Deadweight Loss

Dear Professor Cram:

I am doing my microeconomics paper at present, and am working on this question: "Assuming the supply and demand curves for cars given below, calculate the deadweight loss that results from a tax of $100 per car collected by the sellers. (Hint: graph the curves.) Note that P=15,000-2,500Q and P=10,000 where P is in dollars and Q is in millions of cars per month."

I have confirmed with my tutor that P=15,000-2,500Q is the demand curve and that P=10,000 is the supply curve. I am struggling to graph this, can you help please?

Anne M., New Zealand

Thank you for using College-Cram.com and thank you for your excellent question about deadweight loss.

Deadweight loss is an economic inefficiency – in this case introduced by a tax on a product. The tax raises the price to the buyer but not for the seller, resulting in equilibrium for supply and demand moving from the point of efficiency. To calculate the deadweight loss we need to know the supply and demand curves (so we can calculate the quantity demanded at market efficiency and with the tax imposed) and the amount of the tax. You provided us with all this information, so let's begin.

Original Demand Quantity: The Demand curve you provided tells us that before the tax is imposed the quantity demanded at a price of $10,000 is 2 (million cars per month). How did I get that? Here goes:

    The formula you gave us for the demand curve is

      10,000 = 15,000 – 2,500Q

    which reads, at a price of $10,000 the quantity demanded is calculated from a formula of 15,000 minus 2,500 times the quantity demanded. To solve, we add 2,500Q to both sides and subtract 10,000 from both sides – this part is algebra, not economics, giving us:

      2,500Q = 15,000 – 10,000, or
      2,500Q = 5,000

    Now, we divide both sides by 2,500 to isolate Q

      Q = 5,000/2,500 = 2

That is the 2 million car demand I referred to at the beginning.

New Demand Quantity: To calculate the deadweight loss from adding $100 tax we start by calculating the amount of cars that will NOT be sold due to the increase in price. We use the same demand curve you provided, but at the new price of 10,100:

      10,100 = 15,000 – 2,500Q, or
      Q = 4,900/2,500, or
      Q = 1.96

We were selling 2,000,000 cars per month, but now will only sell 1,960,000 cars per month.

Deadweight Loss: Sales drop by 40,000 cars per month, which is represented on the graph below as the base of the yellow triangle. The tax revenue loss of $100 per car NOT sold is represented as the height of the yellow triangle. The calculated deadweight loss in this case is the area of the yellow triangle, or 1/2 x base x height: 

  • deadweight loss = 1/2 x base x height; or
  • deadweight loss = 1/2 x 40,000 x $100, or
  • deadweight loss = $2,000,000

Normally supply is NOT a constant and there is also deadweight loss below the horizontal line to reach down to the supply curve – not in your example. I think we're done. Here is what the graph looks like:

Graph of the Deadweight Loss

I hope this helps. Let us know if you need anything else.

Good studying,

Professor Cram