0 ? ??

where: t represents time, usually measured in years,

? ? is the population in time t,

? 0 is the starting population size, and

r is the population growth rate.

1. Sketch the exponential population growth formula on a graph, with time on the horizontal axis

and population on the vertical axis. Mark ? 0 and interpret this point. (2 marks)

2. Re-arrange the formula above to give a formula for r. (3 marks)

3. Using this formula, compute the average annual population growth rate for both countries

between 2011 and 2015. (2 marks)

4. Assuming these growth rates remain constant, estimate the 2030 populations of China and

India. What are their projected populations for 2037? Write down a general formula for both

countries’ population in year t. (6 marks)

5. Using the formula you wrote down in question (4), in what year will the two countries’

population be equal? (3 marks)

6. Assuming that both countries’ average population growth rate doesn’t change, how many years

would it take for China’s population to double in size? How many years would it take for India’s

population to double in size? What assumptions are you making in answering this question? (4

marks)

7. If a country’s population follows an exponential curve indefinitely, is that population

sustainable? Explain your answer in detail. (5 marks)

Section B: Malthusian Disaster

In 1793 the political economist Thomas Malthus noticed that that population growth in the United

States had been doubling every 25 years (which is geometric growth), but that the level of food

production had only increased by a fixed amount each year (which is arithmetic, or linear growth).

In An Essay on the Principle of Population, as It Affects the Future Improvement of Society, With Remarks

on the Speculations of Mr Godwin, Mr Condorcet and Other Writers, he wrote:

[. . . ] the power of population is indefinitely greater than the power in the earth to produce

subsistence for man. Population, when unchecked, increases in a geometrical ratio. Subsistence

increases only in an arithmetical ratio. A slight acquaintance with numbers will shew the

immensity of the first power in comparison of the second. By that law of our nature which

makes food necessary to the life of man, the effects of these two unequal powers must be kept

equal. This implies a strong and constantly operating check on population from the difficulty of

subsistence. This difficulty must fall somewhere; and must necessarily be severely felt by a large

portion of mankind.

World population growth 10,000BC-2,000AD.

Source: US Population Bureau/Wikimedia Commons

1. Look at the graph of world population growth above. Does the growth in the population look

arithmetic (linear), or geometric? (1 mark)

2. Assume a population is initially a 0 (when t=0) and that it grows by a ratio r every year. Write

down an expression for the population in year t. (2 marks)

3. Malthus suggested that food supplies are growing at an arithmetic rate. Assume that the annual

food supply is initially b tonnes per year, and that every year it increases by m tonnes. Write

down an expression for the food supply, in tonnes, in year t. (2 marks)

4. Compare the expressions you found in questions (2) and (3). Let the initial population a 0 be

1,000, let the population growth ratio r be 1.05, the initial annual food supply b be 2,100 tonnes,

and the annual increase m be 160. On the same set of axes, where time is the horizontal axis

and people/tonnes are the vertical axis, plot the values for t=0,10,20,30,40 and 50 (4 marks)

5. Now, using the parameters in the previous question, suppose that each person consumes one

tonne of food per year. During which year will the population begin to experience food

shortages? Derive your answer mathematically, rather than graphically. You may assume there

is no food stored from year to year. (4 marks)

6. Find the year that the population’s demand for food exceeds 19,000 tonnes per year. (4 marks)

7. Suppose that the population growth rate is slightly lower, and that r=1.01. Now find the year

that the population’s demand for food exceeds 19,000 tonnes per year. (3 marks)

8. Practically speaking, is it inevitable that, if food is growing arithmetically (m>0) and population

geometrically (r>1), that food supplies will always run out? In reality, does it look like earth is

heading towards a Malthusian Disaster? Provide some evidence from your own research to

support your answer. (5 marks)

S S ection C: Solar Panels Investment

Suppose a family consumes 15kWh of power per day. Concerned about its carbon footprint, the family

would like to ensure 50% of its electricity comes from renewable sources. Rational and economically

minded, the family would like to find the cheapest way to do so, and its planning horizon is the next 15

years. Assume the panels do not degrade over time, and at the end of 15 years, the solar panels will

have zero residual value. Also assume that electricity provided by the solar panels has a per unit cost of

zero (i.e. zero variable cost).

System Type Electricity Generated / day Installation Cost

1 kW system 3.9 kWh / day $6 000

1.5 kW system 5.85 kWh $7 000

2 kW system 7.8 kWh $8 000

3 kW system 11.7 kWh $11 000

4 kW system 15.6 kWh $14 000

Typical solar systems available in Sydney. Source: Clean Energy Council

To make this investment, the family would withdraw from its cash management trust, which is expected

to return a steady 5.15% per year, compounded annually, for the foreseeable future. The remainder of

the family’s power is provided by the electrical grid. They can buy three different `types’ of electricity

from the grid: non-renewable, 50% renewable or 100% renewable. They face the following prices for

energy they purchase from the grid:

Item Units Non-renewable 50% Renewable 100% Renewable

First 1000 kWh $ per kWh $0.2684 $0.2838 $0.2992

>1000 kWh $ per kWh $0.2805 $0.2959 $0.3113

Supply charge $ per day $0.6908 $0.6908 $0.6908

Source: Origin Energy

ECON131 Quantitative Methods assignment 代写

You may assume that electricity prices remain constant, and inflation can be ignored. Assume the power

generated by the solar panels is the same year-round.

1. Which is the cheapest solar system type that would provide 50% of the family electricity

consumption? (1 mark)

2. Assuming that the solar system performs as advertised, what is the family’s quarterly bill from

its energy provider? Assume there are 91 days in a quarter. (2 marks)

3. Using an annual discount rate of 5.15% and ignoring inflation, what is the present value of 15

years’ worth of electricity bills? (2 marks)

4. Other than buying solar panels, what is the quarterly cost of the next best alternative, which still

provides 50% renewable energy? (3 marks)

5. What is the present value of 30 years’ worth of this solution? Again, ignore inflation, and use a

discount rate of 5.15%. (3 marks)

6. Conditional on using at least 50% renewable energy, what is the net present value (NPV) of

purchasing the solar panel system named in question (1)? Hint: to answer this question you will

need to consider the present value of renewable energy sources and the present value residual

electricity bills along with any associated installation costs. (4 marks)

7. Interpret your result from question (6). Is buying solar panels a good idea? Explain your answer.

(2 marks)

8. Under the same assumptions as above, assume the family is not committed to purchasing

renewable energy (i.e. the family is happy with consuming non-renewable energy from the grid.)

What is the NPV of purchasing solar panels now? (3 marks)

9. Will the family in question (8) purchase the solar panel system named in question (1)? (2 marks)

10. Some governments have offered subsidies to consumers to install solar panels in their homes.

Why? (3 marks)

END OF ASSIGNMENT

Assessment cover sheet

Declaration

I certify that:

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This assessment is my own work, based on my personal study and/or research;

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I have acknowledged all material and sources used in the preparation of this assessment, including any

material generated in the course of my employment;

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If this assessment was based on collaborative preparatory work, as approved by the teachers of the unit, I

have not submitted substantially the same final version of any material as another student;

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Neither the assessment, nor substantial parts of it, have been previously submitted for assessment in this or

any other institution;

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I have not copied in part, or in whole, or otherwise plagiarised the work of other students;

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The assessment is within the word and page limits specified in the unit outline;

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third party;

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I understand that this assessment may undergo electronic detection for plagiarism, and a copy of the

assessment may be retained in a database and used to make comparisons with other assessments in future.

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ECON131 Quantitative Methods assignment 代写