(f) (1 Mark) Which investment option should Nathan recommend to the AREH for 2030? Justify your answer. (g) (5 Marks) Instead of a 100% increase in demand in 2030, assume new demand fer green hydrogen in 2030 will increase 3% at every price level. Redo (d), (e) and (f). That is, determine the AREH's Optimal pricing and investment decisions in 2030 based on the value of :r. (h) (2 Marks) Based on your answers above, briey discuss how the interplay of economies of scale and market demand determines the ARE-H's pricing and investment decisions. (i) (2 Marks) 15 reported last weeE, another international consortium also plans to build the world's biggest renewable energy hub named the Western Green Energy,r Hub (WGEH) along the south coast of Western Australia. Briefly,r discuss how this will aect the AREH's pricing and investment decisions. In terms of the production of green hydrogen, the AREH plans to power the electrolysis process by solar. The total production cost of green hydrogen depends on the AREH's investment in infrastructure and solar panels. There are two investment options: Small and Large invest- ments: Option 1. Small Investment. Under this option, the AREH makes an investment of 1.5 billion dollars annually and the annual total production cost of green hydrogen (including the investment cost) is TC(Q) = 60 + 1.5 billion. Option 2. Large Investment. Under this option, the AREH makes an investment of 5 billion dollars annually and the annual total production cost of green hydrogen (including the investment cost) is TC(Q) = 40 + 5 billion. Note that a higher level of investment, while incurring higher fixed costs, leads to a lower marginal cost of production. (b) (3 Marks) What would be the pricing strategy for green hydrogen suggested by Nathan to the AREH under each option? Note. If p(Q) = a - 6Q, then MR(Q) = a - 26Q. (c) (1 Mark) Which investment option should Nathan recommend to the AREH? Justify your answer. Now the AREH is asking Nathan to prepare a demand forecast for 2030. Based on the recent demand growth of green hydrogen, Nathan estimates that compared to 2025, demand for green hydrogen in 2030 will increase 100% at every price level In other words, in 2030 we have Q = 0.5. (1+ 100%) = 1 billion kg/year when the price is p = $9, and Q = 2.5. (1+100%) = 5 billion kg/year when the price is p = $5. (d) (2 Marks) Derive step-by-step the demand curve for green hydrogen facing the AREH in 2030. Next Nathan moves on to estimate the production cost of green hydrogen in 2030. Based on this article, capital costs for solar PV installations fell by 79% from 2010 to 2019. Following this trend, it is estimated that the marginal cost of production of green hydrogen will drop 20% from 2025 to 2030. Accordingly, Nathan estimates that the total cost of production of green hydrogen under each investment option is: Option 1. Small Investment. Under this option, the AREH makes an investment of 1.5 billion dollars annually and the annual total production cost of green hydrogen (including the investment cost) is TC(Q) = 4.80 + 1.5 billion. Option 2. Large Investment. Under this option, the AREH makes an investment of 5 billion dollars annually and the annual total production cost of green hydrogen (including the investment cost) is TC(Q) = 3.20 +5 billion. (e) (3 Marks) What would be the pricing strategy for green hydrogen suggested by Nathan to the AREH under each option in 2030?ofhon Green cloctricity Safely Zero carbon hosting products hydropan TO2 Ha H2 Hz O Transported through ritaora Background Knowledge In a bid to combat climate change and build a carbon-free future, governments and businesses are actively seeking renewable energy sources. Hydrogen (H), the most common element in the universe, has been proposed as a fuel of the future. Due to its high reactivity with other elements such as oxygen, hydrogen generally does not appear pure on Earth. The most common technique to obtain hydrogen is to extract it from water (HO) via a process called electrolysis (i.e., run electricity through water), and green hydrogen is produced from electrolysis powered by renewable energy such as solar or wind. Hydrogen can be stored and transported (by converting it into ammonia), and be used to power factories, appliances and hydrogen fuel cell vehicles. Many countries have committed to invest in green hydrogen to decarbonize the economy: The European Union plans to invest $430 billion in green hydrogen by 2030, China, Japan and South Korea have together pledged to put 8 million hydrogen fuel cell cars on the road. You may go over the following articles to learn more about hydrogen: Article 1, Article 2, and this video explains the production and use of green hydrogen. Story and Problem Nathan has just been hired as a consultant to the Asian Renewable Energy Hub (AREH). The AREH is planning to build the world's largest renewable energy plant in the Pilbara Region of Western Australia. To attract more investors to fund the project, the AREH asked Nathan to prepare a demand forecast for green hydrogen in 2025. After conducting a market survey and taking the demand growth of green hydrogen into consideration, Nathan obtains the following two data observations: Q = 0.5 billion kg/year when the price is p = $9/kg, and @ = 2.5 billion kg/year when the price is p = $5/kg. Suppose Nathan believes that the demand of green hydrogen facing the AREH in 2025 can be reasonably approximated by the following linear demand curve: P(Q) = a - bQ. (a) (2 Marks) Show step-by-step that a = 10 and b = Tips; i.e., Nathan submits the following demand forecast to the AREH: 2 P(Q) = 10 - 1 billion 3