Question

1. The price of Appalachian coal is currently $80 per ton.  
   
   1. If the discount rate is 5%, what do we expect the price of coal to be next year? Explain how you know.
      
   2. Congress passes a tax on coal that will come into effect next year.  This will decrease the demand for coal next year.  What will happen to the price and quantity of coal extracted this year? What is this effect called?
      
   3. Instead, Congress decides to fund research into electric vehicle technologies that will increase the demand for electricity (and therefore coal) in the future. What will happen to the price and quantity of coal extracted this year?
      
2. Explain two reasons why real-world oil prices don’t evolve smoothly at the rate of interest the way our stylized model predicts.
   
3. Explain in words why having renewables be more competitive with coal in the future increases the extraction of coal today, but decreases in natural gas prices from fracking decreased the extraction of coal today.

Answer 1

Solution

a.Discount rate of Coal = 5% ; Price of Coal = $80 per Ton

Price of Coal next year = 80 * 1.05 i.e., $84 per Ton

Since the discount rate is given ; If we want present value of anything we divide the value by the dicount rate but if we want future value we multiply the value with the discount rate.

Present Value = (Future Value / ((1+Discount Rate) ^ n) ) where " n" is the number of years  

b.The price and the quantity of the coal extracted will increase because the demand for the same increases this year.

This effect is called Demand Shift where the demand shift outwards because the prices are expected to increase in the future,so the consumers buy the coal today itself instead of purchasing it in the next year.

c.So,here since the demand for electricity is expected to increase in the future it will lead to increase in the demand for coal (since coal is a source of power generation),consumers will be expecting that the price of the same in the future will increase.So,they prepone their future purchase So,the present demand of the coal will increase due to which the price and amount of coal extracted will rise

The real world oil will evolve accordingly because of many factors ; some of which are follows :

a.The oil prices are not purely based on the market forces of demand and supply.The major oil producing countries have formed a cartel (OPEC) which artificially controls the price of the oil  by altering the amount of oil produced.If they want the oil price to be more,they simple reduce the amount of oil production by imposing curbs in the proportion of quota system among their members.

b.Due to geo-political tensions,the oil prices may change expecting a supply and /or demand shock.

c.They are different countries that are not part of OPEC like the USA,Russia,Venezula,etc., but produce oil on a very large scale.When they increase their production it leads to supply glut leading to fall in the international oil prices.

d.Global developments liek recession,political situations,etc., also dictate the global oil prices.

Having renewables be more competitive with coal in the future increases the extraction of coal today because i future the price of coal is expected to fall as it will be in competive environment with that of renewabel resources.So,the coal companies will extract more coal today due to following reasons:

Extracting more coal today means more sales can be done today so more profits today.They are expecting their demand growth to atleast reduce in the future once the renewables market picks up.

Since the renewables are not that competitive to coal presently the suppliers are trying to cash-in as much as possible before renewables come in

Since prices of coal will be more (since lack of much renewables),the production/ extraction of the same presently is also high

Natural gas is produced majorly through fracking.It is like a by-product of coal production,so when the natural gas prices reduce,the benefit / incentive derived out of coal is also reduced proportionally so the extraction of coal today also decreases.

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