demand for sulfur dioxide by coal-fired electricity electricity producers is: P= 1,000 - 16Q where Q is quantity of sulfur dioxide measured in thousands of tons, and P is price per ton of sulfur dioxide.
a)With no policies or restrictions on sulfur emisssions, how much sulfur will be emitted by coal-fired utilities (hint: what is the price of sulfur emissions to electricity producers with no regulations?
b)Economists have determined that the socially optimal quantity of sulfur emissions is 50,000 tons. If the govt wanted to tax sulfur emissions, what would be the amount of the tax that would result in the socialy optimal level of emissions?
Please help. I am totally lost. I know the price of 50,000 would be $200 according to the demand equation, but don't I need a supply curve or another curve to determine the tax by subtracting the difference between the two curves? Please help. How do I do this?
To answer your questions, let's break them down step by step.
a) With no policies or restrictions on sulfur emissions, the price of sulfur emissions would be the price per ton of sulfur dioxide in the demand equation. In this case, the demand equation is P = 1,000 - 16Q. To find the price of sulfur emissions, we need to solve for P when Q is equal to zero (since no sulfur dioxide is emitted):
P = 1,000 - 16(0)
P = 1,000
Therefore, without any regulations, the price of sulfur emissions to electricity producers would be $1,000 per ton.
b) The socially optimal quantity of sulfur emissions is given as 50,000 tons. If the government wants to tax sulfur emissions to achieve this optimal level of emissions, we need to determine the amount of the tax that would result in the desired quantity.
To do this, we can calculate the difference between the quantity demanded without regulation (Qd) and the socially optimal quantity (Qso). In this case, Qd can be found by setting the price equal to $1,000 (without regulations) in the demand equation:
$1,000 = 1,000 - 16Qd
16Qd = 0
Qd = 0
Now we can determine the tax amount by subtracting the desired quantity from the quantity demanded without regulation:
Tax amount = Qd - Qso
Tax amount = 0 - 50,000
Tax amount = -50,000
The negative tax amount implies that a subsidy is needed instead of a tax to achieve the socially optimal quantity. This means that the government would need to provide a subsidy of 50,000 tons to encourage coal-fired electricity producers to reduce their sulfur emissions to the socially optimal level of 50,000 tons.
Please note that in this particular scenario, we only considered the demand equation to determine the price and the quantity demanded without regulation. The supply curve was not explicitly given. If you had the supply curve, you could indeed compare it with the demand curve to determine the tax or subsidy amount required to achieve the socially optimal level of emissions.