A town is endowed with an oil reserve. The total stock of oil from the reserve is 110 barrels. The town must sell all 110 barrels within two time periods, so the quantity extracted will be q₁ +92 = 110, where 71, for example, is the quantity extracted in period 1. The price per barrel that the town can sell the oil for is pt 150 in each period. There is a constant cost of extraction c= 50, such that the resource rent earned by each barrel in each period is T = Pt-c. If the interest rate is 20%, how much bil will the town extract in period 1 and in period 2 (what should q₁ and q2 be) if it wanted to extract efficiently (i.e. maximize profits)?
A town is endowed with an oil reserve. The total stock of oil from the reserve is 110 barrels. The town must sell all 110 barrels within two time periods, so the quantity extracted will be q₁ +92 = 110, where 71, for example, is the quantity extracted in period 1. The price per barrel that the town can sell the oil for is pt 150 in each period. There is a constant cost of extraction c= 50, such that the resource rent earned by each barrel in each period is T = Pt-c. If the interest rate is 20%, how much bil will the town extract in period 1 and in period 2 (what should q₁ and q2 be) if it wanted to extract efficiently (i.e. maximize profits)?
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:A town is endowed with an oil reserve. The total stock of oil from the reserve is 110 barrels. The town
must sell all 110 barrels within two time periods, so the quantity extracted will be q1 +42 = 110, where
91, for example, is the quantity extracted in period 1. The price per barrel that the town can sell the
oil for is på = 150 – in each period. There is a constant cost of extraction e = 50, such that the
resource rent earned by each barrel in each period is Te = Pt – c. If the interest rate is 20%, how much
oil will the town extract in period 1 and in period 2 (what should q and q2 be) if it wanted to extract
efficiently (i.e. maximize profits)?
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