Section A: Wind Power Generation

By the end of 2011, the United States’ wind generation will be the following percentage of the world’s installed wind generation capacity;

= Total US generation capacity  x    100%  Total world generation capacity

= 46919 x 100%

237,669

=19.7413%

Thus, by the end of 2011, US produced 19.7413% of the worlds’ installed wind generation capacity.

Assuming that all other countries capacity does not grow from the 2011 figures, United States will have to expand its capacity in order to have 40 percent of the world’s capacity. Calculating;

Ceteris paribus,At 19.7413%, US’ generation =46,919

Thus, at 40 percent, generation will be = 40 x 46919                                                                                                                                             19.7413

            = 95,067

Thus, US will have to increase its capacity by;

            = 95,067- 46,919

            = 48,148.

Note: 1GW = 1000MW

So, if wind generation capacity increased by 41GW in 2011, it means it increased by 41 x 1000

            = 41,000MW.

Thus, generation capacity in 2010 was:

            = 237,669-41000 MW

            = 196,669 MW.

In the same way, wind generation in 2009 was:

            =196,669 -39,000

            = 157,669 MW.

Thus world wind generation increased by the following percentage during 2010.

            =39,000 x 100

               157,669

            =24.735%.      

Calculating increase in Wind Power Generation between end of 2009 and 2011;

Production by end of 2009 = 157,669 MW.

Production by end of 2011= 237,669 MW

Calculating total change;

            = 237,669- 157,669 MW

            = 80,000 MW

Calculating percentage change;

            =80,000 x 100

                   157, 669

            = 50.739%.

Percentage change between 2011 and 2010;

=237,669-196,669   x 100%

         196,669

= 20.8%

Assuming the same rate of change remains constant at 20.8% until 2020;

2012 production = 120.8 x 237,669       = 287, 104

                                    100 

2013 production = 120.8 x 287,104       = 346,821

                                    100

2014 production = 120.8 x 346,821       = 418, 960

                                    100

2015 production = 120.8 x 418, 960      = 506,104

                                    100

2016 production = 120.8 x 506,104     = 611,374

                                    100

2017 production = 120.8 x 611,374     = 738,540

                                    100

2018 production = 120.8 x 738,540     = 892,156

                                    100

2019 production = 120.8 x 892,156   = 1,077,725

                                    100

Finally;

2020 production = 120.8 x 1077.725 = 1,301,891

Under the same assumption as question 5 above, the world wind generation will triple in;

The triple value will be

= 3 x 237,669  

= 713,007

Assuming r= 20.8%

            n = ln (FV/PV) 

            n = ln (713,007/237,669) 

            n = 1.099/0.182

               = 6 years

The formula will be;

The m value will be equal to the PV*m

So,  FV= m*PV

To calculate the number of years n;

n =  ln (FV/PV) 

Thus,

n = ln (m* PV/PV)

According to the Global Wind Energy Council, the worldwide wind capacity has been increasing significantly since the end of 2011. Indeed, this increase is within my expectation with reference

However, it should be noted that the generation capacity has not tripled yet, but instead has doubled. This is a remarkable improvement in wind power generation all over the world. It can be argued that the overall wind energy generation capacity has sufficiently increased due to  the continuing boom of economies like India and China, which have installed numerous wind power stations. In addition, the use of wind power on commercial basis has increased worldwide, thereby increasing the demand for the product, allowing an increasing in its supply. However, the value has not tripled yet, owing to the fact that most developing nations in the world are yet to adopt the technique, thereby reducing the growth capacity.  

Question One

Consumption function model

C = aY + b

Where a = MPC

b = autonomous consumption

Y = GDP

C = consumption

It is worth pointing out that the consumption function  model of human well-being because it is a mathematical function that expresses the level of consumer spending in terms of determinants such as income and accumulated wealth. Normally, income and wealth  are used as indicators of the welfare of people within a given economy. 

Supposing a country has two regions, A and B. Their GDP is denoted as Y^A and Y^B respectively, the country’s overall GDP will be:

C = (aY^A + b) + (aY^B + b)

C= b + aY^A + aY^B

C= b + aY^A + aY^B

The formula of GDP of B as a function of C, Y^A

aY^B = C- b – aY^A

Thus,

Y^B = C- b – aY^A                                                                                                                                                 a

Assuming that GDP in region A is fixed, the function can be represented as follows, with the GDP in region B on the vertical axis and consumption on the horizontal axis. 

Ordinarily, in C = b + aY, b is the intercept while a is the slope of the function. They are both positive. However, in this case, the graph has been inverted. For this reason, the intercept and slope are both negative.

Thus, the slope is –a

 On the other hand, the intercept is denoted as –b.

 It can, therefore, be concluded that region B is associated with a lower level of wellbeing as compared to region A. Primarily; this can be attributed to the negative slope associated with its GDP, as shown in the graph in question 4 above.

Supposing region A was very rich and the region B was very poor, the GDP will be an important measurement of the well-being. Also, it could be used to capture the inequality in the well-being of the people in the two economies. Fundamentally, region A will be associated with a higher GDP as compared to region B. on the other hand, region B will be characterized by a lower GDP. Consequently, the GDP per capita in region A will be higher than that of region B, thereby capturing the inequality between the well being of individuals in region A and region B.

A loaf of bread costs approximately $6 whereas an opera ticket costs about $150. It is worth pointing out that these goods have different contributions to the GDP of the country. In this case, the loaf of bread has greater weight on the calculation of the GDP than the opera ticket. Precisely, this is due to the fact that although a loaf has a low price, it is a basic need. For this reason, it carries greater weight and contributes more to the GDP of the country, than an opera ticket which is only a luxury good. The different weights and values assigned to the two goods adequately reflect their contribution to human welfare, with the bread having a higher contribution to human wellness than an opera ticket.

Question Two

Supposing that two countries have identical and extensive forests. Country 1 decides to capitalize on the asset by harvesting and selling the timber as paper and building materials thereby earning $100 million in the process. On the other hand, country 2 protects its forests and does not harvest. In this scenario, country 2 is much better off than country 1 because it has preserved its natural resources. Contrariwise, country 1 has exploited it forests leading to not only the encroachment of the environment but also depletion of its natural resources. According to natural resources economics, country 1 will be experiencing the Hotelling’s rent, indicating an increase in the scarcity of natural resources in the country. Therefore, country 2 is much better off than country 1. 

According to the ecological footprint, the human population is living beyond the earth’s natural bio-capacity. Unfortunately, this has been the case since 1986, after the bio-capacity exceeded the 1.0 mark, indicating that the planets ecological services are used faster than they are renewed. In this regard, it is unsustainable.

Graph drawn using excel

If we assume that the total land use can be approximated by a linear function;

y = mx + b

Where;

b = intercept

m= slope

x=  value

The linear equation becomes

Y = mx+0.6

If the trend of land use continues, then the land use in 2060 will be unsustainable. Mathematically;

Current growth rate; = 1.2-1.15                                                                                                                                                    1.2                                  = 0.04

Using a growth rate of 0.2

FV = PV (1+r) ^ⁿ

= 1.2 (1+0.04) ^⁵⁴

=10

According to the EF, the largest component of land use is fishing ground. It is also growing at a significantly fast rate. In 1969, the EF for this component was estimated at 0.2. In 1979, the value increased to 0.3. In 1989, the value was estimated at 0.4 percent. In 1999, the value was at 0.5. As at 2006, the value was estimated at 0.6

Estimating rate of growth;

= 0.6-0.5 

= 0.2 or 20%

Using the data presented in figure 2, policies must be enacted to ensure sustainable use of land resources and a favorable ecological footprint. One such policy should aim at enhancing the sustainability of the environment as well as address the spatial dimensions of environmental problems while offering solutions for the same. The EF is one such policy tool that  can be used to achieve these objectives, given the fact that it can be utilized in making socio-political decision with respect to the optimal scale. Indeed, this can ensure the sustainable use of land resources in the world.

Calculating the price of electricity

If;

 5,352,613 kWh = 664,476

Then,

2,595,743 kWh = ?

Solution;

= 2,595,743 x 664,476

5,352,613

= 322,236

Hence, the private savings will be;

= 664,476-322,236

= $342,240

Question 2

Tones of CO₂ emission that LED lighting will prevent;

Change in carbon emission;

= 5,352,613 -2,595,743 kWh

= 2,756,870 kWh

CO2 emission prevented

If 1kWh = 1.07 kg of C0₂ emission,

Then; 2,756,870 kWh = ?

Solution;

= 2,756,870 x 1.07

= 2,949,850.9 kg of C0₂ emission were prevented.

With respect to social cost;

 In economics, social cost refers to the costs borne by the society as a result of actions by firms. Often, it results from actions such as air, noise and water pollution. In this case, CO2 emmision is a social cost as it results in air pollution, which significantly affects the society, while the firms producing it do not bear the associated costs.

Assuming the social cost of 1 tone of C0₂ emission = $18

Then the social savings will be;

= 2,949.8509 x 18

= $53,097.31 

Total savings from LED lights after 12 years;

= 12 x $53,097.31

= $637,167.7944

Using the following formula;

PV= FV* [1/(1+r)ⁿ

$637,167.7944 =   FV * 1     

So;

Assuming r= 5.2% or 0.052

FV =    $637,167.7944 (1+ 0.052) ^¹² 

= $1,170,692.117

Thus, the City of Sydney should accept a maximum price of $1,170,692.117.   

Reference List

Global Wind Energy Council (2017). “GWEC, Global Wind Report Annual Market Update. [Online] Global Wind Energy Council. Available at: https://www.gwec.net/wp-content/uploads/2012/06/Global-Cumulative-Installed-Wind-Capacity-2001-2016.jpg  [Accessed 15 Nov 2017].