Question

Suppose the demand curve and the supply curve in a market are both linear. To begin, there was a $5 tax per unit, and the $5 tax resulted in a deadweight loss of $1,500. Now, the tax per unit is higher, with the higher tax resulting in a deadweight loss of $6,000. What is the amount of the new tax per unit?

Answer 1

The new amount of Tax per unit is $10. Explanation: Dead weight loss is loss in efficiency that arises in the economy due to imposition of tax or price ceiling or price flooring or existence of imperfect competition. If the government imposes taxes then the quantity sold in the economy is less than the equilibrium quantity because now consumer has to pay higher price for the product and the seller receives less price for the product. Dead weight loss is the sum of the consumption and production distortion. Dead Weight loss is calculated using the formula below: DWL = { x(Change in Price or Tax Amount) x (Change in Quantity) Here, t = 5 and DWL = 1500 1500 = { * 5 * (Change in Quantity) Change in Quantity = 600 This means that increase in price by $5 decreases quantity by 600, We know that our demand and supply curves are linear, so decrease in quantity due to $1 of tax will be: 600 = 120 By using trial and hit method, if the tax amount is $10 then it will decrease the quantity by 1200: 120 x 10 = 1200 So, our Dead weight loss will be: 6000 = { x 10 x 1200 Therefore $10 will be the tax amount that will create $6000 of dead weight loss. This is also shown with the help of diagram:

Price $10 $5 tax DWL=1500 Quantity 600= Change in Quantity due to $5 tax 1200= Change in quantity due to $10 tax

or

Under linear demand and supply, the dead weight loss increases as the square of the tax increase.

It means if tax is increased by 2 times, then dead weight loss will be increased by 4 times

Times increase in dead weight loss = New dead weight loss / Old dead weight loss = $6000 / $1500 = 4 times

Dead weight loss is 4 times increased

It means tax will be increased 2 times

Thus new tax will be $5 * 2 times = $10