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550 words economic 4day/Exercise 1 Natural Resource Economics

550 words economic 4day/Exercise 1 Natural Resource Economics
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Exercise 1
Natural Resource Economics
Do the following exercise using excel and explain the results intuitively (very briefly) in words. Then submit your work (the excel file + the word file + diagram, if any) using Turnitin.
Suppose we are now at the start of year t = 0. We believe that the world will end in 20 years time. Whatever happens after year t = 19 is deemed to be irrelevant to human well-being. An initial stock of 100 (million tons, say) of a non-renewable resource exists. The problem is to decide how this stock is to be used over the 20 years.
We assume a non-linear demand function,
P(R) = Ke-aR , where a = 0.2 and K = 100.
We wish to maximise the sum of discounted utility over the specified time period by choosing an optimal extraction path. Assume, the discount rate is 10%. Using Excel Solver, find out the optimal time path of R. Now plot two charts: the resource net price and the resource usage, over the relevant time periods.
Now, do the above process again with the following change in the model: a decrease in the discount rate from 10% to 5%.
Intuitively (briefly) explain your results.

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