# 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!

Marginal Cost should not be horizontal!!!

Hello,

Firstly, this is just an abstraction to make the problem a little bit easier. In reality the marginal cost curve might be slightly increasing, but for simplicity it makes sense to just assume that it is flat. We do the same thing when we assume that the demand curve is a straight line... Remember, these are just models and models often abstract away unnecessary detail.

There are also a lot of circumstances where it might make sense to assume that the marginal cost curve is horizontal, too!

A firm which produces software which is distributed online is likely to have a flat marginal cost curve as their only cost of selling an additional unit is the bandwidth required by the end user to download the software (and this cost is likely to be the same for the first person downloading it as the 50th person downloading it)

Consider a firm producing pharmaceutical goods.

The most significant component of their costs are fixed costs. Even if the marginal cost curve is increasing, it is so insignificant compared to their total costs that it does not really matter if we assume that the curve is flat (i.e, if the price of manufacturing a drug is 10 cents for the first customer and it is 20 cents for the thousandth customer, but the price they charge is $80 per unit, does it really matter if we just assume that the marginal cost curve is flat?).