This problem requires the use of algebra. Consider the scenario given in the previous problem with a total quantity of 60 barrels of oil. Note that in each period, MB = 100-2Q. What is the dynamically efficient allocation if the discount rate is 10 percent per period?

Previous Problem

For this problem you'll make use of a two-period model like the one in Figure 8.4. Suppose each period's net marginal benefit curve for oil is a straight line with a vertical intercept of $100 and a horizontal intercept of 50 barrels. Assume the discount rate is zero. What is the dynamically efficient allocation in each period if the total quantity of oil is 120 barrels? What is the dynamically efficient allocation in each period if the total quantity of oil is 60 barrels? Illustrate your answers with graphs.

Figure 8.4

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Marginal Benefit MB In Period 1 MB in Period 2 Consumption in Period 1 Discounted Present Value in Period 1 of MB In Period 2 Consumption in Period 2 Equal Division Dynamically Efficient Division Fixed Quantity of Depletable Resource