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19.f. Exhaustible Resources
Everyone lives for 2 periods: 0 and 1. The total amount of oil (Q)
available for the two periods is QT. The demand in period 0 is D0,
and D1 in period 1. Assuming R=10%, the present value (PV) of
D1 is 10% below D1. The present value of both periods’ demands
is the horizontal sum of D0+PV(D1). The intersection of this
demand with supply S gives the price P0. This price must be equal
to PV(D1)--otherwise it would pay to increase sales in whichever
period has the higher price. Given the price P0, people who want
oil today will buy Q0. People who want oil for period 1 will buy
Q1. The price P0 is the price next year’s people pay to set aside oil
for period 1. The quantities Q0 and Q1 add up to QT--The oil is
exactly used up in the two periods. If there were a third period,
and if the PV of what people were willing to pay in that period
were above P0, then some oil would be conserved for that period.
Otherwise nothing would be conserved, but only because the third
period people didn’t value the oil enough to make it worth
Returning to the two-period world, suppose that the government
decides that the free market is not conserving enough oil, and it
forces people to consume only Q0’ in period 0. This would cause
a loss equal to the right shaded area. The conserved oil becomes
available for period 1, and period 1 people can increase their
consumption from Q1 to Q1’, but the resulting gain (left shaded
area) is smaller than the loss. Conclusion: The market
automatically conserves resources at an optimal rate, so that we
only run out of resources if it’s in our economic interest to run out.
Forced conservation of any good (through recycling, mileage
requirements for cars, etc.) only wastes resources.