ECON131 Quantitative Methods assignment 代写

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  • ECON131 Quantitative Methods assignment 代写

     
    ECON131
    Quantitative Methods in
    Economics, Business and Finance
    Session 1, 2017
    Assignment
    Due: June 16th, 2017, 11 am
    2
    PLEASE READ THIS DOCUMENT CAREFULLY
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    shown.

    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
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    due date. Please see BESS for advice on this procedure.
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    information on plagiarism and how to avoid it, please refer to the unit outline.
    3
    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)
    4
    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)
    5
    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
    6
    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)
    7
    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
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    ECON131 Quantitative Methods assignment 代写