Assume that the demand and supply for a non-renewable resource across two different time periods are represented by the following equations:
Current Period
(Inverse Demand) P = 300 - .5Q

(Inverse Supply) P = 75 + .25Q

Future Period

(Inverse Demand) P= 600 - .5Q

(Inverse Supply) P = 200 +.5Q

1. 1. Solve for the equilibrium price and quantity for the use of this non-renewable resource by the current generation if there were no resource constraints or consideration of other generations. Show all your work.
2. 2. Solve for the equilibrium price and quantity for the use of this non-renewable resource by the future generation if there were no resource constraints or consideration other generations. Show all your work.
   3. Given the equilibrium quantities desired by each generation, do we have a scarcity problem if only 400 units of the non-renewable resource are available in total for both generations? Why or why not? (Hint: Think about your answers to parts a and b).
3. 4. Calculate the Marginal Net Benefit equations for each period of time using the equations given above. (Don’t worry about taking the Present Value of any MNB equations in this step.)
4. 5. Algebraically and graphically, solve for and depict the efficient allocation of the non-renewable resource across both generations if the available supply of the non-renewable resource is limited to 400 units in total for both generations. Assume that the future generation is 10 years from today. Assume a discount rate of 7.25%. Feel free to round up the denominator of your discount factor to a whole number. Be sure to carefully represent your answer graphically.
5. 6. Using your answers from part e, resolve for the prices that prevail for the resource in the current year and in year ten.

g. Explain how the optimal allocation between both generations would change as either the discount rate or the number of years in the future increased. How would this change affect what you depicted graphically? You do not need to resolve for a new discount rate or a number of years. I want to you explain what would happen conceptually in your graph. In your answer be sure to explain how increasing the
discount rate or the number of years affects the optimal allocation. What specifically is changing and why is it changing?

h. Could it ever be the case that the current generation would consume all 400 units of the resource given the parameters in this specific problem? Why or why not?

Answer rating: 100% (QA)

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