# Deadweight loss

Deadweight loss is the lost welfare because of a market failure or intervention. In this case, it is caused because the monopolist will set a price higher than the marginal cost. This means there will be people willing to pay more than the cost of production which will not be able to purchase the good because the monopolist is maximizing profit.

The above diagram illustrates the deadweight loss generated by a monopoly. From this, we can see that the dead weight loss monopoly formula is:

**1÷2 (P - MC) (Qc - Qm)**

MC = marginal cost

P = price

Qc = Quantity provided in competitive market

Qm = Quantity produced by a monopoly.

Therefore, to find the value of the deadweight loss (DWL) we will need to find the values for MC, P, Qc, Qm which we will do in the following example.

**Example - Calculate deadweight loss with numbers! **

Suppose that the demand curve is represented by P = 10 - 2Q and MC = 2.

1. Find Qc

To find Qc we need to find the point where MC = the demand curve.

Therefore, we let 2 = 10 - 2Q. We solve for Q and find that Q = 4.

Therefore, Qc = 4.

2. Find Qm

This point corresponds to the point where Marginal Revenue (MR) = Marginal Cost (MC)

Firstly, we need to know what the marginal revenue equation is. Well, if the demand curve is linear (a straight line) then it will always have a slope twice the size of the demand curve and the same intercept term. Since demand is: P = 10 - 2Q this means that MR = 10 - 4q.

Now we equate MR = MC such that 2 = 10 - 4Q and re-arranging we will find Q = 2.

Therefore, Qm = 2

3. Find price

To find the price, we get our function P = 10 - 2Q and we substitute in our value for Qm.

P = 10 - 2(2) = 6

We now have all the pieces of information that we need. If we plug them all into our DWL formula **1÷2 (P - MC) (Qc - Qm) **we will get:

**1÷2 (6 - 2) (4 - 2) = 4**

therefore, our dead weight loss will be 4. And that's how we calculate the size of the deadweight loss!

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