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ECON131: Microeconomics - Quantitative Methods in Economics, Business and Finance - Assessment Answer

January 15, 2017
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Solution Code : 1EIDB


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Microeconomics Assignment

Assignment Task

Section A: Wind Power Generation

Wind power generation capacity has been growing worldwide since the early 1990s. Table 1 shows the installed wind generation capacity (measured in megawatts, MW) in the top 10 countries, as at the end of 2011.


  1. At the end of 2011, what percentage of the world’s installed wind generation capacity was in >China?
  2. Consider table 1. If you assume that other countries’ capacity doesn’t grow from the 2011 figures, what amount would China have to expand its capacity in order to have 40% of the world’s capacity?
  3. World installed wind generation capacity increased by 41 GW in 2011, and by 39 GW in 2010. Bywhat percentage did world wind power generation increase during 2010?
  4. By what percentage did world wind power generation increase, between the end of 2009 andthe end of 2011?
  5. Suppose the annual rate of increase in (3) continues each year, from the end of 2011. By whatpercentage will world wind power generation have increased by the end of 2020?
  6. Under the same assumptions as (5), how long will it take for world wind power capacity todouble?
  7. Write a general expression for the number of years it would take for world wind power capacityto increase times over, if it grows at the rate given in (3).
  8. In reality, what has happened to worldwide wind power generation capacity since the end of2011? Is this in line with your expectations of growth based on your answer to (5)? Explain why this may or may not be the case. Provide evidence from your own research to support your answer. (6 marks)

Section B: Gross Domestic Product (GDP)

In this section, we consider some issues with measuring “well-being” and “sustainability.” For a much more detailed discussion of these topics, see the report by Stiglitz, Sen, and Fitoussi (2009).

A central focus of sustainability is the measurement of human “well-being,” so that economic policies can be designed and evaluated against the rubric of maximizing the welfare of the people affected.

A popular way to measure people’s well-being is by Gross Domestic Product (GDP), which is the final value of all goods and services in the economy. GDP includes everything produced by the economy, including investment and goods and services not consumed by individuals.

The following model for consumption is proposed:

C = aY + b (1)

where C is consumption, a is the marginal propensity to consume, b is autonomous consumption, and Y is GDP.

  1. In what sense is equation 1 a model of human well-being? (3 marks)
  2. Suppose a country was comprised of two regions, A and B. The GDP of each region is given by YAand YB, respectively. Assuming equation 1 holds, write down an expression for the whole country’s GDP and its level of consumption.
  3. Re-write this equation as a formula for the level of GDP in region B (denoted YB), as a functionYB(C,YA) of total consumption (C) and GDP in region A (YA).
  4. Treating GDP in region A as a fixed number, sketch this function with GDP in region B on thevertical axis and consumption on the horizontal axis.
  5. What is the slope of the function? Is GDP in region B associated with a higher, or lower, level ofwell-being? Explain your answer.
  6. Suppose region A was very rich, and region B was very poor. Does GDP, as a measurement ofwell-being, capture this inequality?
  7. A loaf of bread costs about $6. A ticket to the opera costs about $150. How much does each onecontribute to GDP? Do you think this adequately reflects its contribution to human well-being?
  8. Suppose two identical countries possess identical, extensive forests. Country 1 decides tocapitalize on this asset, by harvesting and selling the timber as paper pulp and building materials within a year, earning $100 million in the process. Country 2 decides to protect its forests, and doesn’t harvest. According to the GDP measure of human wealth, which country is better off? Do you agree? Explain why or why not?

Section C: Ecological Footprint

The Ecological footprint (EF) measures how much of the regenerative capacity of the biosphere is used up by human activities. It is the sum of productive land and water area required to support the population and provide the resources it consumes, absorb its waste and provide infrastructure (Stiglitz et al., 2009, p. 244).


  1. According to the EF, is the human population living at, beyond or below the Earth’s naturalbiocapacity? For how long has this been the case? Is this sustainable?
  2. If you assume that the total land use can be approximated by a linear function, what is theapproximate slope of the total land use of the EF? What are the units of measurement in this function? Give the equation of, and sketch this line, with EF on the vertical axis and year on the horizontal axis.
  3. If this trend of total land use continues, what will land use be in 2050?
  4. Which is the largest component of land use according to the EF? At what rate is it growing?
  5. Use the data presented in figure 2, along with your answers to this section, to suggest a policy tomake land use sustainable.

Section D: LED Lighting

The City of Sydney is an area covering over 26km2, and is one of Australia’s most important social and economic centres. As part of Sydney 2030, a study into the city’s long-term sustainability, the city council committed to reducing its carbon footprint 70% over the next 20 years.

A study found that around 31% of the city’s carbon emissions arise from public lighting. So, in 2011, the City of Sydney announced a project to replace its lighting systems with energy efficient LED lights. It would choose lighting systems based on both their economic and environmental value. After a consultation period, the City chose a supplier in late 2011 to replace 6,448 luminaries (lights).

Before the project, suppose that the 6,448 luminaries slated for replacement consumed 5,252,613 kWh of electricity annually. In 2010/11, the annual lighting bill was $654,476. Suppose that the new LED lights will consume considerably less power, just 2,595,743 kWh per year.

  1. Bulk, unmetered power is billed on a “per KWh” basis, with no additional costs. What will theannual electricity bill be when all the lights are installed? (Assume the price of electricity is constant.) What are the private savings for the City of Sydney in the first year? (In other words, how much less will the city pay?)
  2. The City of Sydney calculates carbon emissions on the assumption that each kWh of electricitycauses 1.07kg of CO2 emissions. On this assumption, how many tonnes of CO2 emissions per year will the project prevent? The City of Sydney assumes a social cost of $17 per tonne of CO2. Using your own research briefly explain what is meant by the term “social cost” in this situation and calculate the social savings of this project, in the first year?
  3. Suppose the City of Sydney decides to award the contract if, after including CO2 savings inrevenue, the project breaks even at the end of the 12th year. What is the highest price the City should accept for this project? Ignore inflation, and assume a social discount rate of 5%.

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Section A

1. Total wind generation installed capacity in the world = 237,669 MW

Total wind generation installed capacity in China = 62,364 MW

Percentage share of China = (62364/237669)*100 = 26.24%

2. Let us assume that for China to account for 40% of the global capacity, incremental capacity is X MW

Thus, total global installed capacity = 237669 + X

Also, (40/100)*(237669 + X) = (62364+X)

Solving the above, we get X = 54,506 MW

Thus, the incremental capacity China would have to put to account for 40% of the wing energy capacity is 54,506 MW.

3. Total installed capacity at the end of 2011 = 237669 MW

Increase in capacity during 2011 = 41 GW or 41,000 MW

Hence, installed capacity at the end of 2010 = 237669 – 41000 = 196,669 MW

Increase in capacity during 2010 = 39 GW or 39,000 MW

Hence, installed capacity at the end of 2009= 196,669 – 39,000 = 157,669 MW

Hence, percentage increase in capacity in 2010 = (39000/157669)*100 = 24.74%

4. Total installed capacity at the end of 2011 = 237,669 MW

Total installed capacity at the end of 2009 = 157,669 MW

Percentage increase = [(237,669-157,669)/157,669]*100 = 50.74%

5. The annual growth rate in wind energy capacity is assumed to be 24.74% p.a.The above growth rate continues from end of 2011 to end of 2020 i.e. for 9 yearsPercentage increase in wind power installed capacity from the end of 2011 to the end of 2020 = (1.24749 -1)*100 = 631.23%

6. Let the time required to double be assumed as T years

Current capacity = 237669 MW

Expected capacity = Twice of the existing or 2*237669

Thus, (2*237669) = 237669*1.2474T

Solving the above, we get T = 3.135 years

7. Let the time required in years for the installed capacity to become m times be equal to T Further, it is assumed that the annual growth rate is 24.74% p.a.

Hence, the requisite expression is highlighted below.m = 1.2474TThe above can also be expressed in the form of logarithmic function as highlighted below.Log m = T log 1.2474

8. The actual growth in the wind energy installed capacity has been significantly lower than the growth rate predicted in the computations above (Brown, 2014). This may be attributed to the following reasons (GEWC, 2015).

  • Dropping of the crude oil prices to more than $ 100 per barrel to less than $ 40 per barrel which has resulted in less emphasis on renewable energy sources including wind energy which is comparatively costly.
  • The US has emerged as a major oil producer with the shale gas and oil revolution owing to which it has achieved near self-sufficiency which has reduced the focus on wind energy as an energy source.
  • The growth rate in China has slowed down since 2013-2014 owing to which the installation of new wind power capacity has suffered since the demand for energy has been tepid.
  • There has been a drop in the prices of carbon credits linked with wind power projects which have also adversely impacted the feasibility of these projects and hence slowing the erection of the same.

Section B

1. The given equation is a model of well-being since it tends to capture a linear relationship between the GDP and the consumption. Hence, the consumption is dependent on the GDP. Thus, as the GDP of a particular nation would increase, the consumption would also increase which would increase the living standard of a given individual. Hence, the given equation tends to express human well-being in relation with economic well being represented through the use of GDP.

2. Based on the equation highlighted, the respective consumption of the two regions A and B can be stated as indicated below.

CA = aYA + bA

CB = aYB + bB

The combined consumption function C = CA + CB

The requisite equation is highlighted as shown below.

C = a(YA+YB) + bA + bB

3. The objective is to obtain a formula for YB in terms of the other variables which may be achieved as indicated below.

C = a(YA+YB) + bA + bB

C- bA - bB = a(YA+YB)

(C- bA - bB)/a = YA+YB

Hence, YB = [(C- bA - bB)/a] - YA

4. The requisite graph is shown below.


5. The slope for the function is 1/a. GDP in region B is associated with a lower level of well-being since for a given value of C, there are constants in the form of b/a and YA which would subtracted from the consumption to arrive at the GDP value for the region B.

6. Yes, GDP as a measurement of well-being does capture this inequality. This is because if the region A is very rich, then the same would be reflected in the GDP of A which would lead to YA being higher. As a result, for a given consumption level, the value of YB would be small only which would be reflective of the poor economic status of the nation B.

7. The contribution of the loaf of bread and a movie ticket would be $ 6 and $ 150 respectively. This is because GDP is the sum total of the value of the goods and services produced in a given nation. This clearly does not adequately reflect the contribution to the human well-being even though bread fulfils the basic necessity of food but still it is priced considerably lower than a movie ticket which tends to provide mere entertainment. Thus, their respective values individually do not reflect the contribution they make to the human well-being.

8. Since country 1 has capitalised on the forest wealth and generated earnings to the tune of $ 100 million, hence the GDP of this country would be higher in comparison to country 2 which does not exploit the forest resources. Thus, if GDP is the grading metric, it is apparent that country 1 seems better off as the GDP increases. However, this is not an accurate assessment as the extensive forests play a significant role in the ecological balance and their intrinsic worth could be significantly higher than the commercial gains derived. Also, GDP as an evaluation metric does not consider the incremental environmental cost which is essentially not direct. Thus, essentially country 2 which decides to conserve the rich forests would be better off in the long run n comparison to country 1.

Section C

1. The human population is living beyond the Earth’s natural bio-capacity. This has been the case since 1987 when the ecological footprint crossed 1. Clearly, this trend is not sustainable and needs to be rectified.

2. Ecological footprint in 1986 =1

Ecological footprint in 2005 = 1.3

Thus slope = (1.3-1)/(2005-1986) = 0.016 per year

The unit of measurement is number of earths per year.

The requisite graph is indicated below.


3. Ecological footprint in 2005 = 1.3

Number of years to 2050 = 2050-2005 = 45

Hence, expected ecological footprint in 2050 at the given rate = 1.3 + 45*0.016 = 2.01

Thus, more than 2 earths would be required to sustain human race.

4. The largest component of land use in accordance with EF is carbon uptake land,

Level in 1961 = 0.05

Level in 2005 = 0.65

Total increase = 0.65-0.05 = 0.6

Number of years elapsed = 2005-1961 = 44 years

Rate of growth = 0.6/44 or 0.0136 per year (assuming a linear trend)

5. It is apparent that major land use pertains to carbon uptake land, crop land and grazing land. It is essential that the amount of carbon emissions need to be lowered so that the carbon uptake increase is contained which is of utmost importance. This can be achieved by migrating to the renewable sources of energy to the extent possible. Also, energy efficiency needs to be enhanced so that wastage of energy is reduced. Further, with regards to crop land, the emphasis should be on environmentally friendly practices such as organic farming which tend to maintain the soil fertility in the long run. Also, practices such as mulching, drip irrigation need to be practised so as to lower the overall water consumption. Further, for grazing, there should be dedicated parcels of land where the same can be sustained. Grazing activity in areas where plant growth is is nascent stage need to be regulated. Through the above measures, the ecological footprint may be improved.

Section D

1. Annual consumption of electricity by original luminaries = 5,252,613 Kwh

Annual lighting bill in 2010/2011 = $654,476

Annual consumption of electricity by LED’s = 2,595,743 Kwh

Annual light bill with LED = 654,476*(2,595,743/5,252,613) = $ 323,430

Annual savings during the first year = 654476 – 323430 = $ 331,046

Hence, during the first year, the city would save $ 331,046 on public lighting.

2. Total saving of electricity annually due to energy efficient LED’s = 5,252,613 - 2,595,743 = 2,656,870

Savings in terms of CO2 emissions = 2,656,870 * 1.07 = 2,842,851 kg or 2,842.85 tonnes

Owing to higher carbon dioxide emissions, there is climate change which tends to impact the health of people along with their respective energy usage for heating and cooling. Further, it also impacts the energy prices along with the crop productivity. These incremental costs are clubbed together and referred to as social costs (EPA, nd).

Social savings of the project in the first year = 2,842.85*17 = $ 48,328.5

3. The project breakeven is achieved at the end of the 12th year. Also, the discount factor = 5% pa.

The maximum price that should be paid for the project would be equal to the net present value of the social savings expected from the project over a 12 year period as has been computed below.


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