Question

The world has a finite amount of the fossil fuel Fuel-o, for which there is no substitute. We know we only need Fuel-o for 2 periods, since a cost-effective renewable substitute will be available after that.

The global inverse demand for Fuel-o in each period (1 and 2) is described by:

P = 9 – 0.3q, where P is the unit price of Fuel-o and q is the quantity extracted in the current period.

The marginal cost of each unit of Fuel-o is constant at 1.

The amount of Fuel-o available is 30 units.

The discount/interest rate is 20%.

SHOW ALL WORK!

1. What is q₁ -- the dynamically efficient amount of Fuel-o that should be extracted in period 1? P₁? MUC₁?
2. What is q₂ -- the dynamically efficient amount of Fuel-o that should be extracted in period 2? P₂? MUC₂ (not the PV)?
3. In general terms, how would this change if the discount rate fell to 5% (don’t calculate)?
4. Graph the present value of the marginal net befits in period 1 and period 2 on a single graph.
5. Draw separate graphs for period 1 and period 2, showing the demand curve in that period, along with the q extracted for each period, and the corresponding P.
6. If new sources of Fuel-o were suddenly discovered, so that the available supply doubles to 60, would P, q₁ and q₂ change? If so, why and how?

Answer 1

As the proverb goes- "Rome wasn't built in a day", similarly it will take time for us to adapt to fossil fuels. We are definitely trying to reach there. It's just that there are some constraints such as infrastructure, money, availability etc, which needs to be overcome in order to reach there.

Some trade-offs include:

1. Difficulty in commuting for general public who can't afford a car immediately, that runs on fossil fuel.

2. Ample space and resources would be required to dispose off the instruments and vehicles that run on fossil fuel.

3. Power plants etc, needs to shut down since there won't be any need of fossil fuel, electricity etc. Hence a lot amount of manpower will be out of job. Economy will go for a toss.

4. New machines, plants etc. needs to be built. The entire earth needs to be shut down for a considerable period, till the time every renewable source and energy generator takes the place of fossil fuels.