# equilibria with free competition and with a monopoly

Here's what I think I know about the answer: to get the $ value of DWL you have to take the area of the aggregate surplus under perfect competition and substract the area of the aggregate surplus under monopoly (helps to make a little graph.) The funny thing is, my main problem is I don't know the geometry necessary to do that. There may be another method, I'll leave it to you.

Here's the problem:

I am considering giving a patent for a new drug. The public demand is given by: P = 120 - 10Q, where Q is quantity of the drug and P is price. If the marginal cost of production is given by MC = 2Q, what will be the monetary value of the efficiency loss of granting the company monopoly power (meaning a patent)?

Remember that a marginal revenue function can be derived from a linear demand function by doubling the slope of that function.

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#### Solution Preview

Hello!

Let's first determine the equilibria with free competition and with a monopoly.

Under perfect competition, equilibrium arises when demand is equal to MC. So we have:

120 - 10Q = 2Q

12Q = 120

Q = 10

Now, plugging this equilibrium Q into the demand equation, we get that the equilibrium price is 20.

Under a monopoly, equilibrium arises when Marginal Revenue is equal to MC. We use the general formula that states that when demand is of the form A - B*Q, then marginal income is A - 2B*Q. So in this case, marginal revenue is 120-20Q. Now we find the equilibrium:

120 - 20Q = 2Q

22Q = 120

Q = 5.4545...

Plugging this Q into the demand ...

#### Solution Summary

Determine equilibria with free competition and with a monopoly.