This post goes over the math required to show the difference between surplus and equilibrium in a perfectly competitive and monopolistically competitive market. Note that a monopolistically competitive market's math and graph will be the same for a monopoly or an oligopoly. Here are the equations to work with:
P = 40 - 8Q
MC = 8
To find equilibrium Q and P for the PC market we set MC=P and solve for Q so:
8=40-8Q, add 8Q and subtract 8 from both sides to get:
8Q=32 or Q = 4
If Q equals 4, P = 8 (but we knew that already from MC)
To find equilibrium Q and P for the monopolistically competitive market we need to double the slope of the inverse demand function to get the marginal revenue function:
MR = 40 – 16Q
Set this equal to our MC to get:
40-16Q = 8 and add 16Q and subtract 8 from both sides to get:
32 = 16Q, or Q = 2
With an equilibrium Q of two, we get a consumer price of 24 (by plugging 2 into our original inverse demand equation).
To find consumer surplus for the PC market, we take the height of the triangle (40 – 8) times the base of the triangle (4) and then divide by two. This gives us:
½(32*4) = 64
In this set up there is no producer surplus because marginal cost is constant at 8, there is no difference between the price received and the cost of production so unfortunately the producer gets no profit or surplus.
The consumer surplus for the monopolistically competitive market can be found by taking the height of the triangle (40 – 24) times the base of the triangle (2) and then divide by two to get:
½(16*2) = 16
So the consumer surplus in the MC market is substantially less (in fact, it is 64-16= 48 less)
However, the producer surplus increases in the MC market because the price charged is now higher than the marginal cost. To get the producer surplus we need to multiply the height of the rectangle (24-8) by the base (2) to get:
The deadweight loss can be found by taking the total surplus from PC and subtracting the total surplus from MC. This gives us:
64 – 16 – 32 = 16
So the deadweight loss that occurs from changing from a perfectly competitive market to a monopolistically competitive market (without given equations) is 32.
We can confirm this by calculating the area of the triangle between the quantities and prices in the MC and the PC market:
½(2*16) = 16, so we know we did it right.
This can be seen in the graph below: