Assume the coal resource is in fixed supply and its stock is 15 units of coal. Assume 2 periods of extraction: present and future and a discount rate of r = 10%. The demand function is given by MB = 10 - 0.5q and the supply function is given by a fixed MC cost of extraction MC = $5/unit of coal. a) What is the optimal extraction rate in a static setup of the problem? Show numerically. Why cannot it be applied to this resource? b) What is the optimal extraction rate each period in a dynamic setup of the problem? Show numerically. c) What are the prices and MUC-marginal user costs each period? Show numerically.
. Assume the coal resource is in fixed supply and its stock is 15 units of coal. Assume 2 periods of extraction: present and future and a discount rate of r = 10%. The demand function is given by MB = 10 - 0.5q and the supply function is given by a fixed MC cost of extraction MC = $5/unit of coal.
a) What is the optimal extraction rate in a static setup of the problem? Show numerically. Why cannot it be applied to this resource?
b) What is the optimal extraction rate each period in a dynamic setup of the problem? Show numerically.
c) What are the prices and MUC-marginal user costs each period? Show numerically.
d) What are the total net benefits obtained if the extraction rate equals the dynamic efficient rate? Show numerically.
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