Monopolist optimizing price: Dead weight loss | Microeconomics | Khan Academy

published on July 22, 2020

Based on what we've done in the last two videos we've been able to figure out what the marginal revenue curve looks like for the monopolist here for the monopolist in the orange market and this is what we got right over here it was aligned with the slope twice is twice as

Steep as the slope of the demand curve and we'll see that that's actually generalizable there's an optional video that I'll do very shortly where I prove it with a little bit of calculus but it's very important to realize that this

Marginal revenue curve looks very different than the marginal revenue curve if we were dealing with perfect competition if we were dealing with perfect competition there would be some equilibrium price in the market and all

Of the competitors would essentially just have to take that price so let's say that that equilibrium price was three dollars per pound then our marginal revenue curve would look like this if we were not a

Monopolist if we were a a one of the many perfect competitors I guess you could view it that way because we would just have to take that price if we wanted to sell 1,000 pounds each of those out each of those pounds we would

Get three dollars per pound and then if we want to sell 1,000 one we'll just get three dollars per pound for the next one it doesn't change we're just taking that price with the monopolist things do change because we are the only producer

In the market the price at which we can get changes depending on what we produce because we are the entire supply for the market and we have this downward sloping marginal revenue curve now with that out of the way let's think about what will

Be the optimal quantity for us to produce if we wanted to maximize profit and if we think in pure economic terms that's what firms try to do they try to there exist to maximize profit and to do that we're going to have to think about

And remember it's not to maximize revenue to maximize revenue we would have said oh well they should just produce three thousand pounds but it's not about maximizing revenue it's about maximizing profit we have to take the

Cost into consideration and to do that we'll have to draw a marginal cost curve and so let's say I did the research let's say we're the owners of this firm and we have a marginal cost curve that looks something like this

Let's say our marginal cost curve looks like this it's important to realize we are the we are the market we are the only producers here so this isn't just our marginal cost curve this is a marginal cost curve for the market or

Another way to think about it this is the supply curve for the market it tells you at any given price how much the market is willing to supply you could view it as a marginal cost or you could view it as a supply curve and

We've talked about it before you can view a supply curve as a marginal cost curve if you want some if you want the market to produce one extra pound what's the minimum price you would have to give that is the marginal cost

Now with this out of the way let's think about what you would produce well you would definitely you would definitely want to produce something you definitely start to produce a few a few pounds right over here because the marginal

Revenue you're getting is way above your marginal cost each incremental pound you're producing right over here you are getting much more revenue you're getting you know five or six dollars of revenue and it's only costing you a little over

A dollar it's just like okay I'm going to keep producing I'm going to keep producing over here you're still each incremental unit you're getting you're still getting more revenue than the cost of that incremental unit and that keeps

Being true all the way until you get to all the way until you get to 2,000 pounds right over here at this point right over here you don't want to produce an incremental unit because if you produce one more unit if you produce

That 2004 right over here then for that two thousand and first pound your cost is going to be slightly higher than the revenue you get in so you will actually take a slight loss on that so you will

Your your total profit will start to go down and you don't want to produce less than this because you'll be leaving a little money on the table you'll be leaving that little incremental pound where the total revenue was just

Slightly higher than or the marginal revenue on that incremental pound was just slightly higher than your marginal costs on that incremental pound so you will produce right over there now this is interesting because this is a

Different this is an a different equilibrium or ggest we say this is a different price or this is a different quantity or this is a different price and quantity than we would get if we were dealing with perfect competition if

We were dealing with perfect competition our equilibrium price and quantity would be where our supply and demand curves intersect it would be right over here it would be a price of $3 per pound and a quantity of 3000 pounds now in order to

Maximize profit we are intersecting between the Marj revenue curve and or our quantity that we want to produce as a monopolist is the intersection between our marginal revenue curve and our marginal cost

Curve which is right over here and so we can see that there is a deadweight loss there is a deadweight loss by hat being a monopoly although it's good for us is good for the monopolist it's not good for society at least in this example and

There's very few where I can imagine it being good but I guess there are a few if you're trying to kind of protect a national industry or something like that over here this is the quantity that we are deciding to produce the consumer

Surplus the consumer surplus is the area above the price and below the demand curve so this right over here is the consumer surplus consumer surplus the producer surplus is looking pretty good and this is essentially what we're

Trying to optimize our producer surplus is this whole area our producer surplus is this whole area right over here producer surplus right over there but we have a deadweight cost there's a total surplus that we would have gotten if we

Went to the society would have gotten if we went to the if we went to if we were dealing with perfect competition right over here that's now being lost but as we lose that we were able to increase the producer surplus and decrease the

Consumer surplus so it's beyond just having this deadweight deadweight loss over here it's also obviously given much more value to the producer to the monopolist and given much less value to the consumer

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