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?

a) To find out how much sulfur will be emitted by coal-fired utilities with no policies or restrictions, we need to determine the quantity where the price of sulfur emissions is zero.

The given equation for the demand of sulfur dioxide by coal-fired electricity producers is: P = 1,000 - 16Q.

When the price, P, is zero, the equation becomes: 0 = 1,000 - 16Q.

To solve for Q, we can rearrange the equation: 16Q = 1,000.

Dividing both sides by 16, we get: Q = 1,000 / 16 = 62.5.

So, without any restrictions or policies, coal-fired utilities will emit 62.5 thousand tons (62,500 tons) of sulfur.

b) The socially optimal quantity of sulfur emissions is given as 50,000 tons. To achieve this level, the government can impose a tax on sulfur emissions that would incentivize electricity producers to reduce their emissions.

The equation for the demand of sulfur dioxide by coal-fired electricity producers is still: P = 1,000 - 16Q.

To determine the tax amount that would result in the socially optimal level of emissions, we need to find the quantity, Q, at which the price equals the socially optimal quantity.

Setting P equal to zero (since the socially optimal quantity is achieved when the price is zero), we get: 0 = 1,000 - 16Q.

Rearranging the equation: 16Q = 1,000.

Dividing both sides by 16, we find: Q = 1,000 / 16 = 62.5.

So, the quantity that would result in the socially optimal level of emissions is still 62.5 thousand tons (62,500 tons).

Therefore, the government would need to impose a tax that reduces the quantity from the initial 62.5 thousand tons to the socially optimal quantity of 50 thousand tons. The amount of the tax would be the difference between the two quantities: 62.5 - 50 = 12.5 thousand tons (12,500 tons).