1. A gold rich country in Africa discovered a large gold deposit and the Government want to manage this resource over a two period (current period and future period) as follows: extract less in period one (current period) and extract more in period two (future period), where the cost of extraction is rising over time. As the chief economist for the country, propose two economy policy options to achieve this extraction path desired by the Government. In proposing the policies, also provide the factors that could hinder the success of the policies (not more than 4 pages). (9 marks)
2. The government of a country has passed a tax law on the extraction of coal, but this law will first take effect 5 years in the future.
   1. Given that the coal mining is characterized by a constant marginal extraction cost (MEC) how would, if at all, this pending law affect the extraction profile over time in terms of both the timing of the extraction and the cumulative amount extracted. Why? (3 marks)
   2. If the coal mining is characterized by an increasing MEC, how would your answer in (a) change, if at all. Why?

Instructions: Please answer the following questions related to current (Period 1) and future (Period 2) demands for groundwater within the context of our two-period model.

Suppose that Period 1 demand for groundwater is given by the linear equation QUOTE PToday=$10-0.4*Q Today. Furthermore, suppose climate change causes Period 2: demand for groundwater to be different linear equations, QUOTE PFuture=$12-0.3*Q future. The current reserves of groundwater to be allocated across both periods is Q=Q1+Q2=16, and future demand is discounted at a rate of so that the present value of future demand is given by 11.08*P2 and the present value of future net benefits is 11.08*NB2. The marginal cost of extraction is constant and equal in both periods: MC1=MC2=$3.

a) Determine the optimal quantity of groundwater to extract in Periods 1 and 2 when users in both periods are considered in one problem. Is more extracted today or in the future, and why? What does the marginal user cost?

b) Determine the number of units extracted in Periods 1 and 2 if current Period 1 user lack secure property rights over the aquifer. That is, solve the problem as if Period 1 users considered only their consumption in their problem.

c) Explain in words/in graphs/in equations (as you prefer) why the quantities extracted in b) represent a loss of overall welfare/net benefits when compared to the extraction in a).

d) What would the discount rate need to be to optimally solve the two-period model with equal quantities extracted in both periods? That is, what r sets present value of demand or net benefits equal in both periods while maintaining equilibrium extraction quantities at Q1*=Q2*=8?

Many parameters characterize the Theory of the Mine. Understanding how each impacts prices, output, and duration of extract are critical in economic analysis.

Explain what happens and why in a competitive mining market where scarcity is present to the 1) price level, 2) price path, 3) extraction level, 4) extraction paths, 5) duration of mining extraction, and 6) the marginal user cost value, when the discount rate is lowered.

Please explain your answers so I can understand the concepts.

a)Use the TWO-PERIOD model of resource extraction to explain/illustrate how an unregulated market optimally allocates a fixed resource over time. Be sure to identify the critical assumptions you need to get this result (e.g. discount rates, market structure, resource constraint, etc.).

b) Explain why firms choose output so that Marginal User Costs are equalized in present value terms over both periods.

c) Explain how to find the asset value of the resource in situ.

d) How do the private optimal extractions change if interest rates rise? What is the intuition?

e) Explain why an unregulated market over-exploits a resource relative to the socially optimal extraction. Show how to find the Deadweight Loss.