Natural Resource Economics Problem -

Continue refining your oil reserve problem. You may want to add some features or make some changes based on the class discussions. For example, if you don't have a graph, please add one.

Make the following additions to your model:

a) Rather than the random distribution assumed above, assume that changes in oil prices are normally distributed with a mean of 2.5%/year with a SD of 3%. (=norm.inv(rand(),2.5%, 3%)

b) Create a data table showing the year oil reserves are depleted varying both the mean price change (0% to 5%) and population growth rates (put the mean price changes on y-axis and population growth rates on x). Use the conditional formatting option to color code your answers.

c) Finally, assume that every 10% increase in price leads to a 1% increase in reserve size. Create a figure that clearly shows how this changes your answers. Create a data table that shows the year of reserve depletion when you vary the assumed responsiveness to reserve size (0% to 10%).

2. The purpose of this problem is to begin developing a market diffusion model for solar photovoltaics. Begin the model development with solar prices (in cents/kWh). Assume that electricity from solar PV is currently about 20 cents/kWh, but that these prices are changing between 0 and -10% per year (some years there are breakthroughs). Use a normal distribution with mean of 4% and SD of 2%. The main competitor for solar is natural gas, which costs just 6 cents/kWh.

Assume an additional 100 units of power are needed every year and that this new demand will be met by either natural gas or solar, depending on which is cheaper. Once the choke price is reached (when solar becomes cost competitive with natural gas for electricity generation), solar begins gaining acceptance. The switch to solar is not instantaneous - it takes time for the new technology to be fully accepted. Typically, for new technologies, market diffusion will follow an S-shaped path. In the simple version of this model, assume that each year that solar is competitive; it captures an additional 2% of the market. (The first year solar is competitive, it only captures 2% of the new demand; 4% in year 2, 6 % in year 3, etc.).

a) Summarize solar's market diffusion for this simple model using appropriate graphs and words. One of the graphs should show installed natural gas and installed solar capacity on an annual basis (vertical axis should go from 0 to 100 units).

b) Develop a second scenario that includes the notion of natural gas scarcity. For this scenario, assume that scarcity is an issue beginning in year 2020. Assume that starting in that year, natural gas prices begin increasing by 2.0 % per year. Calculate the new natural gas prices and see what impact this has on your results.

c) Market diffusion curves are typically not linear, but follow an S-shaped curve. In "Diagnosing the DVD Disappointment: A Life Cycle View", Coplan provides a good historical review of the diffusion of many new technologies. Using this article as a resource, modify your model to include an S-shaped market diffusion path for solar technology. Discuss your findings.

d) Now assume that the starting price for electricity from natural gas (0.06 $/kWh) is made up of several components, one of which is the cost of natural gas itself. In the previous question, you just assumed that the price of electricity from natural gas increased by 2% per year. Instead, assume that the 0.06 $/kWh includes a $0.02 $/kWh scarcity rent charge (marginal user cost). Modify your model to incorporate this new information. Report how this changes the "choke point" for assumed discount rates of 0%, 5%, 10%, and 15% (summary table or perhaps a DATA TABLE would work well for this.)

Attachment:- Assignment File.rar