In this problem you will try to model the future, taking into account population growth, growth in oil demand, and dwindling oil production, using the potential feedbacks between oil supply and demand as represented in the oil price. You can now predict what 2010 will look like and then do a reality check with the real data a few years from now.

We only look at oil and use the following parameters:

Current oil price, OP_o: $50.-/barrel

Current global oil consumption, OD_o: 31 billion barrels oil/year

Current per capita oil demand is oil consumption/global population

Growth in per capita oil demand worldwide, average last 10 years, rod_o: 0.5 %

Current world population, N_o: 6.6 billion people

Current population growth rate, rp_o: 1.14 %

(check http://www.ibiblio.org/lunarbin/worldpop)

Amount of oil left in the ground that can be produced is taken at a very conservative 1300 billion barrels (estimates range from 800-2000). If we assume a Hubbert bell curve for the production over time, we can constrain this amount with an oil supply function over time (see excel file with Hubbert oil supply data for the future).

The next two entries discuss how to approach a problem like this - the true questions to answer for this assignment are listed at the end!

1. As a first tryout, you can look at straightforward exponential growth for OD according to OD = N x OD* where OD* is the per capita oil demand. This can be rephrased as N_t = N_o x e^rpt and OD*_t = OD*_o x e^rodt (Equations 1). Then you multiply N_t with OD*_t and you have the global oil demand, OD_t. You can stick this into Excel with a column for years (from 2007 to 2100) and time since 2007 (2007 -0). It may be wise to keep separate columns for population and for per capita oil demand and then ultimately multiply the population column with the per capita demand column (splitting equation 1 into its two halves). You can put the formulas in the top of the columns with the appropriate FIXED r values and constants, and you will obtain the oil demand for each year assuming constant growth in population and per capita oil demand. Then make a running sum command (cumulate) for oil demand in the next column starting in 2007 and you obtain the cumulative oil demand over time. See when the cumulative oil demand is equal to the amount of oil left, and you have found the EET or "exponential expiration time", or the year that we run out of oil if all growth continues as it is today (the 'Full Speed' ahead scenario).
2. It is unlikely that the world population will keep growing at 1.14 %/year forever and that oil demand will increase at a constant 0.5 %/year. Design a new model for population growth using some form of adaptation to overpopulation, as done before in assignment one. Use for instance rp=rp_o (N_o/N) [equation 2], where rp is the population growth rate, as a simple population growth limiting parameter. This will give you a "slow growth" scenario for population. To estimate the development in per capita oil demand in the future, use the oil price as the growth limiting parameter for the per capita oil demand (OD*). Define the oil price from the ratio of potential oil demand (equation 1, but now with adapting r values for each year) and the Hubbert predicted oil supply (OS) from the excel sheet. Use for oil price OP=OP_o x (OD^5/OS^5) [equation 3], which will create an increasing oil price when calculated demand is larger than Hubbert supply. You can then model the growth rate of oil demand using that oil price, e.g., according to rod = rod_o + rod_o (OP/OP_o) ((OP_o-OP)/OP_o) [equation 4]. The latter, fairly complex expression, was made so that the rod can become negative and the per capita oil demand can decrease over time below its value in 2007 (rod is growth rate of per capita oil demand).

After this intro discussion, now solve the following questions in Excel, with plots to show your results: 1. time versus population at fixed r of 1.14%/year (part of equation 1), 2. time versus population with r dependent on N ('slow growth' scenario discussed above in equation 2), 3. global oil demand with 'slow growth' population scenario but fixed growth rate of 0.5 %/year for per capita oil demand, 4. global oil demand with 'slow growth' population and supply/demand controlled oil price (equation 3) which limits the growth of per capita oil demand (as in equation 4), 5. time versus oil price according to 4. Indicate on the graphs when we would have used up the 1300 bbo reserve, assuming (foolishly?) that we could fulfill the demand (by pumping harder?).

Make columns for time (calendar years), time to be used in the exponents (0,1,2,3,4 etc), the Hubbert supply data column, population at fixed r, population at variable r, the 'slow growth' population r value, OD* at fixed r, OD* at variable r, the variable r for OD, and the OP as a function of Hubbert supply and calculated demand. Then make two global oil demand columns, which you get by multiplying the 'slow growth' population column with the fixed growth per capita oil demand and another one with the slow growth population with the variable growth per capita oil demand. For the two global oil demand colums, make separate columns where you cumulate oil demand and mark when you cross the 1300 bby.

It all sounds like a lot, but ultimately it can be solved in 15 minutes by simply typing in the expressions and referring to the right cells from the years before. Print up the graphs and say a few words of wisdom what this all means.