Deadweight loss is a way to measure economic inefficiency. It measures the distortion to market outcomes in monetary value. Deadweight loss often arises due to market failures or policy interventions from governments or policymakers.
Deadweight losses arise in the case of a monopoly because monopolists set their price above marginal cost. When a monopolist sets their price above marginal cost it results in a subset of consumers who are willing to pay a price higher than the cost of production, but lower than the market price, who miss out on consuming the product. This is an economically inefficient outcome as both the monopolist and the consumer could be made better off if they could achieve a sale at a price between the market price and the marginal cost of production.
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 deadweight loss will be 4. And that's how we calculate the size of the deadweight loss!