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Exercise: monopoly

You have the following information about a monopoly:

  • Derive the MR, find the profit maximizing price and quantity.
    • Find profit, consumer surplus, and dead-weight loss using the price and quantity from the previous question.

Now that we have derived the MR function, set MR=MC and solve for Q.


Choose Q1 (it does not make sense to have a negative quantity in our model),then plug this number into the demand function to obtain its price.


Consumer surplus:

Dead-Weight Loss:


Profit:


  • The government wants to intervene in order to increase consumer surplus, while keeping the monopoly from making a loss.At what price should the firm be forced to sell its goods?
Although the DWL is completely eliminated when the the price is equal to the intersection between the MC and demand curve, the consumer surplus can be further expended by setting the firm's price equal to the intersection between the ATC and demand curve. This is due to the fact that the point at which the ATC intersects the demand is smaller than at the intersection between the MC and demand curve.


Choose Q3 and plug it into either the ATC or demand function in order to find the price.


Let's graph this:


Note that the MC used for this problem isn't really the actual MC. However, this function used for this problem mimics the actual MC's behavior. In order to derive the "real" MC, multiply ATC by Q to obtain the cost function. Then, take its derivative. 






Location: New York, NY, USA

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